>j&1:x|=1< len(old):
+ extra = intersection(upper, perp(old, h), h)
+ candidates.append(basis(old + safe_subspace(extra, ())))
+ def score(F):
+ d = len(F)
+ return sum(weight[d-len(A)] + weight[len(B)-d] for A, B in sides)
+ best = max(candidates, key=score)
+ delta = score(best) - score(old)
+ if delta > 0:
+ assert nondeg(best) and all(inside(A, best) and inside(best, B) for A, B in sides)
+ frames[i] = best; changed += 1; gain += delta
+ changes.append(dict(pass_index=cycle, changed=changed, objective_gain= gain))
+ print('frame search', changes[-1], flush=True)
+ if not changed: break
+ return {i: list(F) for i, F in frames.items()}, changes
diff --git a/research/shrunk-birth-terminal/search/original-runtime/references/verification-driver-tested.py b/research/shrunk-birth-terminal/search/original-runtime/references/verification-driver-tested.py
new file mode 100644
index 0000000000..6d631cfdbd
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/references/verification-driver-tested.py
@@ -0,0 +1,17 @@
+from pathlib import Path
+from hashlib import sha256
+import datetime,importlib.util,json,os,sys,time,pickle
+W=Path(__file__).resolve().parent;P=W/'repo/research/r12-logical-frames'
+name=sys.argv[1];O=W/name;O.mkdir(exist_ok=True)
+def load(name,path):
+ spec=importlib.util.spec_from_file_location(name,path);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module);return module
+config={k:os.environ[k] for k in ('R12_FRAME_MODE','R12_FRAME_ROUNDS','R12_DEFER_MODE')};sources={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')};start=time.monotonic()
+(O/'process.json').write_text(json.dumps(dict(started_utc=datetime.datetime.now(datetime.timezone.utc).isoformat(),config=config,sources=sources),indent=2)+'\n')
+sys.path.insert(0,str(P));ref=load('r12_reflection',P/'reflection_audit.py');d=ref.capture(P/'complex_deferred.py')
+(O/'complex-profile.json').write_text(json.dumps(d['out'],indent=2,sort_keys=True)+'\n')
+adapter=load('r12_birth_checkpoint',W.parent/'research-r12/birth_checkpoint.py');adapter.export_checkpoint(d,O)
+result=ref.audit(d);result['source_sha256']=sha256((P/'complex_deferred.py').read_bytes()).hexdigest();result['audit_sha256']=sha256((P/'reflection_audit.py').read_bytes()).hexdigest()
+(O/'reflection-audit.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+assert sources=={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')}
+receipt=dict(status='PASS complete own-candidate compiler, dirty replay, exact binary frames, exact all-input supports and independent literal reflection',elapsed_seconds=round(time.monotonic()-start,3),config=config,sources=sources,profile_sha256=sha256((O/'complex-profile.json').read_bytes()).hexdigest(),checkpoint_sha256=sha256((O/'FRAMES.pkl').read_bytes()).hexdigest(),reflection_sha256=sha256((O/'reflection-audit.json').read_bytes()).hexdigest())
+(O/'verification.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt,indent=2))
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/LICENSE b/research/shrunk-birth-terminal/search/original-runtime/repo/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/LICENSE
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
+ TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION
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+ You may add Your own copyright statement to Your modifications and
+ may provide additional or different license terms and conditions
+ for use, reproduction, or distribution of Your modifications, or
+ for any such Derivative Works as a whole, provided Your use,
+ reproduction, and distribution of the Work otherwise complies with
+ the conditions stated in this License.
+
+ 5. Submission of Contributions. Unless You explicitly state otherwise,
+ any Contribution intentionally submitted for inclusion in the Work
+ by You to the Licensor shall be under the terms and conditions of
+ this License, without any additional terms or conditions.
+ Notwithstanding the above, nothing herein shall supersede or modify
+ the terms of any separate license agreement you may have executed
+ with Licensor regarding such Contributions.
+
+ 6. Trademarks. This License does not grant permission to use the trade
+ names, trademarks, service marks, or product names of the Licensor,
+ except as required for reasonable and customary use in describing the
+ origin of the Work and reproducing the content of the NOTICE file.
+
+ 7. Disclaimer of Warranty. Unless required by applicable law or
+ agreed to in writing, Licensor provides the Work (and each
+ Contributor provides its Contributions) on an "AS IS" BASIS,
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+ PARTICULAR PURPOSE. You are solely responsible for determining the
+ appropriateness of using or redistributing the Work and assume any
+ risks associated with Your exercise of permissions under this License.
+
+ 8. Limitation of Liability. In no event and under no legal theory,
+ whether in tort (including negligence), contract, or otherwise,
+ unless required by applicable law (such as deliberate and grossly
+ negligent acts) or agreed to in writing, shall any Contributor be
+ liable to You for damages, including any direct, indirect, special,
+ incidental, or consequential damages of any character arising as a
+ result of this License or out of the use or inability to use the
+ Work (including but not limited to damages for loss of goodwill,
+ work stoppage, computer failure or malfunction, or any and all
+ other commercial damages or losses), even if such Contributor
+ has been advised of the possibility of such damages.
+
+ 9. Accepting Warranty or Additional Liability. While redistributing
+ the Work or Derivative Works thereof, You may choose to offer,
+ and charge a fee for, acceptance of support, warranty, indemnity,
+ or other liability obligations and/or rights consistent with this
+ License. However, in accepting such obligations, You may act only
+ on Your own behalf and on Your sole responsibility, not on behalf
+ of any other Contributor, and only if You agree to indemnify,
+ defend, and hold each Contributor harmless for any liability
+ incurred by, or claims asserted against, such Contributor by reason
+ of your accepting any such warranty or additional liability.
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diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/NOTICE b/research/shrunk-birth-terminal/search/original-runtime/repo/NOTICE
new file mode 100644
index 0000000000..50c6d1236d
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/NOTICE
@@ -0,0 +1,321 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/certificates/copied-centers-network.json b/research/shrunk-birth-terminal/search/original-runtime/repo/certificates/copied-centers-network.json
new file mode 100644
index 0000000000..20bbb6806c
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/certificates/copied-centers-network.json
@@ -0,0 +1,684 @@
+{
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+ "8": "4584967478671/1000000000000",
+ "9": "893436888603/200000000000"
+ },
+ "moment_upper": "93758349669268174319758205865410416369669365194946428036263324886438920093698460010858713501882394775456058947688857504496378147740660153782705622445171968788940999158190850771009870660961702451316489933657453673410640256343163004633261783258126014322372415015196690665271304600343211202483869148840537844645971747977878306709988702092424295624899718047484041316483866997928443286860331217210569026228462754909148637641705274404842932443778349005557711550186032457951943018925944743009981965944635321901441335715694527157550303349516161701526749290641/93758350468742040597605202574977284831296217469066320109478051808997924815747809871469598767080130850070960188766796326960503351359516783898648613566748094827463364859111089535641760861980778679585390033605502742408965381060590533232327198822037065411694190195298932243216687627021627901452126335306662762812143738702048772208327890811345239489466958284593481432876514849600866059475807763859342905535630627309663603819191403583929521929211097357482640322392664177893686057570737252740635363274594047705896938069320731874459272819040000000000000000000",
+ "saving": "717/10000000",
+ "strict_gap": "799473866277846996709566868461626852274119892073214726922559004722049349860610885265197736074614901241077938822464125203618856630115942991121576126038522365700920238764631890201019076228268900099948049068998325124717427528599065415563911051089321775180102241577945383026678416698968257186466124918166171990724170465498339188718920943864567240237109440116392647851672422772615476546648773879307167872400514966177486129179086589485432748351924928772206631719941743038644792509730653397329958725804455602353626204716908969469523838298473250709359/93758350468742040597605202574977284831296217469066320109478051808997924815747809871469598767080130850070960188766796326960503351359516783898648613566748094827463364859111089535641760861980778679585390033605502742408965381060590533232327198822037065411694190195298932243216687627021627901452126335306662762812143738702048772208327890811345239489466958284593481432876514849600866059475807763859342905535630627309663603819191403583929521929211097357482640322392664177893686057570737252740635363274594047705896938069320731874459272819040000000000000000000"
+ },
+ "finite_bridge": {
+ "bit": {
+ "W": 188181929,
+ "halving_degree": 9,
+ "m": 575,
+ "maxchild": 529,
+ "wire_bits": 28
+ },
+ "complex": {
+ "W": 537696432,
+ "halving_degree": 20,
+ "m": 784,
+ "maxchild": 756,
+ "s": 421548223824,
+ "scalar_group_upper": 4793351472,
+ "scalar_terms": [
+ {
+ "c": 78437,
+ "copied_center_extra_groups": 56,
+ "h": 28,
+ "invocations": 3276,
+ "local_group_upper": 729892,
+ "v": 3276
+ },
+ {
+ "c": 78437,
+ "copied_center_extra_groups": 56,
+ "h": 28,
+ "invocations": 3276,
+ "local_group_upper": 729892,
+ "v": 3276
+ }
+ ],
+ "wire_bits": 30
+ },
+ "rows": {
+ "coefficient": 852,
+ "contract": "W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential",
+ "degree": 2000,
+ "degree_gap": "6548/25",
+ "suffix_slope": 8000
+ },
+ "semantic": {
+ "B": 9696565176891520488614054257040,
+ "C0": 2358858462850846165593256368932965330169899180021667007021321420800,
+ "C1": 1,
+ "E": 9696565176891520488192506033216,
+ "induction_gap": 533311084729033626873772984137200,
+ "literal_charge": 2771683137698171397039558468,
+ "strict_literal_gap": 9693793493753822316795466474748
+ }
+ },
+ "inherited_commit": "0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52",
+ "kappa": "384569/10000000000",
+ "scope": "Exact finite moments and assembly; producer and corner certificates checked separately. Copied-stream scheduling, simultaneous basis existence, analytic and tape interfaces remain written proof dependencies.",
+ "source_sha256": {
+ "certificates/copied-centers-bit-axes.json": "ed307cef595091b11ba8f8e6ff11302ad8db190227a2fbf34c232fd680206254",
+ "certificates/copied-centers-complex-input.json": "91a9e54b455ecc36c3150abcf4a1c9138691c8faab464b5ce159ba8e376764e7",
+ "certificates/copied-centers-corner-25-23.json": "23b0540ddc1d98a775383bfc65c7cf512aad86b399bf71167220b2a8182f5610",
+ "certificates/copied-centers-input.json": "5f8a57b1a4dd3f271d4e859ad350db3674b74f744127e74a989e7790718cea24",
+ "notes/copied-centers-assembly.tex": "00117892971ae766188ace0af03030c44164fda105e42b70d84f52c3339a7dcb",
+ "notes/copied-centers-bit.tex": "ccc8191ddb51698251ed4461a4c26104501b9b2ee37ce3cbe82fa73e85ae40dd",
+ "notes/copied-centers-complex.tex": "18eac6d5c5755e53230c0c12a633f38b6ce9666ef0322c1aff79394f2952af72",
+ "notes/copied-centers-lemma.tex": "d0ce6d3d504996aadb098227885224e48df46101daec8893523a0a8b7364d8fe",
+ "notes/copied-centers-note.tex": "1099559bea3090399a2496bfb8fdf8966ac39d22fd413e35643af5ee0bb08556",
+ "references/copied-centers/MANIFEST.json": "5636f7beb34ae439f076d36e13d95d3057ce41ccbdba9da63d7727198b093ccb",
+ "scripts/copied_centers/README.md": "8d348a28fc11615fb686f7d47548db06a5000378b54e0e47438d17292b5942b9",
+ "scripts/copied_centers/__init__.py": "13db4f09038a2ff5335cbd4dbd93274b0fb16b3c7b51e4de67cbb2801a3f78e1",
+ "scripts/copied_centers/corners.py": "9eecdc39c67cc18c806a33f0be03986c28591d322881fd60c11f52c625c8067b",
+ "scripts/copied_centers/physical.py": "837345d1f8753eab0e70f105b1d1bb0db965b993da037b1825ddef3672609d7d",
+ "scripts/copied_centers_network.py": "409ebfbd8a41c4c4d089aa0949fcf5a949415dc26f57440ffd48b7bd8881e6a9",
+ "scripts/copied_centers_producer.py": "33afa6fe25677e13656fa8a200a25ed3510ef70c1ff9f1186612cbd9ee75d209",
+ "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782",
+ "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d"
+ },
+ "status": "Conditional copied-center multiplication witness"
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/bit-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/bit-profile.json
new file mode 100644
index 0000000000..36105e819a
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/bit-profile.json
@@ -0,0 +1,69 @@
+{
+ "h": 23,
+ "v": 1771,
+ "R": 28866,
+ "m": 529,
+ "N": 3136441,
+ "W": 108516254,
+ "L": 1792252,
+ "total_rank": 57403754177,
+ "deficit": 1344189,
+ "maxchild": 528,
+ "deferred_slots": 11565,
+ "source": {
+ "repository": "https://github.com/Swapnil-jain/integer-mult-kappa",
+ "commit": "741e7aa078392553815df7926ee17ac5e25a8c38",
+ "sha256": {
+ "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588",
+ "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c"
+ }
+ },
+ "child_multiplicities": {
+ "1": 239511811,
+ "2": 238288050,
+ "3": 53377940,
+ "4": 46970462,
+ "5": 23632224,
+ "6": 7409864,
+ "7": 4105178,
+ "8": 5755750,
+ "9": 2082696,
+ "10": 878416,
+ "11": 1388464,
+ "12": 1080310,
+ "13": 945714,
+ "14": 226688,
+ "15": 2451064,
+ "16": 1508892,
+ "17": 4771074,
+ "18": 2149994,
+ "19": 7367360,
+ "20": 8182020,
+ "21": 1466388,
+ "22": 88550,
+ "484": 6272882,
+ "506": 61280142,
+ "507": 545468,
+ "508": 173558,
+ "509": 293986,
+ "510": 580888,
+ "511": 14168,
+ "512": 322322,
+ "513": 17710,
+ "514": 1129898,
+ "515": 127512,
+ "516": 410872,
+ "517": 99176,
+ "518": 1186570,
+ "519": 340032,
+ "520": 322322,
+ "521": 106260,
+ "522": 1583274,
+ "523": 626934,
+ "524": 2854852,
+ "525": 13711082,
+ "526": 4629394,
+ "527": 5653032,
+ "528": 6233920
+ }
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/certificate.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/certificate.py
new file mode 100644
index 0000000000..5e00159bfe
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/certificate.py
@@ -0,0 +1,114 @@
+#!/usr/bin/env python3
+"""Exact finite assembly for cyclic strips with deferred readouts.
+
+Built on Avi Eisenberg's PR110 (Anthropic Claude assistance), icekylinx's
+PR104 stopped-product and copied-center interfaces, and Zhihao Chen's
+assembly of the RaD interfaces. Integration for eumemic with OpenAI Codex
+assistance. Apache-2.0. General transfer hypotheses remain inherited.
+"""
+import argparse
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(ROOT / 'scripts'))
+from partial_swap_network import moment
+from copied_centers_network import finite_bridge as copied_bridge
+from structured_bulk_assembly import assembly, js
+ATOM = Q(1, 1000)
+OLD = Q(384599, 10**10)
+BETA = Q(1, 10**6)
+COARSE = Q(620523, 5000000000)
+COMPLEX = Q(110616162, 10**12)
+KGRID = 10**15
+
+def profile(name):
+ p = json.loads((HERE / name).read_text())
+ p['child_multiplicities'] = {int(t): c for t, c in p['child_multiplicities'].items()}
+ z = p['child_multiplicities']
+ assert all(0 < t < p['m'] and c > 0 for t,c in z.items())
+ assert sum(t*c for t,c in z.items()) == p['total_rank'] == p['W']*p['m']-p['N']+p['L']
+ assert max(z) == p['maxchild']
+ return p
+
+def contracts(p, a):
+ try: moment(p['m'],p['W'],p['child_multiplicities'],a,True)
+ except ValueError: return False
+ return True
+
+def exact(bit=None, phase=None):
+ bit = profile('bit-profile.json') if bit is None else bit
+ phase = profile('complex-profile.json') if phase is None else phase
+ assert (bit['h'], phase['h']) == (23,24)
+ bm = moment(bit['m'],bit['W'],bit['child_multiplicities'],COARSE,True)
+ cm = moment(phase['m'],phase['W'],phase['child_multiplicities'],COMPLEX,True)
+ assert not contracts(bit,COARSE+Q(1,10**10))
+ assert not contracts(phase,COMPLEX+Q(1,10**12))
+ ab = (1-ATOM)*COARSE+ATOM*OLD
+ assert 0 < OLD < COARSE < ATOM and ab < ATOM
+ a = min(ab,(1-BETA)*COMPLEX-Q(1,10**14))
+ row = dict(h=phase['h'],v=phase['v'],c=phase['additions'],central_disjoint=24)
+ bridge = copied_bridge(bit,phase,[row,row])
+ # Logical readouts are expanded into same-frame shears with |coefficient|<=1.
+ # Exact numerators over42 are split into signed42 chunks and a remainder.
+ # The independent audit counts every chunk and checks this guard covers it.
+ # Each row has <=c+R mixer operations and <=R leaf copies. There are
+ # <=R+q readouts, each containing <=h center coefficients and <=v direct
+ # coefficients; <=4*v*(h+1) scalar groups suffice per readout. A factor
+ # eight covers forward/inverse words, both reflected words, and copies.
+ h,v,R,q,c = (phase[k] for k in ('h','v','R','roots','additions'))
+ local = 8*(c+2*R+(R+q)*v*(h+1)+h*h+h+1)
+ G = phase['N'] + 2*v*local
+ m,W,s = (phase[k] for k in ('m','W','total_rank'))
+ E=64*(W+m+G+1)**3
+ charge=2*G*W*W+8*s+4*W+4+32*m
+ B=s+E; C0=32*m*B*B
+ assert charge= s+E and 2*B+181:
+ mid=(lo+hi)//2
+ if accepts(mid): lo=mid
+ else: hi=mid
+ k=Q(lo,KGRID)
+ assembled=assembly(a,COMPLEX,bridge,k,beta=BETA)
+ assert len(assembled['strict_constraints'])==47 and len(assembled['margins'])==7
+ assert not accepts(lo+1)
+ return dict(status='Finite conditional cyclic/deferred witness',kappa=k,
+ complex_saving=COMPLEX,coarse_bit_saving=COARSE,actual_bit_saving=ab,
+ bit_parameter=a,complex_profile=phase,bit_profile=bit,
+ bit_moment_gap=bm['strict_gap'],complex_moment_gap=cm['strict_gap'],
+ finite_bridge=bridge,assembly=assembled,
+ next_grid_rejections=dict(bit='1e-10',complex='1e-12',kappa='1e-15'))
+
+def main():
+ parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args()
+ assert not sys.flags.optimize
+ result=js(exact()); path=HERE/'certificate.json'
+ if args.write:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+ else:assert result==json.loads(path.read_text()),'Frozen exact certificate mismatch'
+ print('PASS conditional kappa = %s = %.12e; 47 constraints, 7 margins; expanded scalar charge' % (result['kappa'],float(Q(result['kappa']))))
+if __name__=='__main__':main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/complex_deferred.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/complex_deferred.py
new file mode 100644
index 0000000000..00ea2cafd8
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/complex_deferred.py
@@ -0,0 +1,580 @@
+# R12 derived compiler by Chafik Boukhalfa with OpenAI Codex assistance.
+# PR125 source by Joel Pulikkan; all inherited notices below remain attached.
+# This variant replaces the single shrink pass; it is a new candidate.
+#!/usr/bin/env python3
+"""Shrunk lifted frames and saturated deferred readouts on the PR117 complex DAG.
+
+After the role compile, a forward pass shrinks a lifted frame to the minimal
+nondegenerate span of its label and predecessor frames when that merges
+increments of the role chains holding it (16,031 frames). Section D rechecks
+every chain. The shrink step was prepared by Joel Pulikkan with Anthropic
+Claude assistance; everything else is PR114 (eumemic) unchanged.
+
+
+PR117 credits its searched DAG to eumemic with Anthropic Claude assistance;
+this experiment imports and replays that witness unchanged. PR110/PR114
+saturation and exact finite checks are applied to the resulting graph.
+Logical readout macros are realized as signed numerator/42 chunks of magnitude
+at most one. The literal audit expands and charges those same-frame shears,
+checks exact reconstruction, and reverses the chunks under reflection.
+Inherited Avi Eisenberg, Rohan Arun, icekylinx and Swapnil Jain credits retained.
+This integration prepared with OpenAI Codex assistance. Apache-2.0.
+"""
+import array
+import json
+import random
+import struct
+import sys
+import tempfile
+from collections import Counter, defaultdict
+from itertools import combinations
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(ROOT / 'scripts'))
+sys.path.insert(0, str(HERE))
+import importlib.util
+producer_path = HERE / 'producer.py'
+spec = importlib.util.spec_from_file_location('replayed_producer_wrapper', producer_path)
+producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer)
+build = producer.build
+
+P = (1 << 61) - 1
+SHRUNK = 16031
+
+
+def require(ok, msg):
+ if not ok:
+ raise SystemExit('FAIL: ' + msg)
+
+
+def load(prefix):
+ def rd(fh, typ, cnt):
+ a = array.array(typ); a.fromfile(fh, cnt); return a
+ with open(str(prefix) + '.bin', 'rb') as f:
+ h, v, n, q = struct.unpack('<4I', f.read(16))
+ flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n)
+ roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n)
+ with open(str(prefix) + '.labels', 'rb') as f:
+ ranks = rd(f, 'I', n); types = rd(f, 'B', n)
+ args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)]
+ return h, v, n, q, args, core, cover, roots, kind, active, ranks, types
+
+
+# ---------------------------------------------------------------- F2 linear algebra on bit vectors
+def dot(a, b): return bin(a & b).count('1') & 1
+
+
+def reduce(basis):
+ rows = []; piv = []
+ for vec in basis:
+ for p, r in zip(piv, rows):
+ if vec >> p & 1: vec ^= r
+ if vec:
+ p = vec.bit_length() - 1
+ for i in range(len(rows)):
+ if rows[i] >> p & 1: rows[i] ^= vec
+ rows.append(vec); piv.append(p)
+ return rows
+
+
+def kernel(funcs, h):
+ K = reduce(funcs); piv = [r.bit_length() - 1 for r in K]
+ out = []
+ for c in (i for i in range(h) if i not in piv):
+ vec = 1 << c
+ for r, p in zip(K, piv):
+ if r >> c & 1: vec |= 1 << p
+ out.append(vec)
+ return out
+
+
+def restrict(basis, funcs):
+ B = reduce(basis)
+ for f in funcs:
+ if not B: break
+ vals = [dot(b, f) for b in B]
+ if not any(vals): continue
+ k = vals.index(1); pv = B[k]
+ B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k)
+ return reduce(B)
+
+
+def contains(A, B):
+ RB = reduce(B)
+ return len(reduce(RB + list(A))) == len(RB)
+
+
+def cap(A, B):
+ A = reduce(A); B = reduce(B)
+ if not A or not B: return []
+ ker = []; red = []
+ for i, vec in enumerate(A + B):
+ tag = 1 << i
+ for rv, rt in red:
+ if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt
+ if vec: red.append((vec, tag))
+ else:
+ comb_ = 0
+ for k in range(len(A)):
+ if tag >> k & 1: comb_ ^= A[k]
+ ker.append(comb_)
+ return reduce(ker)
+
+
+def nondeg(B):
+ B = reduce(B); k = len(B)
+ if not k: return True
+ M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)]
+ return len(reduce(M)) == k
+
+
+def hopcroft_karp(left, adj):
+ """maximum bipartite matching; adj[x] = sorted list of right vertices."""
+ INF = 1 << 60
+ mate_l = {x: None for x in left}; mate_r = {}
+ while True:
+ dist = {}; queue = []
+ for x in left:
+ if mate_l[x] is None: dist[x] = 0; queue.append(x)
+ else: dist[x] = INF
+ found = INF; head = 0
+ while head < len(queue):
+ x = queue[head]; head += 1
+ if dist[x] >= found: continue
+ for r in adj[x]:
+ y = mate_r.get(r)
+ if y is None: found = min(found, dist[x] + 1)
+ elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y)
+ if found == INF: break
+ gained = 0
+ for x0 in left:
+ if mate_l[x0] is not None: continue
+ stack = [(x0, iter(adj[x0]))]; path = []
+ while stack:
+ x, it = stack[-1]
+ advanced = False
+ for r in it:
+ y = mate_r.get(r)
+ if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1):
+ path.append((x, r))
+ if y is None:
+ for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx
+ gained += 1; stack = []; break
+ stack.append((y, iter(adj[y]))); advanced = True; break
+ else:
+ dist[x] = INF; stack.pop()
+ if path: path.pop()
+ continue
+ if not advanced: break
+ if not gained: break
+ return mate_l
+
+
+from functools import lru_cache
+from fractions import Fraction
+
+def sat_basis(vectors):
+ piv = {}
+ for x in vectors:
+ for p in sorted(piv, reverse=True):
+ if x >> p & 1:
+ x ^= piv[p]
+ if x:
+ p = x.bit_length() - 1
+ for q in piv:
+ if piv[q] >> p & 1:
+ piv[q] ^= x
+ piv[p] = x
+ return tuple((piv[p] for p in sorted(piv, reverse=True)))
+
+def sat_dot(a, b):
+ return (a & b).bit_count() & 1
+
+@lru_cache(None)
+def sat_contained(A, B):
+ for x in A:
+ for r in B:
+ if x >> r.bit_length() - 1 & 1:
+ x ^= r
+ if x:
+ return False
+ return True
+
+@lru_cache(None)
+def sat_cap(A, B):
+ if not A or not B:
+ return ()
+ red = {}
+ out = []
+ for i, x in enumerate(A + B):
+ tag = 1 << i
+ for p in sorted(red, reverse=True):
+ if x >> p & 1:
+ r, t = red[p]
+ x ^= r
+ tag ^= t
+ if x:
+ red[x.bit_length() - 1] = (x, tag)
+ else:
+ y = 0
+ for j, r in enumerate(A):
+ if tag >> j & 1:
+ y ^= r
+ if y:
+ out.append(y)
+ return sat_basis(out)
+
+@lru_cache(None)
+def sat_nondeg(B):
+ return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B)
+
+@lru_cache(None)
+def sat_nonsingular_part(B):
+ rows = list(B)
+ out = []
+ while rows:
+ i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None)
+ if i is not None:
+ a = rows.pop(i)
+ out.append(a)
+ rows = [x ^ a if sat_dot(x, a) else x for x in rows]
+ continue
+ pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None)
+ if pair is None:
+ break
+ i, j = pair
+ a, b = (rows[i], rows[j])
+ out.extend((a, b))
+ rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)]
+ return sat_basis(out)
+
+def saturated_placement(cand, reach):
+ # Each extracted block is orthogonal to previously selected blocks.
+ # A diagonal-one pivot contributes a nondegenerate line; when all
+ # remaining diagonals vanish, a dot-one pair contributes a hyperbolic
+ # plane. The residual radical is discarded, not counted as a frame.
+ cand = {s: sat_basis(B) for s, B in cand.items()}
+ order = sorted(cand, key=lambda s: (Fraction(-(1 << len(cand[s])), max(1, len(reach[s]))**2), -len(cand[s]), s))
+ byT = defaultdict(list); placed = {}
+ for s in order:
+ X = cand[s]; changed = True
+ while changed and X:
+ changed = False
+ for t in sorted(reach[s]):
+ for w in byT[t]:
+ B = placed[w]
+ if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)):
+ X = sat_cap(X, B); changed = True
+ if not X: break
+ if not X: break
+ if X and not sat_nondeg(X):
+ before = X; X = sat_nonsingular_part(X)
+ assert sat_contained(X, before) and sat_nondeg(X)
+ assert len(X) < len(before)
+ changed = True # Extraction can break containment of a smaller target frame.
+ if X:
+ assert sat_nondeg(X) and sat_contained(X, cand[s])
+ placed[s] = X
+ for t in reach[s]: byT[t].append(s)
+ for t, ss in byT.items():
+ ss.sort(key=lambda s: (len(placed[s]), s))
+ assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:]))
+ return placed
+
+def main():
+ with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work:
+ prefix = Path(work) / 'complex'
+ build(24, prefix, central_disjoint=24)
+ h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix)
+ trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count')
+ m = h * h; N = v * v; FULL = (1 << h) - 1
+ tmask = [sum(1 << p for p in T) for T in trip]
+ tid = {T: i for i, T in enumerate(trip)}
+
+ # ------------------------------------------------------------ uses and matching (inherited adjacency)
+ degree = [0] * n; uses = defaultdict(list); c_add = 0
+ for x in range(1, n):
+ if active[x] and args[x][0]:
+ c_add += 1
+ for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos))
+ for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j))
+ def unode(u): return roots[u[1]] if u[0] == 'root' else u[1]
+ def before(x, u):
+ y = unode(u)
+ return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y)
+ def incl(x, y):
+ tx, ty = types[x], types[y]
+ if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y])
+ if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y])
+ if tx == 1 and ty == 3: return bool(core[x] & core[y])
+ if tx == 2 and ty == 3: return not (cover[x] & ~core[y])
+ if tx == 3 and ty == 2: return cover[y] == FULL
+ if tx == 3 and ty == 3: return core[x] == core[y]
+ return False
+ left = []; adj = {}
+ for x in range(1, n):
+ if not (active[x] and args[x][0]): continue
+ rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))})
+ if rs: left.append(x); adj[x] = rs
+ mate = hopcroft_karp(left, adj)
+ links = {x: r for x, r in mate.items() if r is not None}
+ R = c_add + q - len(links)
+ require((c_add,q,len(links),R)==(91770,8120,71185,28705),'selected PR117 graph')
+ print('PR117 graph matched', c_add, q, len(links), R, flush=True)
+ linked_use = {(y, k): x for x, (y, k) in links.items()}
+
+ # ------------------------------------------------------------ root targets, read coefficients, root functionals
+ target = [None] * q
+ for j in range(v): target[j] = j
+ idx = v
+ # PR117 witness stores pair-star roots in natural excluded-point order.
+ for a, b in combinations(range(h), 2):
+ others = [i for i in range(h) if i not in (a, b)]
+ for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1
+ centre_of = {}
+ for j in range(q):
+ if kind[j]:
+ miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover')
+ centre_of[j] = miss.bit_length() - 1
+ require(idx + len(centre_of) == q, 'root order')
+ rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)]
+
+ # ------------------------------------------------------------ lifted binary frames, monotone
+ succ = defaultdict(set); droot = defaultdict(set)
+ for x in range(1, n):
+ if not active[x]: continue
+ for k, u in enumerate(uses[x]):
+ if (x, k) in linked_use: continue
+ (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1]))
+ for x, (y, k) in links.items():
+ u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1]))
+ order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True)
+ K = {}
+ for x in order_desc:
+ rows = [rootfun[j] for j in droot[x]]
+ for t in succ[x]: rows += K[t]
+ K[x] = reduce(rows)
+ def envelope(x):
+ if not args[x][0]: return [tmask[x - 1]]
+ if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1]
+ require(types[x] == 1, 'only ordinary and common-pair labels occur')
+ ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1]
+ require(len(ks) == ranks[x], 'common-pair support')
+ return [core[x] | (1 << k) for k in ks]
+ U = {}
+ for x in range(1, n):
+ if not active[x]: continue
+ if not args[x][0]: U[x] = envelope(x); continue
+ B = kernel(K[x], h)
+ require(contains(envelope(x), B), 'label outside lifted frame')
+ U[x] = B if nondeg(B) else envelope(x)
+ changed = True
+ while changed:
+ changed = False
+ for x in order_desc:
+ if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]):
+ env = envelope(x)
+ if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True
+ dimU = {x: len(reduce(B)) for x, B in U.items()}
+ print('PR117 frames lifted',sum(dimU[x]>ranks[x] for x in U),flush=True)
+
+ # ------------------------------------------------------------ explicit role compile
+ order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x))
+ holds = []; first_node = []; ops = []; edge_key = {}; role_root = {}
+ def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1
+ def serve(s, y, k):
+ u = uses[y][k]
+ if u[0] == 'gate': edge_key[(y, k)] = s
+ else: role_root[s] = u[1]
+ for x in order:
+ free = [k for k in range(len(uses[x])) if (x, k) not in linked_use]
+ if not args[x][0]:
+ for k in free:
+ s = new_role(x); ops.append(('src', s, x)); serve(s, x, k)
+ continue
+ a, b = args[x]
+ ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0))
+ kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1))
+ sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb))
+ if x in links and links[x][0] == a: sa, sb = sb, sa
+ piv, oth = sa, sb
+ ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x)
+ if x in links: serve(oth, *links[x])
+ require(free, 'every use linked at node %d' % x)
+ serve(piv, x, free[0])
+ for k in free[1:]:
+ f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k)
+ require(not edge_key and len(holds) == R, 'compile')
+ Rr = R
+
+ # R12 logical-frame nondegenerate completion and endpoint descent.
+ from r12_frame_opt import optimize as r12_optimize
+ U, dimU, frame_optimization = r12_optimize(U, order, args, succ, holds, role_root, envelope, h, globals())
+ shrunk = frame_optimization['shrunk_frames']
+
+ # ------------------------------------------------------------ B. the word computes every root value
+ rng = random.Random(20261008)
+ xs = [rng.randrange(P) for _ in range(v)]
+ val = [0] * n
+ for i in range(v): val[i + 1] = xs[i]
+ for x in order:
+ if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P
+ leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]}
+ a_ = [0] * Rr
+ for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1]
+ for o in ops:
+ if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P
+ elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P
+ require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values')
+
+ # ------------------------------------------------------------ phase one and garbage reach
+ def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else []
+ prev = {}; pred = defaultdict(list); last = {}
+ for i, o in enumerate(ops):
+ for s in touch(o):
+ if s in prev: pred[i].append(prev[s])
+ prev[s] = i; last[s] = i
+ centre_roles = [s for s, j in role_root.items() if kind[j]]
+ Anc = set(); st = [last[s] for s in centre_roles]
+ while st:
+ i = st.pop()
+ if i not in Anc: Anc.add(i); st.extend(pred[i])
+ touched = set(centre_roles)
+ for i in Anc: touched.update(touch(ops[i]))
+ require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one')
+ reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr
+ for s, j in role_root.items():
+ if kind[j]: reach_all[s] = True
+ else: reach[s].add(target[j])
+ for o in reversed(ops):
+ if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]]
+ elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]]
+
+ # ------------------------------------------------------------ deferral frames, insertion nesting
+ def F0(s): return U[first_node[s]]
+ from r12_defer_opt import repair_candidate, place as r12_place
+ cand = {}
+ for s in range(Rr):
+ if s in touched or reach_all[s]: continue
+ S_ = restrict(F0(s), [tmask[t] for t in reach[s]])
+ S_ = repair_candidate(S_, globals()) if S_ else []
+ if S_: cand[s] = S_
+ print('PR117 candidates',len(cand),flush=True)
+ placed, deferral_optimization = r12_place(cand, reach, F0, h, m, globals())
+ print('PR117 placed',len(placed),flush=True)
+ deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred)
+
+ # ------------------------------------------------------------ C. replay with arbitrary scratch and data
+ inv = lambda a: pow(a % P, P - 2, P); HALF = inv(2); I21 = inv(21)
+ cvec = [None] * Rr; dpart = [dict() for _ in range(Rr)]
+ for s, j in role_root.items():
+ if kind[j]: c = [0] * h; c[centre_of[j]] = 1; cvec[s] = c
+ else: dpart[s][target[j]] = (P - HALF) if j >= v else HALF
+ seed_c = {s: (None if cvec[s] is None else list(cvec[s])) for s in role_root}
+ seed_d = {s: dict(dpart[s]) for s in role_root}
+ def addc(dst, src):
+ if cvec[src] is not None:
+ cvec[dst] = list(cvec[src]) if cvec[dst] is None else [(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])]
+ for t, c in dpart[src].items(): dpart[dst][t] = (dpart[dst].get(t, 0) + c) % P
+ for o in reversed(ops):
+ if o[0] == 'add': addc(o[2], o[1])
+ elif o[0] == 'copy': addc(o[1], o[2])
+ scatter = [[(I21 - (HALF if i in trip[t] else 0)) % P for t in range(v)] for i in range(h)]
+ def readout(y, s, value, sign, seed=False):
+ # Logical readout macro: the literal audit combines its exact rational
+ # target coefficients and expands each numerator/42 into bounded shears.
+ cv = seed_c[s] if seed else cvec[s]; dp = seed_d[s] if seed else dpart[s]
+ if cv is not None:
+ for i, ci in enumerate(cv):
+ if ci:
+ f = sign * ci * value % P; row = scatter[i]
+ for t in range(v): y[t] = (y[t] + f * row[t]) % P
+ for t, c in dp.items(): y[t] = (y[t] + sign * c * value) % P
+ phase1 = sorted(Anc); rest = [i for i in range(len(ops)) if i not in Anc]
+ def replay(seed):
+ rng = random.Random(seed)
+ x = [rng.randrange(P) for _ in range(v)]; z = [rng.randrange(P) for _ in range(Rr)]
+ y0 = [rng.randrange(P) for _ in range(v)]; a = list(z); y = list(y0)
+ for s in range(Rr):
+ if s not in dset: readout(y, s, a[s], -1)
+ for s, leaf in leaf_of.items():
+ if s not in dset: a[s] = (a[s] + x[leaf - 1]) % P
+ def run(i, sign=1):
+ o = ops[i]
+ if o[0] == 'add': a[o[1]] = (a[o[1]] + sign * a[o[2]]) % P
+ elif o[0] == 'copy': a[o[2]] = (a[o[2]] + sign * a[o[1]]) % P
+ for i in phase1: run(i)
+ for s in centre_roles: readout(y, s, a[s], +1, True)
+ for s in deferred: readout(y, s, a[s], -1)
+ for s in deferred:
+ if s in leaf_of: a[s] = (a[s] + x[leaf_of[s] - 1]) % P
+ for i in rest: run(i)
+ for s, j in role_root.items():
+ if not kind[j]: readout(y, s, a[s], +1, True)
+ for i in reversed(range(len(ops))): run(i, -1)
+ for s, leaf in leaf_of.items(): a[s] = (a[s] - x[leaf - 1]) % P
+ return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v))
+ rep = [replay(seed) for seed in (1, 2)]
+ require(all(r == (True, True) for r in rep), 'replay %s' % rep)
+
+ # ------------------------------------------------------------ D. exact F2 frame facts
+ root_frame = {}
+ for s, j in role_root.items():
+ root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h)
+ FULLB = [1 << i for i in range(h)]
+ chain_dims = []
+ for s in range(Rr):
+ seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]]
+ if s in root_frame: seq.append(root_frame[s])
+ seq.append(FULLB)
+ require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s)
+ require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s)
+ chain_dims.append([len(reduce(B)) for B in seq])
+ for s, X in placed.items():
+ require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s)
+ require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s)
+ byT2 = defaultdict(list)
+ for s in deferred:
+ for t in reach[s]: byT2[t].append(s)
+ for t, ss in byT2.items():
+ ss.sort(key=lambda s: (len(placed[s]), s))
+ require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t)
+
+ # ------------------------------------------------------------ E. one-child histogram
+ z = Counter()
+ for s in range(Rr):
+ ds = chain_dims[s]
+ for a, b in zip(ds[:-1], ds[1:-1]):
+ if b > a: z[b - a] += 2 * v
+ lastd = ds[-2]
+ if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform
+ z[h - lastd] += 2 * v # final growth to F
+ z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma
+ levels = defaultdict(set)
+ for s in deferred:
+ for t in reach[s]: levels[t].add(len(placed[s]))
+ for t in range(v):
+ ds = sorted(levels[t] | {0, h - 1})
+ for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts
+ z[h - 1] += 2 * N # data-wire fronts
+ z[(h - 1) ** 2] += 2 * N # data macros
+ z[1] += N # endpoint copies
+ z.pop(0, None)
+ W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L
+ require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass')
+ require(all(0 < t < m for t in z), 'children below m')
+ out = dict(frame_optimization=frame_optimization, deferral_optimization=deferral_optimization, h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_,
+ deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched),
+ deferred_roles=len(deferred),
+ deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())),
+ lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]),
+ replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)'),
+ child_multiplicities=dict(sorted(z.items())))
+ (HERE / 'complex-profile.json').write_text(json.dumps(out, indent=1) + '\n')
+ print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_))
+
+
+if __name__ == '__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/inputs/complex-dag.json.gz b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/inputs/complex-dag.json.gz
new file mode 100644
index 0000000000..a5b0598e4c
Binary files /dev/null and b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/inputs/complex-dag.json.gz differ
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/producer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/producer.py
new file mode 100644
index 0000000000..a93a265f01
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/producer.py
@@ -0,0 +1,17 @@
+"""Pinned PR117 scalar DAG adapter for the saturated deferred compiler.
+
+The searched graph is upstream PR117 work credited to eumemic with Anthropic
+Claude assistance. This adapter preserves that witness and producer unchanged;
+saturation integration is separate OpenAI Codex-assisted work. Apache-2.0.
+"""
+from hashlib import sha256
+from pathlib import Path
+from replayed_producer import build as replayed_build
+
+WITNESS_SHA256 = '3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b'
+
+def build(h, prefix, central_disjoint, base=2):
+ assert (h, central_disjoint, base) == (24,24,2)
+ witness=Path(__file__).resolve().parent/'inputs/complex-dag.json.gz'
+ assert sha256(witness.read_bytes()).hexdigest() == WITNESS_SHA256, 'PR117 DAG pin mismatch'
+ return replayed_build(witness,prefix)
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/r12_defer_opt.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/r12_defer_opt.py
new file mode 100644
index 0000000000..8dfc44cb1c
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/r12_defer_opt.py
@@ -0,0 +1,71 @@
+"""Complete marginal-cost filtering for PR125 saturated deferrals.
+
+Chafik Boukhalfa with OpenAI Codex assistance, Apache-2.0. Retains eumemic's
+PR114/PR125 nested saturated-placement loop; the actual paid marginal score
+uses exterior, first-transition and target-front changes as in DanieleCorso's
+PR126 cost-aware descending construction. Here insertion may be between both
+existing target levels. Degenerate initial caps may contribute a nondegenerate
+part instead of being discarded. All inherited attribution remains attached.
+"""
+from collections import defaultdict
+from fractions import Fraction
+import math,os
+
+
+def repair_candidate(B, algebra):
+ mode=os.environ.get('R12_DEFER_MODE','original')
+ if algebra['nondeg'](B):return B
+ if mode.startswith('radical') or mode=='gain_priority':
+ return list(algebra['sat_nonsingular_part'](algebra['sat_basis'](B)))
+ return []
+
+
+def place(cand,reach,F0,h,m,algebra):
+ mode=os.environ.get('R12_DEFER_MODE','original')
+ assert mode in ('original','cost_filter','radical_cost','radical_original','gain_priority')
+ if mode=='original':return algebra['saturated_placement'](cand,reach),dict(mode=mode)
+ basis=algebra['sat_basis'];inside=algebra['sat_contained'];cap=algebra['sat_cap']
+ nondeg=algebra['sat_nondeg'];part=algebra['sat_nonsingular_part']
+ cand={s:basis(B) for s,B in cand.items()};byT=defaultdict(list);placed={};levels=defaultdict(set)
+ weight=[0]+[round(d*math.log(d)*10**9) for d in range(1,m+1)]
+ def gain(s,d):
+ r=len(F0(s)); ext=m-h
+ assert 0<=d<=r<=h
+ g=weight[r-d]+weight[ext+d]-weight[r]-weight[ext]
+ for t in reach[s]:
+ ds=levels[t]
+ if d in ds:continue
+ a=max((x for x in ds if xd),default=h-1)
+ assert a<=d<=b
+ g+=weight[d-a]+weight[b-d]-weight[b-a]
+ return g
+ if mode=='gain_priority':order=sorted(cand,key=lambda s:(-gain(s,len(cand[s])), -len(cand[s]),s))
+ else:order=sorted(cand,key=lambda s:(Fraction(-(1<=len(X) and not inside(X,B)) or (len(B)0:
+ assert nondeg(best) and inside(lower,best)
+ assert inside(best,original[x]) and all(inside(best,frames[t]) for t in succ[x])
+ frames[x]=best;counts['moves']+=1;counts['integer_score_gain']+=gain
+ counts['shrink' if len(best)>p&1:x^=piv[p]
+ if x:
+ p=x.bit_length()-1
+ for q in piv:
+ if piv[q]>>p&1:piv[q]^=x
+ piv[p]=x
+ return tuple(piv[p] for p in sorted(piv,reverse=True))
+
+
+def dot(a,b):return (a&b).bit_count()&1
+
+
+@lru_cache(None)
+def contained(A,B):return len(basis(A+B))==len(B)
+
+
+@lru_cache(None)
+def complement(A,h):
+ A=basis(A);piv={x.bit_length()-1:x for x in A};result=[]
+ for j in range(h):
+ if j not in piv:
+ x=1<>j&1:x|=1<=0 else -1
+ parts=(sign*42,)*q+((sign*r,) if r else ())
+ check_chunks(numerator,parts)
+ return parts
+
+def reverse_row(row):
+ if row[0]=='old':return (row[0],row[1],row[3],row[2])
+ return row
+
+
+def check_reflection(forward,backward,h,v):
+ def bank(s):return s+v if s1)
+ readcount+=len(parts);maxchunk=max(maxchunk,max(map(abs,parts)))
+ for part in parts:
+ reached.append(t);records.append(struct.pack('len(old):hist[len(F)-len(old)]+=1
+ current[s]=F
+ for event in events:
+ k,a,b,c,F,*rest=event
+ assert c in (-1,1)
+ promote(a,F)
+ if k=='gate':promote(b,F);scalar+=1
+ elif k=='read':
+ for t in b:promote(t,F)
+ scalar+=len(b)
+ else:
+ assert k=='centre';G=rest[0]
+ assert contained(G,F) or contained(F,G)
+ assert nondeg(G);copies[abs(len(F)-len(G))]+=1
+ for t in b:promote(t,G)
+ scalar+=len(b)+2 # temporary copy and erasure
+ digest.update(repr(event).encode()+b'\n')
+ # Each literal role cleanup reaches full space; any unused final
+ # endpoint is still represented explicitly in the expected chain.
+ for s,F in enumerate(expected):promote(s,F)
+ assert current==expected
+ return hist,copies,scalar,digest.hexdigest()
+ start=tm+[ZERO]*v+[sigma.get(s,ZERO) for s in range(R)]
+ finish=[FULL]*v+[complement(T,h) for T in tm]+[FULL]*R
+ H,C,scalar,digest=framescan(word,start,finish)
+ revstart=[None]*len(start);revfinish=[None]*len(start)
+ for s in range(len(start)):
+ revstart[swap(s)]=complement(finish[s],h);revfinish[swap(s)]=complement(start[s],h)
+ HR,CR,scalarR,reverse_digest=framescan(reverse,revstart,revfinish)
+ assert (H,C,scalar)==(HR,CR,scalarR)
+ z=Counter({r:2*v*n for r,n in (H+C).items()})
+ for s in range(R):z[h*h-h+len(sigma.get(s,ZERO))]+=2*v
+ z[(h-1)**2]+=2*v*v;z[1]+=v*v
+ z.pop(0,None)
+ assert dict(sorted(z.items()))=={int(r):n for r,n in d['out']['child_multiplicities'].items()},'Literal reflected child histogram'
+ assert sum(r*n for r,n in z.items())==d['out']['total_rank']
+ G=v*v+2*v*scalar
+ safe=8*(d['c_add']+2*R+(R+q)*v*(h+1)+h*h+h+1) if 'c_add' in d else 8*(d['out']['additions']+2*R+(R+q)*v*(h+1)+h*h+h+1)
+ assert safe>=scalar
+ return dict(h=h,v=v,R=R,exact_fresh_source_map=True,exact_integer_old_readout_transpose=True,
+ exact_arbitrary_dirty_cancellation_by_dependency_cut=True,
+ reflected_word_rule='Reverse literal order including each bounded readout chunk, negate every shear, swap X/Y ports, complement every frame; auxiliary bank is separate.',
+ reflected_scalar_map='X becomes X-Y; Y unchanged; all auxiliary coordinates restored.',
+ two_stage_scalar_map='(X,Y) becomes (-Y,X+Y) before inherited endpoint correction.',
+ literal_frame_incidences_both_directions=True,all_frames_nondegenerate=True,
+ reflected_residual_rank_histogram_equal=True,child_multiplicities=dict(sorted(z.items())),
+ word_blocks=len(word),expanded_scalar_operations_per_stage=scalar,
+ expanded_old_readout_additions=readcount,largest_readout_numerator_over_42=maxcoef,
+ unsplit_old_readout_macros=unsplit_readcount,split_readout_macros=split_macros,
+ largest_bounded_chunk_numerator_over_42=maxchunk,
+ bounded_readout_chunks_sha256=chunk_digest.hexdigest(),
+ scalar_readout_normalization='Each exact numerator n/42 becomes signed42 chunks plus a signed remainder. Exact reconstruction and chunk magnitude<=1 checked; every same-frame shear is charged; reflection reverses chunk order.',
+ exact_chunk_reconstruction=True,bounded_chunk_coefficients=True,
+ old_readout_coefficients_over_42_sha256=coefficient_digest.hexdigest(),
+ literal_global_scalar_groups=G,conservative_local_G=safe,
+ forward_incidence_sha256=digest,reflected_incidence_sha256=reverse_digest,
+ rejected_controls=rejected,
+ scope='Exact finite source coefficients, dirty cancellation algebra and literal reflected frame/charge ledger. Copied-centre transforms, endpoint correction and residual-to-child/all-size transfer retain their stated inherited contracts.')
+
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--source',type=Path);ap.add_argument('--state',type=Path)
+ ap.add_argument('--output',type=Path);ap.add_argument('--check',type=Path);a=ap.parse_args()
+ assert bool(a.source)!=bool(a.state)
+ d=capture(a.source) if a.source else pickle.loads(a.state.read_bytes())
+ result=audit(d);source=Path(d['source'])
+ result['source_sha256']=sha256(source.read_bytes()).hexdigest()
+ result['audit_sha256']=sha256(Path(__file__).read_bytes()).hexdigest()
+ result=json.loads(json.dumps(result));encoded=json.dumps(result,indent=2,sort_keys=True)+'\n'
+ if a.check:assert result==json.loads(a.check.read_text())
+ if a.output:a.output.write_text(encoded)
+ else:print(encoded,end='')
+ print('PASS exact scalar and literal complement reflection audit',file=sys.stderr)
+
+
+if __name__=='__main__':main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/replayed_producer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/replayed_producer.py
new file mode 100644
index 0000000000..673fbbba70
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/replayed_producer.py
@@ -0,0 +1,179 @@
+"""Replayed h=24 complex producer with all centers disjoint (rational divisor 21).
+
+Copyright 2026 eumemic, Apache-2.0. AI-assisted (Claude). The DAG was found by an
+automated search over producers of the retained paired-triple, pair-star and
+center-disjoint interfaces. The checks below are adapted from
+stopped_product/complex.py (copyright 2026 icekylinx, Apache-2.0, PR #104).
+
+The witness complex-dag.json.gz lists the ordinary
+additions after the v triple inputs and the retained roots: the disjoint sums
+D[t], the pair stars P(a,b,i) and the center-disjoint sums A_i. Every support,
+core, cover, type and rank is recomputed here from the operands; nothing is
+read from the witness except the operand pairs and the root indices.
+"""
+import gzip, json, struct, sys, array
+from fractions import Fraction
+from itertools import combinations
+from pathlib import Path
+
+
+def write_array(f, values):
+ """Little-endian array writer, as partial_swap.binary.write_array."""
+ if sys.byteorder != 'little' and values.itemsize > 1:
+ values = array.array(values.typecode, values)
+ values.byteswap()
+ values.tofile(f)
+
+
+def build(witness, prefix):
+ w = json.loads(gzip.decompress(Path(witness).read_bytes()))
+ h, v, d = w['h'], w['v'], w['central_disjoint']
+ assert (h, d, w['center_denominator']) == (24, 24, 21)
+ triples = list(combinations(range(h), 3))
+ assert v == len(triples)
+ args = [(0, 0)]; support = [0]; core = [0]; cover = [0]; types = [0]; ranks = [0]
+ for j, t in enumerate(triples):
+ mask = sum(1 << a for a in t)
+ args.append((0, 0)); support.append(1 << j); core.append(mask); cover.append(mask)
+ types.append(1); ranks.append(1)
+ flat = w['args']
+ assert len(flat) % 2 == 0
+ for k in range(0, len(flat), 2):
+ a, b, x = flat[k], flat[k+1], len(args)
+ assert 0 < a < x and 0 < b < x, 'Operands must precede their sum'
+ assert not support[a] & support[b], 'Ordinary additions must be cancellation-free'
+ args.append((a, b)); support.append(support[a] | support[b])
+ core.append(core[a] & core[b]); cover.append(cover[a] | cover[b])
+ if core[x].bit_count() >= 2:
+ types.append(1); ranks.append(support[x].bit_count())
+ else:
+ types.append(2); ranks.append(cover[x].bit_count())
+ n = len(args)
+ point_masks = [sum(1 << j for j, t in enumerate(triples) if a in t) for a in range(h)]
+ full_support = (1 << v) - 1
+ roots, kind = [], []
+ assert len(w['D']) == v
+ for t, node in zip(triples, w['D']):
+ assert 0 < node < n
+ assert support[node] == full_support & ~(point_masks[t[0]]|point_masks[t[1]]|point_masks[t[2]])
+ target_mask = sum(1 << a for a in t)
+ if types[node] == 2:
+ assert not cover[node] & target_mask
+ else:
+ assert types[node] == 1
+ assert not support[node] & (point_masks[t[0]]^point_masks[t[1]]^point_masks[t[2]])
+ roots.append(node); kind.append(0)
+ stars = [(a, b, i) for a, b in combinations(range(h), 2) for i in range(h) if i not in (a, b)]
+ assert len(w['P']) == len(stars)
+ pair_outputs = {}
+ for (a, b, i), node in zip(stars, w['P']):
+ assert 0 < node < n
+ assert support[node] == point_masks[a] & point_masks[b] & ~point_masks[i]
+ assert types[node] == 1
+ assert not support[node] & (point_masks[a]^point_masks[b]^point_masks[i])
+ pair_outputs[a, b, i] = node
+ roots.append(node); kind.append(0)
+ assert len(w['A']) == d
+ for i, node in enumerate(w['A']):
+ assert 0 < node < n
+ assert support[node] == full_support & ~point_masks[i]
+ assert types[node] == 2 and cover[node] == ((1 << h)-1) ^ (1 << i)
+ assert ranks[node] == h-1
+ roots.append(node); kind.append(1)
+ # Every A_i avoids i, so sum A_i = (h-3)T. The decoder is T=sum A_i/21
+ # and the scatter is T-(1/2)sum_{i in target} A_i.
+ decoder = Fraction(1, h-3)
+ assert decoder == Fraction(1, 21)
+ scatter_coefficients = [decoder, decoder-Fraction(1, 2)]
+ for coefficient in scatter_coefficients:
+ odd_denominator = coefficient.denominator
+ while odd_denominator % 2 == 0:
+ odd_denominator //= 2
+ assert 21 % odd_denominator == 0 and abs(coefficient) <= 1
+ for source in triples:
+ assert sum(i not in source for i in range(h))*decoder == 1
+ Dset = set(range(d))
+ for triple in triples:
+ k = len(Dset.intersection(triple))
+ assert 2*(3-k)-2*(d-k) == 2*(3-d)
+ patterns = {}
+ for target in triples:
+ chosen = len(Dset.intersection(target))
+ if chosen not in patterns:
+ patterns[chosen] = target
+ for chosen, target in patterns.items():
+ target_set = set(target)
+ for source in triples:
+ k = len(Dset.intersection(source))
+ total_coefficient = Fraction(2*(3-k)-2*(d-k), 2*(3-d))
+ scalar = Fraction(len((target_set-Dset).intersection(source)), 2)
+ scalar -= Fraction(len((target_set & Dset)-set(source)), 2)
+ scalar += Fraction(chosen-1, 2)*total_coefficient
+ assert scalar == Fraction(len(target_set.intersection(source))-1, 2)
+ for j, t in enumerate(triples):
+ masks = [point_masks[a] for a in t]
+ two = (masks[0]&masks[1]&~masks[2]) | (masks[0]&masks[2]&~masks[1]) | (masks[1]&masks[2]&~masks[0])
+ actual = 0
+ for a, b in combinations(t, 2):
+ excluded = next(i for i in t if i not in (a, b))
+ actual |= support[pair_outputs[a, b, excluded]]
+ assert actual == two
+ assert masks[0]&masks[1]&masks[2] == 1 << j
+ assert [((k-1)+(k == 0)-(k == 2)) for k in range(4)] == [0, 0, 0, 2]
+
+ def contained(x, y):
+ tx, ty = types[x], types[y]
+ if tx == 1 and ty == 1: return not(core[y]&~core[x] or cover[x]&~cover[y])
+ if tx in (1, 2) and ty == 2: return not cover[x]&~cover[y]
+ return False
+ active = [0]*n; stack = list(roots)
+ while stack:
+ x = stack.pop()
+ if not x or active[x]: continue
+ active[x] = 1
+ if args[x][0]: stack.extend(args[x])
+ degree = [0]*n
+ for x in range(1, n):
+ if active[x]:
+ if types[x] == 1:
+ assert core[x].bit_count() >= 2 and ranks[x] == support[x].bit_count()
+ else:
+ assert types[x] == 2 and ranks[x] == cover[x].bit_count()
+ if active[x] and args[x][0]:
+ for y in args[x]:
+ assert y < x and contained(y, x), 'Binary frame nesting failed'
+ degree[y] += 1
+ for x in roots: degree[x] += 1
+ H = [0]*(h+1); c = 0; loss = 0
+ for x in range(1, n):
+ if not active[x]: continue
+ r = ranks[x]
+ if args[x][0]:
+ c += 1; H[r] += degree[x]-1; H[h-r] += 1
+ for y in args[x]:
+ assert r >= ranks[y]
+ H[r-ranks[y]] += 1
+ else: H[1] += degree[x]
+ for x, k in zip(roots, kind):
+ r = ranks[x]
+ if k: H[r] += 1; H[h] += 1; loss += r
+ else: H[h-1-r] += 1; H[1] += 1
+ q = len(roots); R = c+q
+ result = dict(h=h, v=v, c=c, q=q, R=R, loss=loss, central_disjoint=d, histogram=H,
+ rank_sum=sum(r*m for r, m in enumerate(H)))
+ assert loss == h*(h-1) and result['rank_sum'] == h*R+2*loss
+ result['center_denominator'] = 21
+ result['scalar_validation'] = dict(ordinary_supports_exact=True, centers_exact=True,
+ center_decoder='sum A_i / 21', scatter_coefficients=list(map(str, scatter_coefficients)),
+ rational_scalar_identity_exact=True, mixed_center_scatter_exact=True, binary_frames_nested=True,
+ binary_frames_nondegenerate=True)
+ with open(str(prefix)+'.bin', 'wb') as f:
+ f.write(struct.pack('<4I', h, v, n, q))
+ write_array(f, array.array('I', (a for pair in args for a in pair)))
+ write_array(f, array.array('Q', core)); write_array(f, array.array('Q', cover))
+ write_array(f, array.array('I', roots)); write_array(f, array.array('I', kind))
+ write_array(f, array.array('B', active))
+ with open(str(prefix)+'.labels', 'wb') as f:
+ write_array(f, array.array('I', ranks)); write_array(f, array.array('B', types))
+ Path(str(prefix)+'.json').write_text(json.dumps(result, indent=2)+'\n')
+ return result
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/screen.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/screen.py
new file mode 100644
index 0000000000..7705719dd6
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/r12-logical-frames/screen.py
@@ -0,0 +1,528 @@
+# R12 derived compiler by Chafik Boukhalfa with OpenAI Codex assistance.
+# PR125 source by Joel Pulikkan; all inherited notices below remain attached.
+# This variant replaces the single shrink pass; it is a new candidate.
+#!/usr/bin/env python3
+"""Shrunk lifted frames and saturated deferred readouts on the PR117 complex DAG.
+
+After the role compile, a forward pass shrinks a lifted frame to the minimal
+nondegenerate span of its label and predecessor frames when that merges
+increments of the role chains holding it (16,031 frames). Section D rechecks
+every chain. The shrink step was prepared by Joel Pulikkan with Anthropic
+Claude assistance; everything else is PR114 (eumemic) unchanged.
+
+
+PR117 credits its searched DAG to eumemic with Anthropic Claude assistance;
+this experiment imports and replays that witness unchanged. PR110/PR114
+saturation and exact finite checks are applied to the resulting graph.
+Logical readout macros are realized as signed numerator/42 chunks of magnitude
+at most one. The literal audit expands and charges those same-frame shears,
+checks exact reconstruction, and reverses the chunks under reflection.
+Inherited Avi Eisenberg, Rohan Arun, icekylinx and Swapnil Jain credits retained.
+This integration prepared with OpenAI Codex assistance. Apache-2.0.
+"""
+import array
+import json
+import random
+import struct
+import sys
+import tempfile
+from collections import Counter, defaultdict
+from itertools import combinations
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(ROOT / 'scripts'))
+sys.path.insert(0, str(HERE))
+import importlib.util
+producer_path = HERE / 'producer.py'
+spec = importlib.util.spec_from_file_location('replayed_producer_wrapper', producer_path)
+producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer)
+build = producer.build
+
+P = (1 << 61) - 1
+SHRUNK = 16031
+
+
+def require(ok, msg):
+ if not ok:
+ raise SystemExit('FAIL: ' + msg)
+
+
+def load(prefix):
+ def rd(fh, typ, cnt):
+ a = array.array(typ); a.fromfile(fh, cnt); return a
+ with open(str(prefix) + '.bin', 'rb') as f:
+ h, v, n, q = struct.unpack('<4I', f.read(16))
+ flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n)
+ roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n)
+ with open(str(prefix) + '.labels', 'rb') as f:
+ ranks = rd(f, 'I', n); types = rd(f, 'B', n)
+ args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)]
+ return h, v, n, q, args, core, cover, roots, kind, active, ranks, types
+
+
+# ---------------------------------------------------------------- F2 linear algebra on bit vectors
+def dot(a, b): return bin(a & b).count('1') & 1
+
+
+def reduce(basis):
+ rows = []; piv = []
+ for vec in basis:
+ for p, r in zip(piv, rows):
+ if vec >> p & 1: vec ^= r
+ if vec:
+ p = vec.bit_length() - 1
+ for i in range(len(rows)):
+ if rows[i] >> p & 1: rows[i] ^= vec
+ rows.append(vec); piv.append(p)
+ return rows
+
+
+def kernel(funcs, h):
+ K = reduce(funcs); piv = [r.bit_length() - 1 for r in K]
+ out = []
+ for c in (i for i in range(h) if i not in piv):
+ vec = 1 << c
+ for r, p in zip(K, piv):
+ if r >> c & 1: vec |= 1 << p
+ out.append(vec)
+ return out
+
+
+def restrict(basis, funcs):
+ B = reduce(basis)
+ for f in funcs:
+ if not B: break
+ vals = [dot(b, f) for b in B]
+ if not any(vals): continue
+ k = vals.index(1); pv = B[k]
+ B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k)
+ return reduce(B)
+
+
+def contains(A, B):
+ RB = reduce(B)
+ return len(reduce(RB + list(A))) == len(RB)
+
+
+def cap(A, B):
+ A = reduce(A); B = reduce(B)
+ if not A or not B: return []
+ ker = []; red = []
+ for i, vec in enumerate(A + B):
+ tag = 1 << i
+ for rv, rt in red:
+ if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt
+ if vec: red.append((vec, tag))
+ else:
+ comb_ = 0
+ for k in range(len(A)):
+ if tag >> k & 1: comb_ ^= A[k]
+ ker.append(comb_)
+ return reduce(ker)
+
+
+def nondeg(B):
+ B = reduce(B); k = len(B)
+ if not k: return True
+ M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)]
+ return len(reduce(M)) == k
+
+
+def hopcroft_karp(left, adj):
+ """maximum bipartite matching; adj[x] = sorted list of right vertices."""
+ INF = 1 << 60
+ mate_l = {x: None for x in left}; mate_r = {}
+ while True:
+ dist = {}; queue = []
+ for x in left:
+ if mate_l[x] is None: dist[x] = 0; queue.append(x)
+ else: dist[x] = INF
+ found = INF; head = 0
+ while head < len(queue):
+ x = queue[head]; head += 1
+ if dist[x] >= found: continue
+ for r in adj[x]:
+ y = mate_r.get(r)
+ if y is None: found = min(found, dist[x] + 1)
+ elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y)
+ if found == INF: break
+ gained = 0
+ for x0 in left:
+ if mate_l[x0] is not None: continue
+ stack = [(x0, iter(adj[x0]))]; path = []
+ while stack:
+ x, it = stack[-1]
+ advanced = False
+ for r in it:
+ y = mate_r.get(r)
+ if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1):
+ path.append((x, r))
+ if y is None:
+ for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx
+ gained += 1; stack = []; break
+ stack.append((y, iter(adj[y]))); advanced = True; break
+ else:
+ dist[x] = INF; stack.pop()
+ if path: path.pop()
+ continue
+ if not advanced: break
+ if not gained: break
+ return mate_l
+
+
+from functools import lru_cache
+from fractions import Fraction
+
+def sat_basis(vectors):
+ piv = {}
+ for x in vectors:
+ for p in sorted(piv, reverse=True):
+ if x >> p & 1:
+ x ^= piv[p]
+ if x:
+ p = x.bit_length() - 1
+ for q in piv:
+ if piv[q] >> p & 1:
+ piv[q] ^= x
+ piv[p] = x
+ return tuple((piv[p] for p in sorted(piv, reverse=True)))
+
+def sat_dot(a, b):
+ return (a & b).bit_count() & 1
+
+@lru_cache(None)
+def sat_contained(A, B):
+ for x in A:
+ for r in B:
+ if x >> r.bit_length() - 1 & 1:
+ x ^= r
+ if x:
+ return False
+ return True
+
+@lru_cache(None)
+def sat_cap(A, B):
+ if not A or not B:
+ return ()
+ red = {}
+ out = []
+ for i, x in enumerate(A + B):
+ tag = 1 << i
+ for p in sorted(red, reverse=True):
+ if x >> p & 1:
+ r, t = red[p]
+ x ^= r
+ tag ^= t
+ if x:
+ red[x.bit_length() - 1] = (x, tag)
+ else:
+ y = 0
+ for j, r in enumerate(A):
+ if tag >> j & 1:
+ y ^= r
+ if y:
+ out.append(y)
+ return sat_basis(out)
+
+@lru_cache(None)
+def sat_nondeg(B):
+ return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B)
+
+@lru_cache(None)
+def sat_nonsingular_part(B):
+ rows = list(B)
+ out = []
+ while rows:
+ i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None)
+ if i is not None:
+ a = rows.pop(i)
+ out.append(a)
+ rows = [x ^ a if sat_dot(x, a) else x for x in rows]
+ continue
+ pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None)
+ if pair is None:
+ break
+ i, j = pair
+ a, b = (rows[i], rows[j])
+ out.extend((a, b))
+ rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)]
+ return sat_basis(out)
+
+def saturated_placement(cand, reach):
+ # Each extracted block is orthogonal to previously selected blocks.
+ # A diagonal-one pivot contributes a nondegenerate line; when all
+ # remaining diagonals vanish, a dot-one pair contributes a hyperbolic
+ # plane. The residual radical is discarded, not counted as a frame.
+ cand = {s: sat_basis(B) for s, B in cand.items()}
+ order = sorted(cand, key=lambda s: (Fraction(-(1 << len(cand[s])), max(1, len(reach[s]))**2), -len(cand[s]), s))
+ byT = defaultdict(list); placed = {}
+ for s in order:
+ X = cand[s]; changed = True
+ while changed and X:
+ changed = False
+ for t in sorted(reach[s]):
+ for w in byT[t]:
+ B = placed[w]
+ if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)):
+ X = sat_cap(X, B); changed = True
+ if not X: break
+ if not X: break
+ if X and not sat_nondeg(X):
+ before = X; X = sat_nonsingular_part(X)
+ assert sat_contained(X, before) and sat_nondeg(X)
+ assert len(X) < len(before)
+ changed = True # Extraction can break containment of a smaller target frame.
+ if X:
+ assert sat_nondeg(X) and sat_contained(X, cand[s])
+ placed[s] = X
+ for t in reach[s]: byT[t].append(s)
+ for t, ss in byT.items():
+ ss.sort(key=lambda s: (len(placed[s]), s))
+ assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:]))
+ return placed
+
+def main():
+ with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work:
+ prefix = Path(work) / 'complex'
+ build(24, prefix, central_disjoint=24)
+ h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix)
+ trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count')
+ m = h * h; N = v * v; FULL = (1 << h) - 1
+ tmask = [sum(1 << p for p in T) for T in trip]
+ tid = {T: i for i, T in enumerate(trip)}
+
+ # ------------------------------------------------------------ uses and matching (inherited adjacency)
+ degree = [0] * n; uses = defaultdict(list); c_add = 0
+ for x in range(1, n):
+ if active[x] and args[x][0]:
+ c_add += 1
+ for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos))
+ for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j))
+ def unode(u): return roots[u[1]] if u[0] == 'root' else u[1]
+ def before(x, u):
+ y = unode(u)
+ return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y)
+ def incl(x, y):
+ tx, ty = types[x], types[y]
+ if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y])
+ if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y])
+ if tx == 1 and ty == 3: return bool(core[x] & core[y])
+ if tx == 2 and ty == 3: return not (cover[x] & ~core[y])
+ if tx == 3 and ty == 2: return cover[y] == FULL
+ if tx == 3 and ty == 3: return core[x] == core[y]
+ return False
+ left = []; adj = {}
+ for x in range(1, n):
+ if not (active[x] and args[x][0]): continue
+ rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))})
+ if rs: left.append(x); adj[x] = rs
+ mate = hopcroft_karp(left, adj)
+ links = {x: r for x, r in mate.items() if r is not None}
+ R = c_add + q - len(links)
+ require((c_add,q,len(links),R)==(91770,8120,71185,28705),'selected PR117 graph')
+ print('PR117 graph matched', c_add, q, len(links), R, flush=True)
+ linked_use = {(y, k): x for x, (y, k) in links.items()}
+
+ # ------------------------------------------------------------ root targets, read coefficients, root functionals
+ target = [None] * q
+ for j in range(v): target[j] = j
+ idx = v
+ # PR117 witness stores pair-star roots in natural excluded-point order.
+ for a, b in combinations(range(h), 2):
+ others = [i for i in range(h) if i not in (a, b)]
+ for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1
+ centre_of = {}
+ for j in range(q):
+ if kind[j]:
+ miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover')
+ centre_of[j] = miss.bit_length() - 1
+ require(idx + len(centre_of) == q, 'root order')
+ rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)]
+
+ # ------------------------------------------------------------ lifted binary frames, monotone
+ succ = defaultdict(set); droot = defaultdict(set)
+ for x in range(1, n):
+ if not active[x]: continue
+ for k, u in enumerate(uses[x]):
+ if (x, k) in linked_use: continue
+ (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1]))
+ for x, (y, k) in links.items():
+ u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1]))
+ order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True)
+ K = {}
+ for x in order_desc:
+ rows = [rootfun[j] for j in droot[x]]
+ for t in succ[x]: rows += K[t]
+ K[x] = reduce(rows)
+ def envelope(x):
+ if not args[x][0]: return [tmask[x - 1]]
+ if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1]
+ require(types[x] == 1, 'only ordinary and common-pair labels occur')
+ ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1]
+ require(len(ks) == ranks[x], 'common-pair support')
+ return [core[x] | (1 << k) for k in ks]
+ U = {}
+ for x in range(1, n):
+ if not active[x]: continue
+ if not args[x][0]: U[x] = envelope(x); continue
+ B = kernel(K[x], h)
+ require(contains(envelope(x), B), 'label outside lifted frame')
+ U[x] = B if nondeg(B) else envelope(x)
+ changed = True
+ while changed:
+ changed = False
+ for x in order_desc:
+ if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]):
+ env = envelope(x)
+ if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True
+ dimU = {x: len(reduce(B)) for x, B in U.items()}
+ print('PR117 frames lifted',sum(dimU[x]>ranks[x] for x in U),flush=True)
+
+ # ------------------------------------------------------------ explicit role compile
+ order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x))
+ holds = []; first_node = []; ops = []; edge_key = {}; role_root = {}
+ def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1
+ def serve(s, y, k):
+ u = uses[y][k]
+ if u[0] == 'gate': edge_key[(y, k)] = s
+ else: role_root[s] = u[1]
+ for x in order:
+ free = [k for k in range(len(uses[x])) if (x, k) not in linked_use]
+ if not args[x][0]:
+ for k in free:
+ s = new_role(x); ops.append(('src', s, x)); serve(s, x, k)
+ continue
+ a, b = args[x]
+ ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0))
+ kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1))
+ sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb))
+ if x in links and links[x][0] == a: sa, sb = sb, sa
+ piv, oth = sa, sb
+ ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x)
+ if x in links: serve(oth, *links[x])
+ require(free, 'every use linked at node %d' % x)
+ serve(piv, x, free[0])
+ for k in free[1:]:
+ f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k)
+ require(not edge_key and len(holds) == R, 'compile')
+ Rr = R
+
+ # R12 logical-frame nondegenerate completion and endpoint descent.
+ from r12_frame_opt import optimize as r12_optimize
+ U, dimU, frame_optimization = r12_optimize(U, order, args, succ, holds, role_root, envelope, h, globals())
+ shrunk = frame_optimization['shrunk_frames']
+
+ # ------------------------------------------------------------ B. the word computes every root value
+ rng = random.Random(20261008)
+ xs = [rng.randrange(P) for _ in range(v)]
+ val = [0] * n
+ for i in range(v): val[i + 1] = xs[i]
+ for x in order:
+ if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P
+ leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]}
+ a_ = [0] * Rr
+ for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1]
+ for o in ops:
+ if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P
+ elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P
+ require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values')
+
+ # ------------------------------------------------------------ phase one and garbage reach
+ def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else []
+ prev = {}; pred = defaultdict(list); last = {}
+ for i, o in enumerate(ops):
+ for s in touch(o):
+ if s in prev: pred[i].append(prev[s])
+ prev[s] = i; last[s] = i
+ centre_roles = [s for s, j in role_root.items() if kind[j]]
+ Anc = set(); st = [last[s] for s in centre_roles]
+ while st:
+ i = st.pop()
+ if i not in Anc: Anc.add(i); st.extend(pred[i])
+ touched = set(centre_roles)
+ for i in Anc: touched.update(touch(ops[i]))
+ require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one')
+ reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr
+ for s, j in role_root.items():
+ if kind[j]: reach_all[s] = True
+ else: reach[s].add(target[j])
+ for o in reversed(ops):
+ if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]]
+ elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]]
+
+ # ------------------------------------------------------------ deferral frames, insertion nesting
+ def F0(s): return U[first_node[s]]
+ from r12_defer_opt import repair_candidate, place as r12_place
+ cand = {}
+ for s in range(Rr):
+ if s in touched or reach_all[s]: continue
+ S_ = restrict(F0(s), [tmask[t] for t in reach[s]])
+ S_ = repair_candidate(S_, globals()) if S_ else []
+ if S_: cand[s] = S_
+ print('PR117 candidates',len(cand),flush=True)
+ placed, deferral_optimization = r12_place(cand, reach, F0, h, m, globals())
+ print('PR117 placed',len(placed),flush=True)
+ deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred)
+
+ # SCREENING ONLY: scalar/dirty replay intentionally deferred to full verification.
+ # ------------------------------------------------------------ D. exact F2 frame facts
+ root_frame = {}
+ for s, j in role_root.items():
+ root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h)
+ FULLB = [1 << i for i in range(h)]
+ chain_dims = []
+ for s in range(Rr):
+ seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]]
+ if s in root_frame: seq.append(root_frame[s])
+ seq.append(FULLB)
+ require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s)
+ require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s)
+ chain_dims.append([len(reduce(B)) for B in seq])
+ for s, X in placed.items():
+ require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s)
+ require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s)
+ byT2 = defaultdict(list)
+ for s in deferred:
+ for t in reach[s]: byT2[t].append(s)
+ for t, ss in byT2.items():
+ ss.sort(key=lambda s: (len(placed[s]), s))
+ require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t)
+
+ # ------------------------------------------------------------ E. one-child histogram
+ z = Counter()
+ for s in range(Rr):
+ ds = chain_dims[s]
+ for a, b in zip(ds[:-1], ds[1:-1]):
+ if b > a: z[b - a] += 2 * v
+ lastd = ds[-2]
+ if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform
+ z[h - lastd] += 2 * v # final growth to F
+ z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma
+ levels = defaultdict(set)
+ for s in deferred:
+ for t in reach[s]: levels[t].add(len(placed[s]))
+ for t in range(v):
+ ds = sorted(levels[t] | {0, h - 1})
+ for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts
+ z[h - 1] += 2 * N # data-wire fronts
+ z[(h - 1) ** 2] += 2 * N # data macros
+ z[1] += N # endpoint copies
+ z.pop(0, None)
+ W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L
+ require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass')
+ require(all(0 < t < m for t in z), 'children below m')
+ out = dict(frame_optimization=frame_optimization, deferral_optimization=deferral_optimization, h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_,
+ deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched),
+ deferred_roles=len(deferred),
+ deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())),
+ lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]),
+ replay=dict(screening_only=True, scratch_restored=None, y_plus_x=None),
+ child_multiplicities=dict(sorted(z.items())))
+ (HERE / 'screen-profile.json').write_text(json.dumps(out, indent=1) + '\n')
+ print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_))
+
+
+if __name__ == '__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/SOURCE.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/SOURCE.json
new file mode 100644
index 0000000000..e7f712ae00
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/SOURCE.json
@@ -0,0 +1,69 @@
+{
+ "attribution": "Avi Eisenberg / ikeboy (PR62 and PR110, Anthropic Claude assistance); Rohan Arun (PR111, Anthropic Claude assistance); Swapnil Jain (round-seven bit word); icekylinx (retained stopped-product, copied-center and finite assembly interfaces); Zhihao Chen and RaD (retained assembly). PR117 scalar DAG is separate upstream work by eumemic with Anthropic Claude assistance, retained byte for byte with its original attribution. Saturated deferred-frame integration and verification for eumemic with OpenAI Codex assistance. Shrunk-frame step by Joel Pulikkan with Anthropic Claude assistance (PR114 base). Original source notices remain authoritative.",
+ "package_files": {
+ "bit-profile.json": "7293f330518b78650bd86d76b93681e43f3a55541cdb8110993714148a4b4a6a",
+ "bit_round7.py": "35d261a9248c2e06f9179e3c47e554a96b8fe763a9a3de2731256b8c0fbc74b0",
+ "certificate.json": "e5965daf4346b6a695384f8eda957d954529add921cb384f969856cdef81f845",
+ "certificate.py": "fa1846facc5eeb33017afd96e9a7b440d3a3d7ff813f76312f1ea865bf2277ca",
+ "complex-profile.json": "7e7c0c28c0983d117b3006b96719a6102ce31ec0273160dd7fc8b9a0fef0dbeb",
+ "complex_deferred.py": "fa1125e85ec73b185dc9eee117f62d10356bb6422c07ec793a7f77296c87707e",
+ "controls/pr114-complex-profile.json": "a54d2a6023ff73f7476057b5f6a4ff02e65ded840b7254d906aadde2dd01940d",
+ "inputs/complex-dag.json.gz": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b",
+ "inputs/deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c",
+ "inputs/witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588",
+ "producer.py": "017e50713943e6c2a98d1c23ec93e7da9580896de1b6bde24563b4b6961c74c0",
+ "reflection-audit.json": "7caee26f3747b88b41137527175d41b08c4849a7302368bd50b1cfae74779c5a",
+ "reflection_audit.py": "6761fb01f93ef89f2455388b2f5a71f19c0bbd870e6aaeba457ede0a949a163b",
+ "replayed_producer.py": "99c1e3694ae06a7ce7a370b04ecb45ea3fcfe69a6e6e7f4c4606e0a6c74c3184",
+ "test_controls.py": "87dbc9945a5057cf1b7b6ba776590f5c20548f5b2b63893b34bd6280f534f036",
+ "verify.py": "b49c45f0fa06ab7de987110f3756c445220e1b2e08127cfa891eca7330e6d8da"
+ },
+ "provenance": {
+ "base": "https://github.com/CrocSwap/integer-mult-bounds/pull/110",
+ "cyclic_strips": "https://github.com/CrocSwap/integer-mult-bounds/pull/111",
+ "round7_commit": "741e7aa078392553815df7926ee17ac5e25a8c38",
+ "round7_repository": "https://github.com/Swapnil-jain/integer-mult-kappa",
+ "round7_sha256": {
+ "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c",
+ "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588"
+ },
+ "saturated_base": {
+ "commit": "7dfa16edfa5d6452f2b10dadcbef20d26222827e",
+ "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/114"
+ },
+ "scalar_dag": {
+ "commit": "cbb05ce504d571546d9b7794c186a613c659c3bf",
+ "file": "inputs/complex-dag.json.gz",
+ "pull_request": "https://github.com/CrocSwap/integer-mult-bounds/pull/117",
+ "sha256": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b"
+ }
+ },
+ "reflection": {
+ "receipt": "reflection-audit.json",
+ "script": "reflection_audit.py"
+ },
+ "repository_files": {
+ "certificates/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf",
+ "scripts/audit_short_guards.py": "c2c929c956e617bee739963b517b9069e0d067cfebc6820f401a4e90a1769eb1",
+ "scripts/certify.py": "2348d95008276c5d5764f7e028c3918e484582cd589bd4d9b82919161745e53e",
+ "scripts/compact_control_layer.py": "e814c9f8d84f2e5d3aa2e06c36697f27f110218addc40ff8df2801fde861ff9f",
+ "scripts/complex_circuit.py": "d623617f7c5cb3189580883a8ab30c0bd3832688ae3f1f0c1f881bbbbff8e0c1",
+ "scripts/complex_network.py": "0da395e67ac04fa213494e71012c1b19b544596d34cdce5a3b172b1fb6af5f1b",
+ "scripts/copied_centers/__init__.py": "13db4f09038a2ff5335cbd4dbd93274b0fb16b3c7b51e4de67cbb2801a3f78e1",
+ "scripts/copied_centers/corners.py": "9eecdc39c67cc18c806a33f0be03986c28591d322881fd60c11f52c625c8067b",
+ "scripts/copied_centers/physical.py": "837345d1f8753eab0e70f105b1d1bb0db965b993da037b1825ddef3672609d7d",
+ "scripts/copied_centers_network.py": "409ebfbd8a41c4c4d089aa0949fcf5a949415dc26f57440ffd48b7bd8881e6a9",
+ "scripts/exclusion_circuit.py": "b253f9d7318becda1c1f3b24e2287ed44a9c27fcea00cf9d531afb950d0457a0",
+ "scripts/fast_gaussian.py": "11430c2df0783b933dc91080595bb7514bb052b8c7b12107e27a1ef701e31e43",
+ "scripts/paired_exclusion_circuit.py": "8f05f04cf06217befd6d0ee0f2d7d0c5c5eb32cfab8c9a8ca7917fd6d620b7d2",
+ "scripts/paired_network.py": "991223dc3c1374284c361ed017e42bf732dd971fa0bea2be2282cfb18257b3f7",
+ "scripts/partial_swap_network.py": "acdd81b4dea2815f8838a0c3ea8ac4968f2bc13fd7c99173473d865779096782",
+ "scripts/prepare_layers.py": "a6e2adc612f264b1c0e51d18ce6315de9ae5e2ae2420aa22e99a22d8bf304947",
+ "scripts/search_network.py": "3a4faa5037d9b8e7ca5828afac193a96b6966a8b114f14937921795b24ec4f6a",
+ "scripts/shared_point_circuit.py": "c9bb7a5df92d260a4e3ad532b53e26936730d7c93f7facfb0784957c1e81c8ba",
+ "scripts/shared_point_network.py": "a85e7f0d8c42d6a27e3846308571ca324a1824ac5c2d59e4daa5c7673c33c697",
+ "scripts/structured_bulk_assembly.py": "e99467e14211fba699878ed036e1e2362eb8e395dc22f9ecdcecc7fbf2cc736d"
+ },
+ "schema": 1,
+ "scope": "Frozen finite producer, profiles, exact assembly and reflection audit; inherited all-size transfer remains conditional."
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit-profile.json
new file mode 100644
index 0000000000..36105e819a
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit-profile.json
@@ -0,0 +1,69 @@
+{
+ "h": 23,
+ "v": 1771,
+ "R": 28866,
+ "m": 529,
+ "N": 3136441,
+ "W": 108516254,
+ "L": 1792252,
+ "total_rank": 57403754177,
+ "deficit": 1344189,
+ "maxchild": 528,
+ "deferred_slots": 11565,
+ "source": {
+ "repository": "https://github.com/Swapnil-jain/integer-mult-kappa",
+ "commit": "741e7aa078392553815df7926ee17ac5e25a8c38",
+ "sha256": {
+ "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588",
+ "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c"
+ }
+ },
+ "child_multiplicities": {
+ "1": 239511811,
+ "2": 238288050,
+ "3": 53377940,
+ "4": 46970462,
+ "5": 23632224,
+ "6": 7409864,
+ "7": 4105178,
+ "8": 5755750,
+ "9": 2082696,
+ "10": 878416,
+ "11": 1388464,
+ "12": 1080310,
+ "13": 945714,
+ "14": 226688,
+ "15": 2451064,
+ "16": 1508892,
+ "17": 4771074,
+ "18": 2149994,
+ "19": 7367360,
+ "20": 8182020,
+ "21": 1466388,
+ "22": 88550,
+ "484": 6272882,
+ "506": 61280142,
+ "507": 545468,
+ "508": 173558,
+ "509": 293986,
+ "510": 580888,
+ "511": 14168,
+ "512": 322322,
+ "513": 17710,
+ "514": 1129898,
+ "515": 127512,
+ "516": 410872,
+ "517": 99176,
+ "518": 1186570,
+ "519": 340032,
+ "520": 322322,
+ "521": 106260,
+ "522": 1583274,
+ "523": 626934,
+ "524": 2854852,
+ "525": 13711082,
+ "526": 4629394,
+ "527": 5653032,
+ "528": 6233920
+ }
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit_round7.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit_round7.py
new file mode 100644
index 0000000000..3c5df409a6
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/bit_round7.py
@@ -0,0 +1,129 @@
+#!/usr/bin/env python3
+"""One-child bit profile of Swapnil Jain's round-seven deferred word (h=23), under PR104's opposite-bank rule.
+
+Reads the two frozen round-seven data files (vendored in inputs/; pinned by SHA-256 below) from a directory given on
+the command line, e.g. a checkout of https://github.com/Swapnil-jain/integer-mult-kappa at
+741e7aa078392553815df7926ee17ac5e25a8c38 (certificates/round7/), or PR97's imported copy
+(research/deferred-signed/swapnil-round7/certificates/round7/). The frame dimensions are the ones recorded in
+the data file; Swapnil's check_frames.py re-derives each of them exactly and PR97 replays the word.
+
+Every projector residual of rank r is one child of width r (PR104, notes/stopped-product-factorization.tex):
+ each slot: its chain steps from the deferral frame sigma_u to F, and one exterior child m - (h - dim sigma_u);
+ each retained centre: one copied transform of width h-1;
+ each target y_T: its chain 0 -> deferred readout levels -> t_T^perp; each data wire X_S: its chain of V frames;
+ each data pair: one data residual of width (h-1)^2 and one endpoint copy.
+Usage: python3 research/deferred-stopped/bit_round7.py DIR (writes bit-profile.json next to this file)
+Prepared by Avi Eisenberg (ikeboy) with Anthropic Claude assistance. Apache-2.0.
+"""
+import gzip
+import hashlib
+import json
+import sys
+from collections import Counter, defaultdict
+from itertools import combinations
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+PINS = {'witness_23.json.gz': 'b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588',
+ 'deferred_23.json.gz': '8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c'}
+
+
+def require(ok, msg):
+ if not ok:
+ raise SystemExit('FAIL: ' + msg)
+
+
+def main(directory):
+ data = {}
+ for name, digest in PINS.items():
+ raw = (Path(directory) / name).read_bytes()
+ require(hashlib.sha256(raw).hexdigest() == digest, 'pinned hash of ' + name)
+ data[name] = json.loads(gzip.decompress(raw))
+ W, D = data['witness_23.json.gz'], data['deferred_23.json.gz']
+ h = D['h']; R = D['R']; trip = list(combinations(range(h), 3)); v = len(trip); m = h * h; N = v * v
+ tid = {T: i for i, T in enumerate(trip)}
+ args = {int(n): (tuple(a) if a else None) for n, a in W['args'].items()}
+ late = {int(n): (list(e), list(l)) for n, (e, l) in W['late'].items()}
+ ops = [tuple(o[:2]) + (tuple(o[2]),) if o[0] == 'fan' else tuple(o) for o in D['ops']]
+ hold, start = D['hold'], D['start']
+ out = {s: (c, tuple(T)) for s, c, T in D['out']}; ret = {s: c for s, c in D['ret']}
+ sigma = dict(zip(D['readout_order'], D['sigma'])); sel = set(D['readout_order'])
+ f = [0] * R
+ for s, B in sigma.items(): f[s] = len(B)
+ vstart = dict(zip(D['vleaf_slots'], D['vleaf_start']))
+ node_dims = {n: d for n, d in D['node_dims']}
+ late_dims = {(n, tuple(lt)): d for n, lt, d in D['late_dims']}
+ pivslot = {o[3]: o[1] for o in ops if o[0] == 'add'}
+
+ def start_key(s):
+ n0 = hold[s][0]
+ if args[n0] is None: return ('v', s)
+ st = start[s]; k = st[2] if len(st) > 2 else None; dec = late.get(n0)
+ if dec is None or k in dec[0]: return ('n', n0)
+ lt = dec[1]; return ('c', n0, tuple(lt[lt.index(k):]))
+
+ def chain(s):
+ ch = [('sigma', s) if s in sel else ('0',), start_key(s)]
+ for idx, n in enumerate(hold[s]):
+ if idx > 0: ch.append(('n', n))
+ if args[n] is not None and pivslot.get(n) == s and n in late:
+ lt = late[n][1]
+ for i in range(len(lt) - 1): ch.append(('c', n, tuple(lt[i:])))
+ if s in out: ch.append(('out',))
+ if s in ret: ch.append(('ret',))
+ ch.append(('F',)); return ch
+
+ def dim(key):
+ k = key[0]
+ if k == '0': return 0
+ if k == 'F': return h
+ if k in ('out', 'ret'): return h - 1
+ if k == 'n': return node_dims[key[1]]
+ if k == 'c': return late_dims[key[1], key[2]]
+ if k == 'sigma': return f[key[1]]
+ if k == 'v': return len(vstart[key[1]])
+ raise KeyError(key)
+
+ # garbage supports (transpose sweep) for the deferred levels on each target
+ cov = [set() for _ in range(R)]
+ for s, (c, T) in out.items(): cov[s].add(tid[T])
+ for s, c in ret.items(): cov[s].update(t for t, T in enumerate(trip) if c in T)
+ for o in reversed(ops):
+ if o[0] == 'add': cov[o[2]] |= cov[o[1]]
+ elif o[0] == 'fan':
+ for g in o[2]: cov[o[1]] |= cov[g]
+ levels = defaultdict(set)
+ for s in sel:
+ for t in cov[s]: levels[t].add(f[s])
+
+ z = Counter()
+ for s in range(R):
+ ds = [dim(k) for k in chain(s)]
+ require(all(b >= a for a, b in zip(ds, ds[1:])) and ds[-1] == h, 'monotone chain %d' % s)
+ for a, b in zip(ds, ds[1:]):
+ if b > a: z[b - a] += 2 * v
+ z[m - (h - f[s])] += 2 * v
+ z[h - 1] += 2 * v * h
+ for t in range(v):
+ ls = sorted(levels[t] | {0, h - 1})
+ for a, b in zip(ls, ls[1:]): z[b - a] += 2 * v
+ for n, us in D['xs_order']:
+ ds = [1] + [len(vstart[s]) for s in us] + [h]
+ ds = [d for i, d in enumerate(ds) if i == 0 or d != ds[i - 1]]
+ require(all(b > a for a, b in zip(ds, ds[1:])), 'data-wire chain')
+ for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v
+ z[(h - 1) ** 2] += 2 * N
+ z[1] += N
+ Wb = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = Wb * m - N + L
+ require(sum(t * c for t, c in z.items()) == s_, 'bit rank mass')
+ require(all(0 < t < m for t in z), 'children below m')
+ prof = dict(h=h, v=v, R=R, m=m, N=N, W=Wb, L=L, total_rank=s_, deficit=N - L, maxchild=max(z),
+ deferred_slots=len(sel), source=dict(repository='https://github.com/Swapnil-jain/integer-mult-kappa',
+ commit='741e7aa078392553815df7926ee17ac5e25a8c38', sha256=PINS),
+ child_multiplicities=dict(sorted(z.items())))
+ (HERE / 'bit-profile.json').write_text(json.dumps(prof, indent=1) + '\n')
+ print('PASS bit: R=%d, deferred slots %d, maxchild %d, rank mass %d' % (R, len(sel), max(z), s_))
+
+
+if __name__ == '__main__':
+ main(sys.argv[1] if len(sys.argv) > 1 else '.')
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.json
new file mode 100644
index 0000000000..6e0a5f02d1
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.json
@@ -0,0 +1,313 @@
+{
+ "actual_bit_saving": "1240189553/10000000000000",
+ "assembly": {
+ "absorption_gap": "1423799823581924404745614798375593/2500553080248572986091654124313081000000000000000",
+ "margins": {
+ "Gaussian_arithmetic": "331855646931470668996733908345875686919/2000442464198858388873323299450464800000000",
+ "bulk_exposure": "55308025686919/500000000000000000",
+ "compact_phase_layer": "276540120138391202270175686919/2500553080248572986091654124313081",
+ "coordinate_movement": "55308025686919/500000000000000000",
+ "dimension": "2499999975000000000000000000000000/2500553080248572986091654124313081",
+ "original_prefix": "27656512566919368800003660346024313081/250055308024857298609165412431308100000000",
+ "scalar_work": "442481698305308624750313358810675686919/2000442464198858388873323299450464800000000"
+ },
+ "minimum_margin": "276540120138391202270175686919/2500553080248572986091654124313081",
+ "parameters": {
+ "C0": 3646615615709474302231996852324339320426087077316912790823030645920872744002225026973564928,
+ "C1": 1,
+ "a_bit": "55308025686919/500000000000000000",
+ "a_complex": "55308081/500000000000",
+ "alpha_squared_power": "414822684355688646962150000000/2500553080248572986091654124313081",
+ "beta": "1/1000000",
+ "c": "276540125669193660346024313081/2500000000000000000000000000000000",
+ "delta": "1/800000000",
+ "epsilon": "2499999975000000000000000000000000/2500553080248572986091654124313081",
+ "eta": "1/100000000",
+ "kappa": "110591581647/1000000000000000",
+ "lambda_": "49994469197486616125686919/50000000000000000000000000",
+ "lambda_prime": "24997234598770962075686919/25000000000000000000000000",
+ "q": "2765401229037924313081/25000000000000000000000000",
+ "sigma": "499944691919/500000000000",
+ "tau": "499944691974313081/500000000000000000"
+ },
+ "recurrence": {
+ "internal": "499944691974313081/500000000000000000",
+ "leaf": "499944691974308081/500000000000000000",
+ "reservations": "2499723459874330806339653975686919/2500000000000000000000000000000000"
+ },
+ "strict_constraints": {
+ "Gaussian_arithmetic_above_kappa": "138279438527370933799323622918090223447125593/2500553080248572986091654124313081000000000000000",
+ "K_dominates_log": "27654012290379240365408770962075686919/250055308024857298609165412431308100000000",
+ "K_geometry": "27656512566919368800003660346024313081/250055308024857298609165412431308100000000",
+ "alpha_below_one": "2500138257564217297444691974313081/2500553080248572986091654124313081",
+ "alpha_below_one_fourth": "2498893789511150231503805524313081/10002212320994291944366616497252324",
+ "alpha_positive": "414822684355688646962150000000/2500553080248572986091654124313081",
+ "artificial_boundary": "14003650357141687868693766988962529075686919/2000442464198858388873323299450464800000000",
+ "beta_below_one": "999999/1000000",
+ "beta_positive": "1/1000000",
+ "bit_positive": "55308025686919/500000000000000000",
+ "bulk_exposure_above_kappa": "12234863419/500000000000000000",
+ "c_below_one": "2499723459874330806339653975686919/2500000000000000000000000000000000",
+ "c_positive": "276540125669193660346024313081/2500000000000000000000000000000000",
+ "cell_above_band": "2499861692435782702555308025686919/5001106160497145972183308248626162",
+ "compact_leaf": "55558025686919/25000000000000000000000000",
+ "compact_phase_layer_above_kappa": "1423799823581924404745614798375593/2500553080248572986091654124313081000000000000000",
+ "compact_reservations": "2765401229037924313081/2500000000000000000000000000000000",
+ "complex_above_bit": "55313081/500000000000000000",
+ "complex_below_one_over32": "15569691919/500000000000",
+ "coordinate_movement_above_kappa": "12234863419/500000000000000000",
+ "delta_below_one_eighth": "99999999/800000000",
+ "delta_positive": "1/800000000",
+ "dimension_above_kappa": "2499723434879863032597553406237485745614798375593/2500553080248572986091654124313081000000000000000",
+ "epsilon_below_one": "553105248572986091654124313081/2500553080248572986091654124313081",
+ "epsilon_positive": "2499999975000000000000000000000000/2500553080248572986091654124313081",
+ "gamma_sublinear": "138282564217297444691974313081/2500553080248572986091654124313081",
+ "guard_width": "553105248572986091654124313081/2500553080248572986091654124313081",
+ "lambda_above_internal": "55308025686919/50000000000000000000000000",
+ "lambda_above_sigma": "5586616125686919/50000000000000000000000000",
+ "lambda_above_tau": "55308025686919/50000000000000000000000000",
+ "lambda_prime_above_lambda": "55308025686919/50000000000000000000000000",
+ "lambda_prime_below_one": "2765401229037924313081/25000000000000000000000000",
+ "leaf_saving_above_bit": "1/100000000000000",
+ "literal_scalar_guard": "14065616197378741718443193606139245678291196",
+ "original_prefix_above_kappa": "25005532226285553442840945988745608375593/2500553080248572986091654124313081000000000000000",
+ "phase_boundary": "331855646931470668996733908345875686919/2000442464198858388873323299450464800000000",
+ "phase_local": "442481698305308624750313358810675686919/2000442464198858388873323299450464800000000",
+ "prime_interval_packing": "553105248572986091654124313081/2500553080248572986091654124313081",
+ "q_below_internal": "55308025686919/25000000000000000000000000",
+ "q_below_leaf": "55558025686919/25000000000000000000000000",
+ "q_below_reservations": "2765401229037924313081/2500000000000000000000000000000000",
+ "q_positive": "2765401229037924313081/25000000000000000000000000",
+ "record_suffix": "553105248572986091654124313081/2500553080248572986091654124313081",
+ "row_product_gap": "6389/25",
+ "scalar_work_above_kappa": "276562002744668378491297935999090223447125593/2500553080248572986091654124313081000000000000000",
+ "short_record_fallback": "1249861686846006107497739648634368046048805957712561/1250276540124286493045827062156540500000000000000000",
+ "small_field_exposure": "276565128434594889383948626162/2500553080248572986091654124313081"
+ }
+ },
+ "bit_moment_gap": "210811394225115117568018038513239592855337768061996351784199300828041381607148420475711921673436778332750996651783152394205578153858435663243959795913385215868392831844509655226993164072062830500832781615792327068936897853818968534771730481866850519439187068953062899333771640996075361901014500735179763112430083120460814689994116646689670445286414265265018468311435502209195246240538069975559360544007937885404793780372701951022292660282948582656517071290400479729799954952580125532795274568021525151839594883237275569314958070368193662075730567130277424969924134425921633872848924585639423998410253779062359718371205767101510073996880454144801457072151080008705648366603197414406872289670642046369219405455128737300640897667220951127018547660455087533581513233999285275099394371781290865408274484542745086391849285198194905751058992419590161634431610100995441112613134240446609058758039909343152776920263419910572835208525277494067408376961456317/225678505065634612156474913616400633538202019254665477026878220214422133931127460164253533068001699469116755578965090566731480236912032281717920888140691998261537790258547549397061712443744511202265657747547567084090291301783866427704803156891369853685579999500594559805069402727752752227038426964007028952158078563045054314475625278140097385695241851533235641996467089273692960018822280793234080014352234618229252999217015923728814468917104222554059646947960375336061268431587018084270516494408656203498548153054913267707164839939006583338918817922618882667407408888179421052689449193499742148706302504238261936554897181289081072466758282367100305194479622149878636307463869297507337915811001244472279386614413535081936912313821531543735588465392499062010570720287729070905437080967709221039366272598541269000920375996285867953823816142239661027100714288630069735295241672325865922423925213948613346461034734632365263739073012128769510020000000000000000000000",
+ "bit_parameter": "55308025686919/500000000000000000",
+ "bit_profile": {
+ "L": 1792252,
+ "N": 3136441,
+ "R": 28866,
+ "W": 108516254,
+ "child_multiplicities": {
+ "1": 239511811,
+ "10": 878416,
+ "11": 1388464,
+ "12": 1080310,
+ "13": 945714,
+ "14": 226688,
+ "15": 2451064,
+ "16": 1508892,
+ "17": 4771074,
+ "18": 2149994,
+ "19": 7367360,
+ "2": 238288050,
+ "20": 8182020,
+ "21": 1466388,
+ "22": 88550,
+ "3": 53377940,
+ "4": 46970462,
+ "484": 6272882,
+ "5": 23632224,
+ "506": 61280142,
+ "507": 545468,
+ "508": 173558,
+ "509": 293986,
+ "510": 580888,
+ "511": 14168,
+ "512": 322322,
+ "513": 17710,
+ "514": 1129898,
+ "515": 127512,
+ "516": 410872,
+ "517": 99176,
+ "518": 1186570,
+ "519": 340032,
+ "520": 322322,
+ "521": 106260,
+ "522": 1583274,
+ "523": 626934,
+ "524": 2854852,
+ "525": 13711082,
+ "526": 4629394,
+ "527": 5653032,
+ "528": 6233920,
+ "6": 7409864,
+ "7": 4105178,
+ "8": 5755750,
+ "9": 2082696
+ },
+ "deferred_slots": 11565,
+ "deficit": 1344189,
+ "h": 23,
+ "m": 529,
+ "maxchild": 528,
+ "source": {
+ "commit": "741e7aa078392553815df7926ee17ac5e25a8c38",
+ "repository": "https://github.com/Swapnil-jain/integer-mult-kappa",
+ "sha256": {
+ "deferred_23.json.gz": "8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c",
+ "witness_23.json.gz": "b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588"
+ }
+ },
+ "total_rank": 57403754177,
+ "v": 1771
+ },
+ "coarse_bit_saving": "620523/5000000000",
+ "complex_moment_gap": "1120907676991709375587467571083583613675514323107449210881795156623730476679332908369675633828609828547699408013724966704466999362228476322550536073425477865821903781068608934724652434185915105821476280707835554190305969731534431792034136981242275885510306743073208513584546756206129639721309235360276551243600523744884826937176020214328142317214679396773991230268354778844685206549974861397955820231211808000505289181911024758652777589422017126655483564105414184271982303920191622773958369915731889103228404461797825046990910884342895126883154008667367948162387895233712466670165382398728821416470882760327554020327490396551350392371803758571065760737832618462497790815846731507580694898835979742744618260624366037437075808017877875989728828939538013318978980990915921668227049349635290036175560530633279260473351540544135441376709651695874126570388867012660974313806428810883182335167580007/5729785626482475083453880928912868090199891077894328437390154678085907947787777170551065795053175425295499005277150151786860288788040509249164976675728598633831731259082317118043077983924941216272575857128488188317581360310229902663321454526224581674689575437986461381738691709567461275868099475629801004180206074232907215575028613840139675146224247781180470831210120187095639606203370194019694000363186599456926657406240962080920816408153979237758439565211054622374231622886675112863813346734480202775285744822553219180447792108305361254841580710053360069403264180909982005303238389319538012371475060400462749261716035566070509613844095475111408101447019396632121482203883977202704954856015697825135147677429303783554053341478566944596465856275121302108324962996326877399164307498504419646510163732515012385754160928876728348713015505212385798910883039803748837277174939722238502400000000000000000000000",
+ "complex_profile": {
+ "L": 2234496,
+ "N": 4096576,
+ "R": 28705,
+ "W": 124390992,
+ "additions": 91770,
+ "child_multiplicities": {
+ "1": 435601232,
+ "10": 7375456,
+ "11": 7019232,
+ "12": 31788944,
+ "13": 12536656,
+ "14": 1497760,
+ "15": 3440800,
+ "16": 854128,
+ "17": 506000,
+ "18": 2906464,
+ "19": 2092816,
+ "2": 267192288,
+ "20": 817696,
+ "21": 1230592,
+ "22": 64768,
+ "23": 8363168,
+ "3": 29238704,
+ "4": 61145040,
+ "5": 26425344,
+ "529": 8193152,
+ "552": 97147952,
+ "554": 3493424,
+ "556": 1445136,
+ "558": 2319504,
+ "560": 582912,
+ "562": 101200,
+ "564": 1307504,
+ "566": 975568,
+ "568": 1364176,
+ "569": 4048,
+ "570": 3643200,
+ "571": 2444992,
+ "572": 837936,
+ "573": 44528,
+ "574": 485760,
+ "6": 15734576,
+ "7": 11876832,
+ "8": 22077792,
+ "9": 4562096
+ },
+ "deferred_dims": {
+ "10": 25,
+ "12": 323,
+ "14": 241,
+ "16": 337,
+ "17": 1,
+ "18": 900,
+ "19": 604,
+ "2": 863,
+ "20": 207,
+ "21": 11,
+ "22": 120,
+ "4": 357,
+ "6": 573,
+ "8": 144
+ },
+ "deferred_roles": 4706,
+ "deficit": 1862080,
+ "h": 24,
+ "lifted_additions": 24792,
+ "links": 71185,
+ "m": 576,
+ "maxchild": 574,
+ "phase_one_ops": 18844,
+ "phase_one_roles": 13555,
+ "replay": {
+ "field": "Z/(2^61-1)",
+ "scratch_restored": true,
+ "seeds": [
+ 1,
+ 2
+ ],
+ "y_plus_x": true
+ },
+ "roots": 8120,
+ "total_rank": 71647349312,
+ "v": 2024
+ },
+ "complex_saving": "55308081/500000000000",
+ "finite_bridge": {
+ "bit_coarse": {
+ "W": 108516254,
+ "halving_degree": 367,
+ "m": 529,
+ "maxchild": 528,
+ "wire_bits": 27
+ },
+ "complex": {
+ "W": 124390992,
+ "halving_degree": 200,
+ "m": 576,
+ "maxchild": 574,
+ "s": 71647349312,
+ "scalar_group_upper": 60347419084480,
+ "scalar_terms": [
+ {
+ "R": 28705,
+ "c": 91770,
+ "description": "Expanded deferred readouts and forward/inverse/reflected words",
+ "h": 24,
+ "invocations": 2024,
+ "local_group_upper": 14907958248,
+ "q": 8120,
+ "v": 2024
+ },
+ {
+ "R": 28705,
+ "c": 91770,
+ "description": "Expanded deferred readouts and forward/inverse/reflected words",
+ "h": 24,
+ "invocations": 2024,
+ "local_group_upper": 14907958248,
+ "q": 8120,
+ "v": 2024
+ }
+ ],
+ "wire_bits": 27
+ },
+ "ordinary_leaf_row_degree": 252,
+ "rows": {
+ "coefficient": 15561,
+ "contract": "W_complex^D_complex * W_coarse^D_coarse * W_old^D_old; prefix and padding; sequential reuse",
+ "degree": 32000,
+ "degree_gap": "6389/25",
+ "suffix_slope": 128000
+ },
+ "semantic": {
+ "B": 14065616197380609244023681038811612751070848,
+ "C0": 3646615615709474302231996852324339320426087077316912790823030645920872744002225026973564928,
+ "C1": 1,
+ "E": 14065616197380609244023681038811541103721536,
+ "exact_grid": "2^(-P)*21^(-K), K=G*(D_complex+1); completed children preserve incoming odd denominator; no child rounding",
+ "fixed_odd_divisor": 21,
+ "induction_gap": 42196848592141827732071043116434838253212544,
+ "literal_charge": 1867525580487432672295425430340,
+ "strict_literal_gap": 14065616197378741718443193606139245678291196
+ }
+ },
+ "kappa": "110591581647/1000000000000000",
+ "next_grid_rejections": {
+ "bit": "1e-10",
+ "complex": "1e-12",
+ "kappa": "1e-15"
+ },
+ "status": "Finite conditional cyclic/deferred witness"
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.py
new file mode 100644
index 0000000000..5e00159bfe
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/certificate.py
@@ -0,0 +1,114 @@
+#!/usr/bin/env python3
+"""Exact finite assembly for cyclic strips with deferred readouts.
+
+Built on Avi Eisenberg's PR110 (Anthropic Claude assistance), icekylinx's
+PR104 stopped-product and copied-center interfaces, and Zhihao Chen's
+assembly of the RaD interfaces. Integration for eumemic with OpenAI Codex
+assistance. Apache-2.0. General transfer hypotheses remain inherited.
+"""
+import argparse
+import json
+import sys
+from fractions import Fraction as Q
+from pathlib import Path
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(ROOT / 'scripts'))
+from partial_swap_network import moment
+from copied_centers_network import finite_bridge as copied_bridge
+from structured_bulk_assembly import assembly, js
+ATOM = Q(1, 1000)
+OLD = Q(384599, 10**10)
+BETA = Q(1, 10**6)
+COARSE = Q(620523, 5000000000)
+COMPLEX = Q(110616162, 10**12)
+KGRID = 10**15
+
+def profile(name):
+ p = json.loads((HERE / name).read_text())
+ p['child_multiplicities'] = {int(t): c for t, c in p['child_multiplicities'].items()}
+ z = p['child_multiplicities']
+ assert all(0 < t < p['m'] and c > 0 for t,c in z.items())
+ assert sum(t*c for t,c in z.items()) == p['total_rank'] == p['W']*p['m']-p['N']+p['L']
+ assert max(z) == p['maxchild']
+ return p
+
+def contracts(p, a):
+ try: moment(p['m'],p['W'],p['child_multiplicities'],a,True)
+ except ValueError: return False
+ return True
+
+def exact(bit=None, phase=None):
+ bit = profile('bit-profile.json') if bit is None else bit
+ phase = profile('complex-profile.json') if phase is None else phase
+ assert (bit['h'], phase['h']) == (23,24)
+ bm = moment(bit['m'],bit['W'],bit['child_multiplicities'],COARSE,True)
+ cm = moment(phase['m'],phase['W'],phase['child_multiplicities'],COMPLEX,True)
+ assert not contracts(bit,COARSE+Q(1,10**10))
+ assert not contracts(phase,COMPLEX+Q(1,10**12))
+ ab = (1-ATOM)*COARSE+ATOM*OLD
+ assert 0 < OLD < COARSE < ATOM and ab < ATOM
+ a = min(ab,(1-BETA)*COMPLEX-Q(1,10**14))
+ row = dict(h=phase['h'],v=phase['v'],c=phase['additions'],central_disjoint=24)
+ bridge = copied_bridge(bit,phase,[row,row])
+ # Logical readouts are expanded into same-frame shears with |coefficient|<=1.
+ # Exact numerators over42 are split into signed42 chunks and a remainder.
+ # The independent audit counts every chunk and checks this guard covers it.
+ # Each row has <=c+R mixer operations and <=R leaf copies. There are
+ # <=R+q readouts, each containing <=h center coefficients and <=v direct
+ # coefficients; <=4*v*(h+1) scalar groups suffice per readout. A factor
+ # eight covers forward/inverse words, both reflected words, and copies.
+ h,v,R,q,c = (phase[k] for k in ('h','v','R','roots','additions'))
+ local = 8*(c+2*R+(R+q)*v*(h+1)+h*h+h+1)
+ G = phase['N'] + 2*v*local
+ m,W,s = (phase[k] for k in ('m','W','total_rank'))
+ E=64*(W+m+G+1)**3
+ charge=2*G*W*W+8*s+4*W+4+32*m
+ B=s+E; C0=32*m*B*B
+ assert charge= s+E and 2*B+181:
+ mid=(lo+hi)//2
+ if accepts(mid): lo=mid
+ else: hi=mid
+ k=Q(lo,KGRID)
+ assembled=assembly(a,COMPLEX,bridge,k,beta=BETA)
+ assert len(assembled['strict_constraints'])==47 and len(assembled['margins'])==7
+ assert not accepts(lo+1)
+ return dict(status='Finite conditional cyclic/deferred witness',kappa=k,
+ complex_saving=COMPLEX,coarse_bit_saving=COARSE,actual_bit_saving=ab,
+ bit_parameter=a,complex_profile=phase,bit_profile=bit,
+ bit_moment_gap=bm['strict_gap'],complex_moment_gap=cm['strict_gap'],
+ finite_bridge=bridge,assembly=assembled,
+ next_grid_rejections=dict(bit='1e-10',complex='1e-12',kappa='1e-15'))
+
+def main():
+ parser=argparse.ArgumentParser();parser.add_argument('--write',action='store_true');args=parser.parse_args()
+ assert not sys.flags.optimize
+ result=js(exact()); path=HERE/'certificate.json'
+ if args.write:path.write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+ else:assert result==json.loads(path.read_text()),'Frozen exact certificate mismatch'
+ print('PASS conditional kappa = %s = %.12e; 47 constraints, 7 margins; expanded scalar charge' % (result['kappa'],float(Q(result['kappa']))))
+if __name__=='__main__':main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex-profile.json
new file mode 100644
index 0000000000..1b07c25523
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex-profile.json
@@ -0,0 +1,85 @@
+{
+ "h": 24,
+ "v": 2024,
+ "additions": 91770,
+ "roots": 8120,
+ "links": 71185,
+ "R": 28705,
+ "m": 576,
+ "N": 4096576,
+ "W": 124390992,
+ "L": 2234496,
+ "total_rank": 71647349312,
+ "deficit": 1862080,
+ "maxchild": 574,
+ "phase_one_ops": 18844,
+ "phase_one_roles": 13555,
+ "deferred_roles": 4706,
+ "deferred_dims": {
+ "2": 863,
+ "4": 357,
+ "6": 573,
+ "8": 144,
+ "10": 25,
+ "12": 323,
+ "14": 241,
+ "16": 337,
+ "17": 1,
+ "18": 900,
+ "19": 604,
+ "20": 207,
+ "21": 11,
+ "22": 120
+ },
+ "lifted_additions": 24792,
+ "replay": {
+ "seeds": [
+ 1,
+ 2
+ ],
+ "scratch_restored": true,
+ "y_plus_x": true,
+ "field": "Z/(2^61-1)"
+ },
+ "child_multiplicities": {
+ "1": 435601232,
+ "2": 267192288,
+ "3": 29238704,
+ "4": 61145040,
+ "5": 26425344,
+ "6": 15734576,
+ "7": 11876832,
+ "8": 22077792,
+ "9": 4562096,
+ "10": 7375456,
+ "11": 7019232,
+ "12": 31788944,
+ "13": 12536656,
+ "14": 1497760,
+ "15": 3440800,
+ "16": 854128,
+ "17": 506000,
+ "18": 2906464,
+ "19": 2092816,
+ "20": 817696,
+ "21": 1230592,
+ "22": 64768,
+ "23": 8363168,
+ "529": 8193152,
+ "552": 97147952,
+ "554": 3493424,
+ "556": 1445136,
+ "558": 2319504,
+ "560": 582912,
+ "562": 101200,
+ "564": 1307504,
+ "566": 975568,
+ "568": 1364176,
+ "569": 4048,
+ "570": 3643200,
+ "571": 2444992,
+ "572": 837936,
+ "573": 44528,
+ "574": 485760
+ }
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex_deferred.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex_deferred.py
new file mode 100644
index 0000000000..d2190bc2b7
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/complex_deferred.py
@@ -0,0 +1,606 @@
+#!/usr/bin/env python3
+"""Shrunk lifted frames and saturated deferred readouts on the PR117 complex DAG.
+
+After the role compile, a forward pass shrinks a lifted frame to the minimal
+nondegenerate span of its label and predecessor frames when that merges
+increments of the role chains holding it (16,031 frames). Section D rechecks
+every chain. The shrink step was prepared by Joel Pulikkan with Anthropic
+Claude assistance; everything else is PR114 (eumemic) unchanged.
+
+
+PR117 credits its searched DAG to eumemic with Anthropic Claude assistance;
+this experiment imports and replays that witness unchanged. PR110/PR114
+saturation and exact finite checks are applied to the resulting graph.
+Logical readout macros are realized as signed numerator/42 chunks of magnitude
+at most one. The literal audit expands and charges those same-frame shears,
+checks exact reconstruction, and reverses the chunks under reflection.
+Inherited Avi Eisenberg, Rohan Arun, icekylinx and Swapnil Jain credits retained.
+This integration prepared with OpenAI Codex assistance. Apache-2.0.
+"""
+import array
+import json
+import random
+import struct
+import sys
+import tempfile
+from collections import Counter, defaultdict
+from itertools import combinations
+from pathlib import Path
+
+HERE = Path(__file__).resolve().parent
+ROOT = HERE.parents[1]
+sys.path.insert(0, str(ROOT / 'scripts'))
+sys.path.insert(0, str(HERE))
+import importlib.util
+producer_path = HERE / 'producer.py'
+spec = importlib.util.spec_from_file_location('replayed_producer_wrapper', producer_path)
+producer = importlib.util.module_from_spec(spec); spec.loader.exec_module(producer)
+build = producer.build
+
+P = (1 << 61) - 1
+SHRUNK = 16031
+
+
+def require(ok, msg):
+ if not ok:
+ raise SystemExit('FAIL: ' + msg)
+
+
+def load(prefix):
+ def rd(fh, typ, cnt):
+ a = array.array(typ); a.fromfile(fh, cnt); return a
+ with open(str(prefix) + '.bin', 'rb') as f:
+ h, v, n, q = struct.unpack('<4I', f.read(16))
+ flat = rd(f, 'I', 2 * n); core = rd(f, 'Q', n); cover = rd(f, 'Q', n)
+ roots = rd(f, 'I', q); kind = rd(f, 'I', q); active = rd(f, 'B', n)
+ with open(str(prefix) + '.labels', 'rb') as f:
+ ranks = rd(f, 'I', n); types = rd(f, 'B', n)
+ args = [(flat[2 * i], flat[2 * i + 1]) for i in range(n)]
+ return h, v, n, q, args, core, cover, roots, kind, active, ranks, types
+
+
+# ---------------------------------------------------------------- F2 linear algebra on bit vectors
+def dot(a, b): return bin(a & b).count('1') & 1
+
+
+def reduce(basis):
+ rows = []; piv = []
+ for vec in basis:
+ for p, r in zip(piv, rows):
+ if vec >> p & 1: vec ^= r
+ if vec:
+ p = vec.bit_length() - 1
+ for i in range(len(rows)):
+ if rows[i] >> p & 1: rows[i] ^= vec
+ rows.append(vec); piv.append(p)
+ return rows
+
+
+def kernel(funcs, h):
+ K = reduce(funcs); piv = [r.bit_length() - 1 for r in K]
+ out = []
+ for c in (i for i in range(h) if i not in piv):
+ vec = 1 << c
+ for r, p in zip(K, piv):
+ if r >> c & 1: vec |= 1 << p
+ out.append(vec)
+ return out
+
+
+def restrict(basis, funcs):
+ B = reduce(basis)
+ for f in funcs:
+ if not B: break
+ vals = [dot(b, f) for b in B]
+ if not any(vals): continue
+ k = vals.index(1); pv = B[k]
+ B = [b ^ pv if val else b for b, val in zip(B, vals)]; B.pop(k)
+ return reduce(B)
+
+
+def contains(A, B):
+ RB = reduce(B)
+ return len(reduce(RB + list(A))) == len(RB)
+
+
+def cap(A, B):
+ A = reduce(A); B = reduce(B)
+ if not A or not B: return []
+ ker = []; red = []
+ for i, vec in enumerate(A + B):
+ tag = 1 << i
+ for rv, rt in red:
+ if vec >> (rv.bit_length() - 1) & 1: vec ^= rv; tag ^= rt
+ if vec: red.append((vec, tag))
+ else:
+ comb_ = 0
+ for k in range(len(A)):
+ if tag >> k & 1: comb_ ^= A[k]
+ ker.append(comb_)
+ return reduce(ker)
+
+
+def nondeg(B):
+ B = reduce(B); k = len(B)
+ if not k: return True
+ M = [sum(dot(B[i], B[j]) << j for j in range(k)) for i in range(k)]
+ return len(reduce(M)) == k
+
+
+def hopcroft_karp(left, adj):
+ """maximum bipartite matching; adj[x] = sorted list of right vertices."""
+ INF = 1 << 60
+ mate_l = {x: None for x in left}; mate_r = {}
+ while True:
+ dist = {}; queue = []
+ for x in left:
+ if mate_l[x] is None: dist[x] = 0; queue.append(x)
+ else: dist[x] = INF
+ found = INF; head = 0
+ while head < len(queue):
+ x = queue[head]; head += 1
+ if dist[x] >= found: continue
+ for r in adj[x]:
+ y = mate_r.get(r)
+ if y is None: found = min(found, dist[x] + 1)
+ elif dist[y] == INF: dist[y] = dist[x] + 1; queue.append(y)
+ if found == INF: break
+ gained = 0
+ for x0 in left:
+ if mate_l[x0] is not None: continue
+ stack = [(x0, iter(adj[x0]))]; path = []
+ while stack:
+ x, it = stack[-1]
+ advanced = False
+ for r in it:
+ y = mate_r.get(r)
+ if (y is None and dist[x] + 1 == found) or (y is not None and dist[y] == dist[x] + 1):
+ path.append((x, r))
+ if y is None:
+ for xx, rr in path: mate_l[xx] = rr; mate_r[rr] = xx
+ gained += 1; stack = []; break
+ stack.append((y, iter(adj[y]))); advanced = True; break
+ else:
+ dist[x] = INF; stack.pop()
+ if path: path.pop()
+ continue
+ if not advanced: break
+ if not gained: break
+ return mate_l
+
+
+from functools import lru_cache
+from fractions import Fraction
+
+def sat_basis(vectors):
+ piv = {}
+ for x in vectors:
+ for p in sorted(piv, reverse=True):
+ if x >> p & 1:
+ x ^= piv[p]
+ if x:
+ p = x.bit_length() - 1
+ for q in piv:
+ if piv[q] >> p & 1:
+ piv[q] ^= x
+ piv[p] = x
+ return tuple((piv[p] for p in sorted(piv, reverse=True)))
+
+def sat_dot(a, b):
+ return (a & b).bit_count() & 1
+
+@lru_cache(None)
+def sat_contained(A, B):
+ for x in A:
+ for r in B:
+ if x >> r.bit_length() - 1 & 1:
+ x ^= r
+ if x:
+ return False
+ return True
+
+@lru_cache(None)
+def sat_cap(A, B):
+ if not A or not B:
+ return ()
+ red = {}
+ out = []
+ for i, x in enumerate(A + B):
+ tag = 1 << i
+ for p in sorted(red, reverse=True):
+ if x >> p & 1:
+ r, t = red[p]
+ x ^= r
+ tag ^= t
+ if x:
+ red[x.bit_length() - 1] = (x, tag)
+ else:
+ y = 0
+ for j, r in enumerate(A):
+ if tag >> j & 1:
+ y ^= r
+ if y:
+ out.append(y)
+ return sat_basis(out)
+
+@lru_cache(None)
+def sat_nondeg(B):
+ return len(sat_basis((sum((sat_dot(a, b) << j for j, b in enumerate(B))) for a in B))) == len(B)
+
+@lru_cache(None)
+def sat_nonsingular_part(B):
+ rows = list(B)
+ out = []
+ while rows:
+ i = next((i for i, x in enumerate(rows) if sat_dot(x, x)), None)
+ if i is not None:
+ a = rows.pop(i)
+ out.append(a)
+ rows = [x ^ a if sat_dot(x, a) else x for x in rows]
+ continue
+ pair = next(((i, j) for i in range(len(rows)) for j in range(i + 1, len(rows)) if sat_dot(rows[i], rows[j])), None)
+ if pair is None:
+ break
+ i, j = pair
+ a, b = (rows[i], rows[j])
+ out.extend((a, b))
+ rows = [x ^ (a if sat_dot(x, b) else 0) ^ (b if sat_dot(x, a) else 0) for k, x in enumerate(rows) if k not in (i, j)]
+ return sat_basis(out)
+
+def saturated_placement(cand, reach):
+ # Each extracted block is orthogonal to previously selected blocks.
+ # A diagonal-one pivot contributes a nondegenerate line; when all
+ # remaining diagonals vanish, a dot-one pair contributes a hyperbolic
+ # plane. The residual radical is discarded, not counted as a frame.
+ cand = {s: sat_basis(B) for s, B in cand.items()}
+ order = sorted(cand, key=lambda s: (Fraction(-(1 << len(cand[s])), max(1, len(reach[s]))**2), -len(cand[s]), s))
+ byT = defaultdict(list); placed = {}
+ for s in order:
+ X = cand[s]; changed = True
+ while changed and X:
+ changed = False
+ for t in sorted(reach[s]):
+ for w in byT[t]:
+ B = placed[w]
+ if (len(B) >= len(X) and not sat_contained(X, B)) or (len(B) < len(X) and not sat_contained(B, X)):
+ X = sat_cap(X, B); changed = True
+ if not X: break
+ if not X: break
+ if X and not sat_nondeg(X):
+ before = X; X = sat_nonsingular_part(X)
+ assert sat_contained(X, before) and sat_nondeg(X)
+ assert len(X) < len(before)
+ changed = True # Extraction can break containment of a smaller target frame.
+ if X:
+ assert sat_nondeg(X) and sat_contained(X, cand[s])
+ placed[s] = X
+ for t in reach[s]: byT[t].append(s)
+ for t, ss in byT.items():
+ ss.sort(key=lambda s: (len(placed[s]), s))
+ assert all(sat_contained(placed[a], placed[b]) for a, b in zip(ss, ss[1:]))
+ return placed
+
+def main():
+ with tempfile.TemporaryDirectory(prefix='deferred-stopped-') as work:
+ prefix = Path(work) / 'complex'
+ build(24, prefix, central_disjoint=24)
+ h, v, n, q, args, core, cover, roots, kind, active, ranks, types = load(prefix)
+ trip = list(combinations(range(h), 3)); require(len(trip) == v, 'triple count')
+ m = h * h; N = v * v; FULL = (1 << h) - 1
+ tmask = [sum(1 << p for p in T) for T in trip]
+ tid = {T: i for i, T in enumerate(trip)}
+
+ # ------------------------------------------------------------ uses and matching (inherited adjacency)
+ degree = [0] * n; uses = defaultdict(list); c_add = 0
+ for x in range(1, n):
+ if active[x] and args[x][0]:
+ c_add += 1
+ for pos, y in enumerate(args[x]): degree[y] += 1; uses[y].append(('gate', x, pos))
+ for j, x in enumerate(roots): degree[x] += 1; uses[x].append(('root', j))
+ def unode(u): return roots[u[1]] if u[0] == 'root' else u[1]
+ def before(x, u):
+ y = unode(u)
+ return (ranks[x], x) < (ranks[y], (n + u[1]) if u[0] == 'root' else y)
+ def incl(x, y):
+ tx, ty = types[x], types[y]
+ if tx == 1 and ty == 1: return not (core[y] & ~core[x]) and not (cover[x] & ~cover[y])
+ if tx in (1, 2) and ty == 2: return not (cover[x] & ~cover[y])
+ if tx == 1 and ty == 3: return bool(core[x] & core[y])
+ if tx == 2 and ty == 3: return not (cover[x] & ~core[y])
+ if tx == 3 and ty == 2: return cover[y] == FULL
+ if tx == 3 and ty == 3: return core[x] == core[y]
+ return False
+ left = []; adj = {}
+ for x in range(1, n):
+ if not (active[x] and args[x][0]): continue
+ rs = sorted({(y, k) for y in args[x] for k, u in enumerate(uses[y]) if before(x, u) and incl(x, unode(u))})
+ if rs: left.append(x); adj[x] = rs
+ mate = hopcroft_karp(left, adj)
+ links = {x: r for x, r in mate.items() if r is not None}
+ R = c_add + q - len(links)
+ require((c_add,q,len(links),R)==(91770,8120,71185,28705),'selected PR117 graph')
+ print('PR117 graph matched', c_add, q, len(links), R, flush=True)
+ linked_use = {(y, k): x for x, (y, k) in links.items()}
+
+ # ------------------------------------------------------------ root targets, read coefficients, root functionals
+ target = [None] * q
+ for j in range(v): target[j] = j
+ idx = v
+ # PR117 witness stores pair-star roots in natural excluded-point order.
+ for a, b in combinations(range(h), 2):
+ others = [i for i in range(h) if i not in (a, b)]
+ for i in others: target[idx] = tid[tuple(sorted((a, b, i)))]; idx += 1
+ centre_of = {}
+ for j in range(q):
+ if kind[j]:
+ miss = FULL & ~cover[roots[j]]; require(bin(miss).count('1') == 1, 'centre cover')
+ centre_of[j] = miss.bit_length() - 1
+ require(idx + len(centre_of) == q, 'root order')
+ rootfun = [(1 << centre_of[j]) if kind[j] else tmask[target[j]] for j in range(q)]
+
+ # ------------------------------------------------------------ lifted binary frames, monotone
+ succ = defaultdict(set); droot = defaultdict(set)
+ for x in range(1, n):
+ if not active[x]: continue
+ for k, u in enumerate(uses[x]):
+ if (x, k) in linked_use: continue
+ (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1]))
+ for x, (y, k) in links.items():
+ u = uses[y][k]; (succ[x].add(u[1]) if u[0] == 'gate' else droot[x].add(u[1]))
+ order_desc = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x), reverse=True)
+ K = {}
+ for x in order_desc:
+ rows = [rootfun[j] for j in droot[x]]
+ for t in succ[x]: rows += K[t]
+ K[x] = reduce(rows)
+ def envelope(x):
+ if not args[x][0]: return [tmask[x - 1]]
+ if types[x] == 2: return [1 << i for i in range(h) if cover[x] >> i & 1]
+ require(types[x] == 1, 'only ordinary and common-pair labels occur')
+ ks = [i for i in range(h) if (cover[x] & ~core[x]) >> i & 1]
+ require(len(ks) == ranks[x], 'common-pair support')
+ return [core[x] | (1 << k) for k in ks]
+ U = {}
+ for x in range(1, n):
+ if not active[x]: continue
+ if not args[x][0]: U[x] = envelope(x); continue
+ B = kernel(K[x], h)
+ require(contains(envelope(x), B), 'label outside lifted frame')
+ U[x] = B if nondeg(B) else envelope(x)
+ changed = True
+ while changed:
+ changed = False
+ for x in order_desc:
+ if args[x][0] and any(not contains(U[x], U[t]) for t in succ[x]):
+ env = envelope(x)
+ if len(reduce(U[x])) != len(reduce(env)) or not contains(U[x], env): U[x] = env; changed = True
+ dimU = {x: len(reduce(B)) for x, B in U.items()}
+ print('PR117 frames lifted',sum(dimU[x]>ranks[x] for x in U),flush=True)
+
+ # ------------------------------------------------------------ explicit role compile
+ order = sorted((x for x in range(1, n) if active[x]), key=lambda x: (ranks[x], x))
+ holds = []; first_node = []; ops = []; edge_key = {}; role_root = {}
+ def new_role(node): holds.append([node]); first_node.append(node); return len(holds) - 1
+ def serve(s, y, k):
+ u = uses[y][k]
+ if u[0] == 'gate': edge_key[(y, k)] = s
+ else: role_root[s] = u[1]
+ for x in order:
+ free = [k for k in range(len(uses[x])) if (x, k) not in linked_use]
+ if not args[x][0]:
+ for k in free:
+ s = new_role(x); ops.append(('src', s, x)); serve(s, x, k)
+ continue
+ a, b = args[x]
+ ka = next(k for k, u in enumerate(uses[a]) if u == ('gate', x, 0))
+ kb = next(k for k, u in enumerate(uses[b]) if u == ('gate', x, 1))
+ sa, sb = edge_key.pop((a, ka)), edge_key.pop((b, kb))
+ if x in links and links[x][0] == a: sa, sb = sb, sa
+ piv, oth = sa, sb
+ ops.append(('add', piv, oth, x)); holds[piv].append(x); holds[oth].append(x)
+ if x in links: serve(oth, *links[x])
+ require(free, 'every use linked at node %d' % x)
+ serve(piv, x, free[0])
+ for k in free[1:]:
+ f = new_role(x); ops.append(('copy', piv, f, x)); serve(f, x, k)
+ require(not edge_key and len(holds) == R, 'compile')
+ Rr = R
+
+ # ------------------------------------------------------------ shrunk frames
+ # Any nondegenerate U_x with label(x) + sum of predecessor frames <= U_x
+ # <= lifted kernel, contained in every successor frame, satisfies the
+ # PR110 frame contract (the inherited label fallback is one such choice).
+ # One forward pass replaces U_x by its minimal span Lb_x when Lb_x is
+ # nondegenerate and that lowers the local one-child cost of the role
+ # chains holding x; a merged increment a+b replaces a and b, and
+ # t*log(m/t) is subadditive. Section D rechecks every resulting chain.
+ import math
+ fcost = lambda t: t * math.log(m / t) if t > 0 else 0.0
+ preds = defaultdict(list)
+ for x, ts in succ.items():
+ for t in ts: preds[t].append(x)
+ occ = defaultdict(list)
+ for s in range(R):
+ for i, x in enumerate(holds[s]): occ[x].append((s, i))
+ def local_cost(x, d):
+ c = 0.0
+ for s, i in occ[x]:
+ hs = holds[s]
+ c += fcost(d - dimU[hs[i - 1]]) if i else fcost(d)
+ if i + 1 < len(hs): c += fcost(dimU[hs[i + 1]] - d)
+ elif s in role_root: c += fcost(h - 1 - d)
+ else: c += fcost(h - d)
+ return c
+ shrunk = 0
+ for x in order:
+ if not args[x][0]: continue
+ Lb = reduce(envelope(x) + [b for p in preds[x] for b in U[p]])
+ if len(Lb) >= dimU[x] or not contains(Lb, U[x]) or not nondeg(Lb): continue
+ if not all(contains(Lb, U[t]) for t in succ[x]): continue
+ if local_cost(x, len(Lb)) < local_cost(x, dimU[x]) - 1e-9:
+ U[x] = Lb; dimU[x] = len(Lb); shrunk += 1
+ print('shrunk frames', shrunk, flush=True)
+ require(SHRUNK is None or shrunk == SHRUNK, 'shrunk frames: %d' % shrunk)
+
+ # ------------------------------------------------------------ B. the word computes every root value
+ rng = random.Random(20261008)
+ xs = [rng.randrange(P) for _ in range(v)]
+ val = [0] * n
+ for i in range(v): val[i + 1] = xs[i]
+ for x in order:
+ if args[x][0]: val[x] = (val[args[x][0]] + val[args[x][1]]) % P
+ leaf_of = {s: first_node[s] for s in range(Rr) if not args[first_node[s]][0]}
+ a_ = [0] * Rr
+ for s, leaf in leaf_of.items(): a_[s] = xs[leaf - 1]
+ for o in ops:
+ if o[0] == 'add': a_[o[1]] = (a_[o[1]] + a_[o[2]]) % P
+ elif o[0] == 'copy': a_[o[2]] = (a_[o[2]] + a_[o[1]]) % P
+ require(all(a_[s] == val[roots[j]] for s, j in role_root.items()), 'root values')
+
+ # ------------------------------------------------------------ phase one and garbage reach
+ def touch(o): return [o[1], o[2]] if o[0] in ('add', 'copy') else []
+ prev = {}; pred = defaultdict(list); last = {}
+ for i, o in enumerate(ops):
+ for s in touch(o):
+ if s in prev: pred[i].append(prev[s])
+ prev[s] = i; last[s] = i
+ centre_roles = [s for s, j in role_root.items() if kind[j]]
+ Anc = set(); st = [last[s] for s in centre_roles]
+ while st:
+ i = st.pop()
+ if i not in Anc: Anc.add(i); st.extend(pred[i])
+ touched = set(centre_roles)
+ for i in Anc: touched.update(touch(ops[i]))
+ require(all(last[s] in Anc for s in centre_roles), 'centres complete in phase one')
+ reach = [set() for _ in range(Rr)]; reach_all = [False] * Rr
+ for s, j in role_root.items():
+ if kind[j]: reach_all[s] = True
+ else: reach[s].add(target[j])
+ for o in reversed(ops):
+ if o[0] == 'add': reach[o[2]] |= reach[o[1]]; reach_all[o[2]] = reach_all[o[2]] or reach_all[o[1]]
+ elif o[0] == 'copy': reach[o[1]] |= reach[o[2]]; reach_all[o[1]] = reach_all[o[1]] or reach_all[o[2]]
+
+ # ------------------------------------------------------------ deferral frames, insertion nesting
+ def F0(s): return U[first_node[s]]
+ cand = {}
+ for s in range(Rr):
+ if s in touched or reach_all[s]: continue
+ S_ = restrict(F0(s), [tmask[t] for t in reach[s]])
+ if S_ and nondeg(S_): cand[s] = S_
+ print('PR117 candidates',len(cand),flush=True)
+ placed = saturated_placement(cand, reach)
+ print('PR117 placed',len(placed),flush=True)
+ deferred = sorted(placed, key=lambda s: (len(placed[s]), s)); dset = set(deferred)
+
+ # ------------------------------------------------------------ C. replay with arbitrary scratch and data
+ inv = lambda a: pow(a % P, P - 2, P); HALF = inv(2); I21 = inv(21)
+ cvec = [None] * Rr; dpart = [dict() for _ in range(Rr)]
+ for s, j in role_root.items():
+ if kind[j]: c = [0] * h; c[centre_of[j]] = 1; cvec[s] = c
+ else: dpart[s][target[j]] = (P - HALF) if j >= v else HALF
+ seed_c = {s: (None if cvec[s] is None else list(cvec[s])) for s in role_root}
+ seed_d = {s: dict(dpart[s]) for s in role_root}
+ def addc(dst, src):
+ if cvec[src] is not None:
+ cvec[dst] = list(cvec[src]) if cvec[dst] is None else [(p + q_) % P for p, q_ in zip(cvec[dst], cvec[src])]
+ for t, c in dpart[src].items(): dpart[dst][t] = (dpart[dst].get(t, 0) + c) % P
+ for o in reversed(ops):
+ if o[0] == 'add': addc(o[2], o[1])
+ elif o[0] == 'copy': addc(o[1], o[2])
+ scatter = [[(I21 - (HALF if i in trip[t] else 0)) % P for t in range(v)] for i in range(h)]
+ def readout(y, s, value, sign, seed=False):
+ # Logical readout macro: the literal audit combines its exact rational
+ # target coefficients and expands each numerator/42 into bounded shears.
+ cv = seed_c[s] if seed else cvec[s]; dp = seed_d[s] if seed else dpart[s]
+ if cv is not None:
+ for i, ci in enumerate(cv):
+ if ci:
+ f = sign * ci * value % P; row = scatter[i]
+ for t in range(v): y[t] = (y[t] + f * row[t]) % P
+ for t, c in dp.items(): y[t] = (y[t] + sign * c * value) % P
+ phase1 = sorted(Anc); rest = [i for i in range(len(ops)) if i not in Anc]
+ def replay(seed):
+ rng = random.Random(seed)
+ x = [rng.randrange(P) for _ in range(v)]; z = [rng.randrange(P) for _ in range(Rr)]
+ y0 = [rng.randrange(P) for _ in range(v)]; a = list(z); y = list(y0)
+ for s in range(Rr):
+ if s not in dset: readout(y, s, a[s], -1)
+ for s, leaf in leaf_of.items():
+ if s not in dset: a[s] = (a[s] + x[leaf - 1]) % P
+ def run(i, sign=1):
+ o = ops[i]
+ if o[0] == 'add': a[o[1]] = (a[o[1]] + sign * a[o[2]]) % P
+ elif o[0] == 'copy': a[o[2]] = (a[o[2]] + sign * a[o[1]]) % P
+ for i in phase1: run(i)
+ for s in centre_roles: readout(y, s, a[s], +1, True)
+ for s in deferred: readout(y, s, a[s], -1)
+ for s in deferred:
+ if s in leaf_of: a[s] = (a[s] + x[leaf_of[s] - 1]) % P
+ for i in rest: run(i)
+ for s, j in role_root.items():
+ if not kind[j]: readout(y, s, a[s], +1, True)
+ for i in reversed(range(len(ops))): run(i, -1)
+ for s, leaf in leaf_of.items(): a[s] = (a[s] - x[leaf - 1]) % P
+ return a == z, all((y[t] - y0[t] - x[t]) % P == 0 for t in range(v))
+ rep = [replay(seed) for seed in (1, 2)]
+ require(all(r == (True, True) for r in rep), 'replay %s' % rep)
+
+ # ------------------------------------------------------------ D. exact F2 frame facts
+ root_frame = {}
+ for s, j in role_root.items():
+ root_frame[s] = [1 << i for i in range(h) if i != centre_of[j]] if kind[j] else kernel([tmask[target[j]]], h)
+ FULLB = [1 << i for i in range(h)]
+ chain_dims = []
+ for s in range(Rr):
+ seq = [placed.get(s, []), F0(s)] + [U[x] for x in holds[s][1:]]
+ if s in root_frame: seq.append(root_frame[s])
+ seq.append(FULLB)
+ require(all(contains(A, B) for A, B in zip(seq, seq[1:])), 'role chain nesting %d' % s)
+ require(all(nondeg(B) for B in seq[1:-1] if B), 'degenerate frame on role %d' % s)
+ chain_dims.append([len(reduce(B)) for B in seq])
+ for s, X in placed.items():
+ require(contains(X, F0(s)) and nondeg(X), 'deferral frame %d' % s)
+ require(all(not any(dot(xv, tmask[t]) for xv in X) for t in reach[s]), 'target frame %d' % s)
+ byT2 = defaultdict(list)
+ for s in deferred:
+ for t in reach[s]: byT2[t].append(s)
+ for t, ss in byT2.items():
+ ss.sort(key=lambda s: (len(placed[s]), s))
+ require(all(contains(placed[p], placed[q_]) for p, q_ in zip(ss, ss[1:])), 'target chain %d' % t)
+
+ # ------------------------------------------------------------ E. one-child histogram
+ z = Counter()
+ for s in range(Rr):
+ ds = chain_dims[s]
+ for a, b in zip(ds[:-1], ds[1:-1]):
+ if b > a: z[b - a] += 2 * v
+ lastd = ds[-2]
+ if s in role_root and kind[role_root[s]]: z[h - 1] += 2 * v # copied centre transform
+ z[h - lastd] += 2 * v # final growth to F
+ z[m - h + ds[0]] += 2 * v # exterior, gauged by sigma
+ levels = defaultdict(set)
+ for s in deferred:
+ for t in reach[s]: levels[t].add(len(placed[s]))
+ for t in range(v):
+ ds = sorted(levels[t] | {0, h - 1})
+ for a, b in zip(ds, ds[1:]): z[b - a] += 2 * v # target fronts
+ z[h - 1] += 2 * N # data-wire fronts
+ z[(h - 1) ** 2] += 2 * N # data macros
+ z[1] += N # endpoint copies
+ z.pop(0, None)
+ W = 2 * N + 2 * v * R; L = 2 * v * h * (h - 1); s_ = W * m - N + L
+ require(sum(t * c for t, c in z.items()) == s_, 'complex rank mass')
+ require(all(0 < t < m for t in z), 'children below m')
+ out = dict(h=h, v=v, additions=c_add, roots=q, links=len(links), R=R, m=m, N=N, W=W, L=L, total_rank=s_,
+ deficit=N - L, maxchild=max(z), phase_one_ops=len(Anc), phase_one_roles=len(touched),
+ deferred_roles=len(deferred),
+ deferred_dims=dict(sorted(Counter(len(X) for X in placed.values()).items())),
+ lifted_additions=sum(1 for x in U if args[x][0] and dimU[x] > ranks[x]),
+ replay=dict(seeds=[1, 2], scratch_restored=True, y_plus_x=True, field='Z/(2^61-1)'),
+ child_multiplicities=dict(sorted(z.items())))
+ (HERE / 'complex-profile.json').write_text(json.dumps(out, indent=1) + '\n')
+ print('PASS complex: R=%d, deferred roles %d, maxchild %d, rank mass %d' % (R, len(deferred), max(z), s_))
+
+
+if __name__ == '__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/controls/pr114-complex-profile.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/controls/pr114-complex-profile.json
new file mode 100644
index 0000000000..90a44f18a8
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/controls/pr114-complex-profile.json
@@ -0,0 +1,85 @@
+{
+ "h": 24,
+ "v": 2024,
+ "additions": 91770,
+ "roots": 8120,
+ "links": 71185,
+ "R": 28705,
+ "m": 576,
+ "N": 4096576,
+ "W": 124390992,
+ "L": 2234496,
+ "total_rank": 71647349312,
+ "deficit": 1862080,
+ "maxchild": 574,
+ "phase_one_ops": 18844,
+ "phase_one_roles": 13555,
+ "deferred_roles": 4706,
+ "deferred_dims": {
+ "2": 863,
+ "4": 357,
+ "6": 573,
+ "8": 144,
+ "10": 25,
+ "12": 323,
+ "14": 241,
+ "16": 337,
+ "17": 1,
+ "18": 900,
+ "19": 603,
+ "20": 208,
+ "21": 11,
+ "22": 120
+ },
+ "lifted_additions": 39989,
+ "replay": {
+ "seeds": [
+ 1,
+ 2
+ ],
+ "scratch_restored": true,
+ "y_plus_x": true,
+ "field": "Z/(2^61-1)"
+ },
+ "child_multiplicities": {
+ "1": 339934848,
+ "2": 358859248,
+ "3": 36626304,
+ "4": 66512688,
+ "5": 30258800,
+ "6": 17062320,
+ "7": 14240864,
+ "8": 23757712,
+ "9": 6290592,
+ "10": 9500656,
+ "11": 9456128,
+ "12": 15430976,
+ "13": 10949840,
+ "14": 1384416,
+ "15": 1275120,
+ "16": 793408,
+ "17": 506000,
+ "18": 2902416,
+ "19": 2092816,
+ "20": 817696,
+ "21": 1230592,
+ "22": 64768,
+ "23": 8363168,
+ "529": 8193152,
+ "552": 97147952,
+ "554": 3493424,
+ "556": 1445136,
+ "558": 2319504,
+ "560": 582912,
+ "562": 101200,
+ "564": 1307504,
+ "566": 975568,
+ "568": 1364176,
+ "569": 4048,
+ "570": 3643200,
+ "571": 2440944,
+ "572": 841984,
+ "573": 44528,
+ "574": 485760
+ }
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/inputs/complex-dag.json.gz b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/inputs/complex-dag.json.gz
new file mode 100644
index 0000000000..a5b0598e4c
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diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/inputs/witness_23.json.gz b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/inputs/witness_23.json.gz
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diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/producer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/producer.py
new file mode 100644
index 0000000000..a93a265f01
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/producer.py
@@ -0,0 +1,17 @@
+"""Pinned PR117 scalar DAG adapter for the saturated deferred compiler.
+
+The searched graph is upstream PR117 work credited to eumemic with Anthropic
+Claude assistance. This adapter preserves that witness and producer unchanged;
+saturation integration is separate OpenAI Codex-assisted work. Apache-2.0.
+"""
+from hashlib import sha256
+from pathlib import Path
+from replayed_producer import build as replayed_build
+
+WITNESS_SHA256 = '3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b'
+
+def build(h, prefix, central_disjoint, base=2):
+ assert (h, central_disjoint, base) == (24,24,2)
+ witness=Path(__file__).resolve().parent/'inputs/complex-dag.json.gz'
+ assert sha256(witness.read_bytes()).hexdigest() == WITNESS_SHA256, 'PR117 DAG pin mismatch'
+ return replayed_build(witness,prefix)
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection-audit.json b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection-audit.json
new file mode 100644
index 0000000000..caace0ada6
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection-audit.json
@@ -0,0 +1,82 @@
+{
+ "R": 28705,
+ "all_frames_nondegenerate": true,
+ "audit_sha256": "6761fb01f93ef89f2455388b2f5a71f19c0bbd870e6aaeba457ede0a949a163b",
+ "bounded_chunk_coefficients": true,
+ "bounded_readout_chunks_sha256": "bb2ad510e5f5113eba2fd520f99bb05725087ae47e1566b7e63eafdefc69d809",
+ "child_multiplicities": {
+ "1": 435601232,
+ "10": 7375456,
+ "11": 7019232,
+ "12": 31788944,
+ "13": 12536656,
+ "14": 1497760,
+ "15": 3440800,
+ "16": 854128,
+ "17": 506000,
+ "18": 2906464,
+ "19": 2092816,
+ "2": 267192288,
+ "20": 817696,
+ "21": 1230592,
+ "22": 64768,
+ "23": 8363168,
+ "3": 29238704,
+ "4": 61145040,
+ "5": 26425344,
+ "529": 8193152,
+ "552": 97147952,
+ "554": 3493424,
+ "556": 1445136,
+ "558": 2319504,
+ "560": 582912,
+ "562": 101200,
+ "564": 1307504,
+ "566": 975568,
+ "568": 1364176,
+ "569": 4048,
+ "570": 3643200,
+ "571": 2444992,
+ "572": 837936,
+ "573": 44528,
+ "574": 485760,
+ "6": 15734576,
+ "7": 11876832,
+ "8": 22077792,
+ "9": 4562096
+ },
+ "conservative_local_G": 14907958248,
+ "exact_arbitrary_dirty_cancellation_by_dependency_cut": true,
+ "exact_chunk_reconstruction": true,
+ "exact_fresh_source_map": true,
+ "exact_integer_old_readout_transpose": true,
+ "expanded_old_readout_additions": 11862944,
+ "expanded_scalar_operations_per_stage": 12160614,
+ "forward_incidence_sha256": "46a00e3137729d00cafcf32969d1f3bc4e4cd293552f74eb47f61e64cf1524c1",
+ "h": 24,
+ "largest_bounded_chunk_numerator_over_42": 42,
+ "largest_readout_numerator_over_42": 55,
+ "literal_frame_incidences_both_directions": true,
+ "literal_global_scalar_groups": 49230262048,
+ "old_readout_coefficients_over_42_sha256": "e0666f81e1d35e002d61b8f2b2b1ca0d1d79cc7fbcbc76063eb333294d875e5e",
+ "reflected_incidence_sha256": "a6de908519fbdfabb1b8c05fd111321fa00181375bfa1cca537161d424ed6515",
+ "reflected_residual_rank_histogram_equal": true,
+ "reflected_scalar_map": "X becomes X-Y; Y unchanged; all auxiliary coordinates restored.",
+ "reflected_word_rule": "Reverse literal order including each bounded readout chunk, negate every shear, swap X/Y ports, complement every frame; auxiliary bank is separate.",
+ "rejected_controls": [
+ "oversized-readout-chunk",
+ "split-readout-sum",
+ "reflected-chunk-order",
+ "inverse-sign",
+ "uncomplemented-frame",
+ "signed-root-readout"
+ ],
+ "scalar_readout_normalization": "Each exact numerator n/42 becomes signed42 chunks plus a signed remainder. Exact reconstruction and chunk magnitude<=1 checked; every same-frame shear is charged; reflection reverses chunk order.",
+ "scope": "Exact finite source coefficients, dirty cancellation algebra and literal reflected frame/charge ledger. Copied-centre transforms, endpoint correction and residual-to-child/all-size transfer retain their stated inherited contracts.",
+ "source_sha256": "fa1125e85ec73b185dc9eee117f62d10356bb6422c07ec793a7f77296c87707e",
+ "split_readout_macros": 32,
+ "two_stage_scalar_map": "(X,Y) becomes (-Y,X+Y) before inherited endpoint correction.",
+ "unsplit_old_readout_macros": 11862912,
+ "v": 2024,
+ "word_blocks": 277775
+}
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection_audit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection_audit.py
new file mode 100644
index 0000000000..9da639268b
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/reflection_audit.py
@@ -0,0 +1,365 @@
+#!/usr/bin/env python3
+"""Literal inverse/reflection and exact finite scalar/frame audit.
+
+Captures an unchanged deferred producer before its output write, then checks
+the scalar computation on every source symbol, the exact signed old-readout
+transpose, the dependency cut and the complete complemented incidence ledger.
+This is finite verification; the inherited residual-to-child implementation,
+all-size transfer and analytic interfaces are not proved by this script.
+"""
+import ast
+from collections import Counter
+from functools import lru_cache
+from hashlib import sha256
+from itertools import combinations
+import argparse,json,pickle,struct,sys
+from pathlib import Path
+sys.dont_write_bytecode=True
+assert not sys.flags.optimize,'Assertions must remain enabled'
+
+
+def capture(source):
+ source=Path(source).resolve();sys.path.insert(0,str(source.parent))
+ tree=ast.parse(source.read_text(),filename=str(source))
+ main=next(n for n in tree.body if isinstance(n,ast.FunctionDef) and n.name=='main')
+ at=next(i for i,n in enumerate(main.body) if isinstance(n,ast.Expr) and isinstance(n.value,ast.Call) and isinstance(n.value.func,ast.Attribute) and n.value.func.attr=='write_text')
+ main.body[at:]=[ast.Return(ast.Call(ast.Name('locals',ast.Load()),[],[]))]
+ ast.fix_missing_locations(tree)
+ ns={'__file__':str(source),'__name__':'reflection_capture'}
+ exec(compile(tree,str(source)+' [read-only capture]','exec'),ns)
+ data=ns['main']();data['source']=str(source);return data
+
+
+def basis(vectors):
+ piv={}
+ for x in vectors:
+ for p in sorted(piv,reverse=True):
+ if x>>p&1:x^=piv[p]
+ if x:
+ p=x.bit_length()-1
+ for q in piv:
+ if piv[q]>>p&1:piv[q]^=x
+ piv[p]=x
+ return tuple(piv[p] for p in sorted(piv,reverse=True))
+
+
+def dot(a,b):return (a&b).bit_count()&1
+
+
+@lru_cache(None)
+def contained(A,B):return len(basis(A+B))==len(B)
+
+
+@lru_cache(None)
+def complement(A,h):
+ A=basis(A);piv={x.bit_length()-1:x for x in A};result=[]
+ for j in range(h):
+ if j not in piv:
+ x=1<>j&1:x|=1<=0 else -1
+ parts=(sign*42,)*q+((sign*r,) if r else ())
+ check_chunks(numerator,parts)
+ return parts
+
+def reverse_row(row):
+ if row[0]=='old':return (row[0],row[1],row[3],row[2])
+ return row
+
+
+def check_reflection(forward,backward,h,v):
+ def bank(s):return s+v if s1)
+ readcount+=len(parts);maxchunk=max(maxchunk,max(map(abs,parts)))
+ for part in parts:
+ reached.append(t);records.append(struct.pack('len(old):hist[len(F)-len(old)]+=1
+ current[s]=F
+ for event in events:
+ k,a,b,c,F,*rest=event
+ assert c in (-1,1)
+ promote(a,F)
+ if k=='gate':promote(b,F);scalar+=1
+ elif k=='read':
+ for t in b:promote(t,F)
+ scalar+=len(b)
+ else:
+ assert k=='centre';G=rest[0]
+ assert contained(G,F) or contained(F,G)
+ assert nondeg(G);copies[abs(len(F)-len(G))]+=1
+ for t in b:promote(t,G)
+ scalar+=len(b)+2 # temporary copy and erasure
+ digest.update(repr(event).encode()+b'\n')
+ # Each literal role cleanup reaches full space; any unused final
+ # endpoint is still represented explicitly in the expected chain.
+ for s,F in enumerate(expected):promote(s,F)
+ assert current==expected
+ return hist,copies,scalar,digest.hexdigest()
+ start=tm+[ZERO]*v+[sigma.get(s,ZERO) for s in range(R)]
+ finish=[FULL]*v+[complement(T,h) for T in tm]+[FULL]*R
+ H,C,scalar,digest=framescan(word,start,finish)
+ revstart=[None]*len(start);revfinish=[None]*len(start)
+ for s in range(len(start)):
+ revstart[swap(s)]=complement(finish[s],h);revfinish[swap(s)]=complement(start[s],h)
+ HR,CR,scalarR,reverse_digest=framescan(reverse,revstart,revfinish)
+ assert (H,C,scalar)==(HR,CR,scalarR)
+ z=Counter({r:2*v*n for r,n in (H+C).items()})
+ for s in range(R):z[h*h-h+len(sigma.get(s,ZERO))]+=2*v
+ z[(h-1)**2]+=2*v*v;z[1]+=v*v
+ z.pop(0,None)
+ assert dict(sorted(z.items()))=={int(r):n for r,n in d['out']['child_multiplicities'].items()},'Literal reflected child histogram'
+ assert sum(r*n for r,n in z.items())==d['out']['total_rank']
+ G=v*v+2*v*scalar
+ safe=8*(d['c_add']+2*R+(R+q)*v*(h+1)+h*h+h+1) if 'c_add' in d else 8*(d['out']['additions']+2*R+(R+q)*v*(h+1)+h*h+h+1)
+ assert safe>=scalar
+ return dict(h=h,v=v,R=R,exact_fresh_source_map=True,exact_integer_old_readout_transpose=True,
+ exact_arbitrary_dirty_cancellation_by_dependency_cut=True,
+ reflected_word_rule='Reverse literal order including each bounded readout chunk, negate every shear, swap X/Y ports, complement every frame; auxiliary bank is separate.',
+ reflected_scalar_map='X becomes X-Y; Y unchanged; all auxiliary coordinates restored.',
+ two_stage_scalar_map='(X,Y) becomes (-Y,X+Y) before inherited endpoint correction.',
+ literal_frame_incidences_both_directions=True,all_frames_nondegenerate=True,
+ reflected_residual_rank_histogram_equal=True,child_multiplicities=dict(sorted(z.items())),
+ word_blocks=len(word),expanded_scalar_operations_per_stage=scalar,
+ expanded_old_readout_additions=readcount,largest_readout_numerator_over_42=maxcoef,
+ unsplit_old_readout_macros=unsplit_readcount,split_readout_macros=split_macros,
+ largest_bounded_chunk_numerator_over_42=maxchunk,
+ bounded_readout_chunks_sha256=chunk_digest.hexdigest(),
+ scalar_readout_normalization='Each exact numerator n/42 becomes signed42 chunks plus a signed remainder. Exact reconstruction and chunk magnitude<=1 checked; every same-frame shear is charged; reflection reverses chunk order.',
+ exact_chunk_reconstruction=True,bounded_chunk_coefficients=True,
+ old_readout_coefficients_over_42_sha256=coefficient_digest.hexdigest(),
+ literal_global_scalar_groups=G,conservative_local_G=safe,
+ forward_incidence_sha256=digest,reflected_incidence_sha256=reverse_digest,
+ rejected_controls=rejected,
+ scope='Exact finite source coefficients, dirty cancellation algebra and literal reflected frame/charge ledger. Copied-centre transforms, endpoint correction and residual-to-child/all-size transfer retain their stated inherited contracts.')
+
+
+def main():
+ ap=argparse.ArgumentParser();ap.add_argument('--source',type=Path);ap.add_argument('--state',type=Path)
+ ap.add_argument('--output',type=Path);ap.add_argument('--check',type=Path);a=ap.parse_args()
+ assert bool(a.source)!=bool(a.state)
+ d=capture(a.source) if a.source else pickle.loads(a.state.read_bytes())
+ result=audit(d);source=Path(d['source'])
+ result['source_sha256']=sha256(source.read_bytes()).hexdigest()
+ result['audit_sha256']=sha256(Path(__file__).read_bytes()).hexdigest()
+ result=json.loads(json.dumps(result));encoded=json.dumps(result,indent=2,sort_keys=True)+'\n'
+ if a.check:assert result==json.loads(a.check.read_text())
+ if a.output:a.output.write_text(encoded)
+ else:print(encoded,end='')
+ print('PASS exact scalar and literal complement reflection audit',file=sys.stderr)
+
+
+if __name__=='__main__':main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/replayed_producer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/replayed_producer.py
new file mode 100644
index 0000000000..673fbbba70
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/replayed_producer.py
@@ -0,0 +1,179 @@
+"""Replayed h=24 complex producer with all centers disjoint (rational divisor 21).
+
+Copyright 2026 eumemic, Apache-2.0. AI-assisted (Claude). The DAG was found by an
+automated search over producers of the retained paired-triple, pair-star and
+center-disjoint interfaces. The checks below are adapted from
+stopped_product/complex.py (copyright 2026 icekylinx, Apache-2.0, PR #104).
+
+The witness complex-dag.json.gz lists the ordinary
+additions after the v triple inputs and the retained roots: the disjoint sums
+D[t], the pair stars P(a,b,i) and the center-disjoint sums A_i. Every support,
+core, cover, type and rank is recomputed here from the operands; nothing is
+read from the witness except the operand pairs and the root indices.
+"""
+import gzip, json, struct, sys, array
+from fractions import Fraction
+from itertools import combinations
+from pathlib import Path
+
+
+def write_array(f, values):
+ """Little-endian array writer, as partial_swap.binary.write_array."""
+ if sys.byteorder != 'little' and values.itemsize > 1:
+ values = array.array(values.typecode, values)
+ values.byteswap()
+ values.tofile(f)
+
+
+def build(witness, prefix):
+ w = json.loads(gzip.decompress(Path(witness).read_bytes()))
+ h, v, d = w['h'], w['v'], w['central_disjoint']
+ assert (h, d, w['center_denominator']) == (24, 24, 21)
+ triples = list(combinations(range(h), 3))
+ assert v == len(triples)
+ args = [(0, 0)]; support = [0]; core = [0]; cover = [0]; types = [0]; ranks = [0]
+ for j, t in enumerate(triples):
+ mask = sum(1 << a for a in t)
+ args.append((0, 0)); support.append(1 << j); core.append(mask); cover.append(mask)
+ types.append(1); ranks.append(1)
+ flat = w['args']
+ assert len(flat) % 2 == 0
+ for k in range(0, len(flat), 2):
+ a, b, x = flat[k], flat[k+1], len(args)
+ assert 0 < a < x and 0 < b < x, 'Operands must precede their sum'
+ assert not support[a] & support[b], 'Ordinary additions must be cancellation-free'
+ args.append((a, b)); support.append(support[a] | support[b])
+ core.append(core[a] & core[b]); cover.append(cover[a] | cover[b])
+ if core[x].bit_count() >= 2:
+ types.append(1); ranks.append(support[x].bit_count())
+ else:
+ types.append(2); ranks.append(cover[x].bit_count())
+ n = len(args)
+ point_masks = [sum(1 << j for j, t in enumerate(triples) if a in t) for a in range(h)]
+ full_support = (1 << v) - 1
+ roots, kind = [], []
+ assert len(w['D']) == v
+ for t, node in zip(triples, w['D']):
+ assert 0 < node < n
+ assert support[node] == full_support & ~(point_masks[t[0]]|point_masks[t[1]]|point_masks[t[2]])
+ target_mask = sum(1 << a for a in t)
+ if types[node] == 2:
+ assert not cover[node] & target_mask
+ else:
+ assert types[node] == 1
+ assert not support[node] & (point_masks[t[0]]^point_masks[t[1]]^point_masks[t[2]])
+ roots.append(node); kind.append(0)
+ stars = [(a, b, i) for a, b in combinations(range(h), 2) for i in range(h) if i not in (a, b)]
+ assert len(w['P']) == len(stars)
+ pair_outputs = {}
+ for (a, b, i), node in zip(stars, w['P']):
+ assert 0 < node < n
+ assert support[node] == point_masks[a] & point_masks[b] & ~point_masks[i]
+ assert types[node] == 1
+ assert not support[node] & (point_masks[a]^point_masks[b]^point_masks[i])
+ pair_outputs[a, b, i] = node
+ roots.append(node); kind.append(0)
+ assert len(w['A']) == d
+ for i, node in enumerate(w['A']):
+ assert 0 < node < n
+ assert support[node] == full_support & ~point_masks[i]
+ assert types[node] == 2 and cover[node] == ((1 << h)-1) ^ (1 << i)
+ assert ranks[node] == h-1
+ roots.append(node); kind.append(1)
+ # Every A_i avoids i, so sum A_i = (h-3)T. The decoder is T=sum A_i/21
+ # and the scatter is T-(1/2)sum_{i in target} A_i.
+ decoder = Fraction(1, h-3)
+ assert decoder == Fraction(1, 21)
+ scatter_coefficients = [decoder, decoder-Fraction(1, 2)]
+ for coefficient in scatter_coefficients:
+ odd_denominator = coefficient.denominator
+ while odd_denominator % 2 == 0:
+ odd_denominator //= 2
+ assert 21 % odd_denominator == 0 and abs(coefficient) <= 1
+ for source in triples:
+ assert sum(i not in source for i in range(h))*decoder == 1
+ Dset = set(range(d))
+ for triple in triples:
+ k = len(Dset.intersection(triple))
+ assert 2*(3-k)-2*(d-k) == 2*(3-d)
+ patterns = {}
+ for target in triples:
+ chosen = len(Dset.intersection(target))
+ if chosen not in patterns:
+ patterns[chosen] = target
+ for chosen, target in patterns.items():
+ target_set = set(target)
+ for source in triples:
+ k = len(Dset.intersection(source))
+ total_coefficient = Fraction(2*(3-k)-2*(d-k), 2*(3-d))
+ scalar = Fraction(len((target_set-Dset).intersection(source)), 2)
+ scalar -= Fraction(len((target_set & Dset)-set(source)), 2)
+ scalar += Fraction(chosen-1, 2)*total_coefficient
+ assert scalar == Fraction(len(target_set.intersection(source))-1, 2)
+ for j, t in enumerate(triples):
+ masks = [point_masks[a] for a in t]
+ two = (masks[0]&masks[1]&~masks[2]) | (masks[0]&masks[2]&~masks[1]) | (masks[1]&masks[2]&~masks[0])
+ actual = 0
+ for a, b in combinations(t, 2):
+ excluded = next(i for i in t if i not in (a, b))
+ actual |= support[pair_outputs[a, b, excluded]]
+ assert actual == two
+ assert masks[0]&masks[1]&masks[2] == 1 << j
+ assert [((k-1)+(k == 0)-(k == 2)) for k in range(4)] == [0, 0, 0, 2]
+
+ def contained(x, y):
+ tx, ty = types[x], types[y]
+ if tx == 1 and ty == 1: return not(core[y]&~core[x] or cover[x]&~cover[y])
+ if tx in (1, 2) and ty == 2: return not cover[x]&~cover[y]
+ return False
+ active = [0]*n; stack = list(roots)
+ while stack:
+ x = stack.pop()
+ if not x or active[x]: continue
+ active[x] = 1
+ if args[x][0]: stack.extend(args[x])
+ degree = [0]*n
+ for x in range(1, n):
+ if active[x]:
+ if types[x] == 1:
+ assert core[x].bit_count() >= 2 and ranks[x] == support[x].bit_count()
+ else:
+ assert types[x] == 2 and ranks[x] == cover[x].bit_count()
+ if active[x] and args[x][0]:
+ for y in args[x]:
+ assert y < x and contained(y, x), 'Binary frame nesting failed'
+ degree[y] += 1
+ for x in roots: degree[x] += 1
+ H = [0]*(h+1); c = 0; loss = 0
+ for x in range(1, n):
+ if not active[x]: continue
+ r = ranks[x]
+ if args[x][0]:
+ c += 1; H[r] += degree[x]-1; H[h-r] += 1
+ for y in args[x]:
+ assert r >= ranks[y]
+ H[r-ranks[y]] += 1
+ else: H[1] += degree[x]
+ for x, k in zip(roots, kind):
+ r = ranks[x]
+ if k: H[r] += 1; H[h] += 1; loss += r
+ else: H[h-1-r] += 1; H[1] += 1
+ q = len(roots); R = c+q
+ result = dict(h=h, v=v, c=c, q=q, R=R, loss=loss, central_disjoint=d, histogram=H,
+ rank_sum=sum(r*m for r, m in enumerate(H)))
+ assert loss == h*(h-1) and result['rank_sum'] == h*R+2*loss
+ result['center_denominator'] = 21
+ result['scalar_validation'] = dict(ordinary_supports_exact=True, centers_exact=True,
+ center_decoder='sum A_i / 21', scatter_coefficients=list(map(str, scatter_coefficients)),
+ rational_scalar_identity_exact=True, mixed_center_scatter_exact=True, binary_frames_nested=True,
+ binary_frames_nondegenerate=True)
+ with open(str(prefix)+'.bin', 'wb') as f:
+ f.write(struct.pack('<4I', h, v, n, q))
+ write_array(f, array.array('I', (a for pair in args for a in pair)))
+ write_array(f, array.array('Q', core)); write_array(f, array.array('Q', cover))
+ write_array(f, array.array('I', roots)); write_array(f, array.array('I', kind))
+ write_array(f, array.array('B', active))
+ with open(str(prefix)+'.labels', 'wb') as f:
+ write_array(f, array.array('I', ranks)); write_array(f, array.array('B', types))
+ Path(str(prefix)+'.json').write_text(json.dumps(result, indent=2)+'\n')
+ return result
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/test_controls.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/test_controls.py
new file mode 100644
index 0000000000..fdeedf7d8d
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/test_controls.py
@@ -0,0 +1,180 @@
+#!/usr/bin/env python3
+"""Negative controls for the shrunk-frame deferred finite witness.
+
+These controls target source omissions, altered inputs, paid rank accounting,
+noncontracting children and invalid exact arithmetic. They do not substitute
+for the full producer and literal reflection checks. Prepared for eumemic with
+OpenAI Codex assistance; Apache-2.0, inherited notices retained.
+"""
+import sys
+sys.dont_write_bytecode = True
+if sys.flags.optimize:
+ raise ValueError('Negative controls require assertions')
+
+import argparse
+import copy
+import gzip
+import importlib.util
+import json
+from pathlib import Path
+import shutil
+import subprocess
+import tempfile
+import unittest
+
+from verify import check_sources, compare_json, digest, safe_file, validate_profile
+
+HERE = Path(__file__).resolve().parent
+REPOSITORY = HERE.parents[1]
+
+
+class FrozenControls(unittest.TestCase):
+ @classmethod
+ def setUpClass(cls):
+ cls.manifest = check_sources(HERE, REPOSITORY)
+ cls.profiles = {label: json.loads((HERE / (label + '-profile.json')).read_text())
+ for label in ('bit', 'complex')}
+ sys.path.insert(0, str(REPOSITORY / 'scripts'))
+ spec = importlib.util.spec_from_file_location('checked_cyclic_certificate', HERE / 'certificate.py')
+ cls.certificate = importlib.util.module_from_spec(spec)
+ spec.loader.exec_module(cls.certificate)
+ cls.certificate.ROOT = REPOSITORY
+
+ def test_all_frozen_profiles_satisfy_physical_ledgers(self):
+ for label, profile in self.profiles.items():
+ validate_profile(profile, label)
+
+ def test_frozen_exact_certificate_recomputed(self):
+ expected = json.loads((HERE / 'certificate.json').read_text())
+ actual = self.certificate.js(self.certificate.exact())
+ self.assertEqual(actual, expected)
+
+ def test_omitted_endpoint_charge_rejected(self):
+ for label, original in self.profiles.items():
+ changed = copy.deepcopy(original)
+ changed['child_multiplicities']['1'] -= changed['N']
+ with self.assertRaisesRegex(ValueError, 'rank mass'):
+ validate_profile(changed, label)
+
+ def test_nonshrinking_recursive_child_rejected(self):
+ for label, original in self.profiles.items():
+ changed = copy.deepcopy(original)
+ changed['child_multiplicities'][str(changed['m'])] = 1
+ with self.assertRaisesRegex(ValueError, 'recursive child'):
+ validate_profile(changed, label)
+
+ def test_understated_role_count_rejected(self):
+ changed = copy.deepcopy(self.profiles['complex'])
+ changed['R'] -= 1
+ with self.assertRaisesRegex(ValueError, 'physical ledger'):
+ validate_profile(changed, 'complex')
+
+ def test_overstated_matching_rejected(self):
+ changed = copy.deepcopy(self.profiles['complex'])
+ changed['links'] += 1
+ with self.assertRaisesRegex(ValueError, 'matching role ledger'):
+ validate_profile(changed, 'complex')
+
+ def test_missing_transitive_dependency_rejected(self):
+ changed = copy.deepcopy(self.manifest)
+ del changed['repository_files']['scripts/exclusion_circuit.py']
+ with self.assertRaisesRegex(ValueError, 'dependency closure'):
+ check_sources(HERE, REPOSITORY, changed)
+
+ def test_omitted_physical_input_rejected(self):
+ changed = copy.deepcopy(self.manifest)
+ del changed['package_files']['inputs/deferred_23.json.gz']
+ with self.assertRaisesRegex(ValueError, 'finite-input closure'):
+ check_sources(HERE, REPOSITORY, changed)
+
+ def test_changed_input_digest_rejected(self):
+ changed = copy.deepcopy(self.manifest)
+ changed['package_files']['inputs/witness_23.json.gz'] = '0' * 64
+ with self.assertRaisesRegex(ValueError, 'hash mismatch'):
+ check_sources(HERE, REPOSITORY, changed)
+
+ def test_omitted_pinned_complex_dag_rejected(self):
+ changed = copy.deepcopy(self.manifest)
+ del changed['package_files']['inputs/complex-dag.json.gz']
+ with self.assertRaisesRegex(ValueError, 'finite-input closure'):
+ check_sources(HERE, REPOSITORY, changed)
+
+ def test_changed_complex_dag_digest_rejected(self):
+ with tempfile.TemporaryDirectory(prefix='shrunk-frames-altered-dag-') as directory:
+ package = Path(directory)
+ for name in self.manifest['package_files']:
+ target = package / name
+ target.parent.mkdir(parents=True, exist_ok=True)
+ shutil.copyfile(HERE / name, target)
+ name = 'inputs/complex-dag.json.gz'
+ path = package / name
+ graph = json.loads(gzip.decompress(path.read_bytes()))
+ graph['args'][0] = graph['args'][1]
+ path.write_bytes(gzip.compress(json.dumps(graph).encode(), mtime=0))
+ with self.assertRaisesRegex(ValueError, 'hash mismatch'):
+ check_sources(package, REPOSITORY, self.manifest)
+ # Rehashing a substituted DAG must not erase its immutable provenance.
+ changed = copy.deepcopy(self.manifest)
+ changed['package_files'][name] = digest(path)
+ with self.assertRaisesRegex(ValueError, 'scalar-DAG provenance digest mismatch'):
+ check_sources(package, REPOSITORY, changed)
+
+ def test_replayed_complex_dag_rejects_duplicated_operand(self):
+ from replayed_producer import build
+ with tempfile.TemporaryDirectory(prefix='shrunk-frames-invalid-dag-') as directory:
+ graph = json.loads(gzip.decompress((HERE / 'inputs/complex-dag.json.gz').read_bytes()))
+ graph['args'][0] = graph['args'][1]
+ path = Path(directory) / 'invalid.json.gz'
+ path.write_bytes(gzip.compress(json.dumps(graph).encode(), mtime=0))
+ with self.assertRaisesRegex(AssertionError, 'cancellation-free'):
+ build(path, Path(directory) / 'invalid-producer')
+
+ def test_manifest_parent_escape_rejected(self):
+ with self.assertRaisesRegex(ValueError, 'Unsafe manifest path'):
+ safe_file(HERE, '../certificate.json')
+
+ def test_changed_regenerated_profile_rejected(self):
+ with tempfile.TemporaryDirectory(prefix='shrunk-frames-negative-') as directory:
+ changed = copy.deepcopy(self.profiles['complex'])
+ changed['child_multiplicities']['1'] += 1
+ path = Path(directory) / 'changed.json'
+ path.write_text(json.dumps(changed))
+ with self.assertRaisesRegex(ValueError, 'Frozen generated record mismatch'):
+ compare_json(path, HERE / 'complex-profile.json')
+
+ def test_next_bit_and_complex_grid_points_rejected(self):
+ from fractions import Fraction as Q
+ module = self.certificate
+ self.assertFalse(module.contracts(module.profile('bit-profile.json'), module.COARSE + Q(1, 10**10)))
+ self.assertFalse(module.contracts(module.profile('complex-profile.json'), module.COMPLEX + Q(1, 10**12)))
+
+ def test_unshrunk_pr114_profile_rejects_new_complex_saving(self):
+ module = self.certificate
+ previous = json.loads((HERE / 'controls/pr114-complex-profile.json').read_text())
+ previous['child_multiplicities'] = {int(t): c for t, c in previous['child_multiplicities'].items()}
+ self.assertEqual((previous['R'], previous['deferred_roles']), (28705, 4706))
+ self.assertTrue(module.contracts(previous, module.Q(109305097, 10**12)))
+ self.assertFalse(module.contracts(previous, module.COMPLEX))
+ self.assertTrue(module.contracts(module.profile('complex-profile.json'), module.COMPLEX))
+
+ def test_optimized_verifier_rejected_before_any_regeneration(self):
+ result = subprocess.run([sys.executable, '-O', str(HERE / 'verify.py')],
+ capture_output=True, text=True)
+ self.assertNotEqual(result.returncode, 0)
+ self.assertIn('optimized Python is forbidden', result.stderr)
+
+
+def main():
+ global REPOSITORY
+ parser = argparse.ArgumentParser(description=__doc__)
+ parser.add_argument('--repository-root', type=Path, default=REPOSITORY)
+ args = parser.parse_args()
+ REPOSITORY = args.repository_root.resolve()
+ suite = unittest.defaultTestLoader.loadTestsFromTestCase(FrozenControls)
+ result = unittest.TextTestRunner(verbosity=2).run(suite)
+ if not result.wasSuccessful():
+ raise SystemExit(1)
+
+
+if __name__ == '__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/verify.py b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/verify.py
new file mode 100644
index 0000000000..b1a718029c
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/research/shrunk-frames/verify.py
@@ -0,0 +1,254 @@
+#!/usr/bin/env python3
+"""Read-only verification of the frozen shrunk-frame deferred finite package.
+
+Regeneration occurs only in a temporary repository-shaped copy. Source hashes,
+complete profile ledgers, the exact certificate, and the independent reflection
+audit are required. General transfer proofs and the inherited round-seven bit
+word/frame justification remain separate dependencies. Prepared for eumemic
+with OpenAI Codex assistance; inherited authorship and licenses are retained.
+"""
+import sys
+sys.dont_write_bytecode = True
+if sys.flags.optimize:
+ raise ValueError('Verification requires assertions; optimized Python is forbidden')
+
+import argparse
+import ast
+from hashlib import sha256
+import json
+from math import comb
+import os
+from pathlib import Path
+import shutil
+import subprocess
+import tempfile
+
+HERE = Path(__file__).resolve().parent
+COMPLEX_DAG_PIN = '3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b'
+BIT_PINS = {
+ 'witness_23.json.gz': 'b2486aa2bb222bacea6e52162a3920780e45dd8edc5d7cb03eabea336a1c6588',
+ 'deferred_23.json.gz': '8c38e947ff9e021e308000dd82bb5e2194eb265d8b75194e22ce783d3e75317c',
+}
+REQUIRED = {
+ 'verify.py', 'test_controls.py', 'producer.py', 'complex_deferred.py',
+ 'bit_round7.py', 'certificate.py', 'bit-profile.json',
+ 'complex-profile.json', 'certificate.json', 'replayed_producer.py',
+ 'inputs/complex-dag.json.gz', 'controls/pr114-complex-profile.json',
+ *('inputs/' + name for name in BIT_PINS),
+}
+DATA_DEPENDENCIES = {'certificates/copied-centers-network.json'}
+
+
+def require(condition, message):
+ if not condition:
+ raise ValueError(message)
+
+
+def safe_file(directory, name):
+ relative = Path(name)
+ require(not relative.is_absolute() and '..' not in relative.parts,
+ 'Unsafe manifest path: ' + name)
+ path = (directory / relative).resolve()
+ require(path.is_relative_to(directory.resolve()) and path.is_file(),
+ 'Missing or escaping manifest file: ' + name)
+ return path
+
+
+def digest(path):
+ return sha256(path.read_bytes()).hexdigest()
+
+
+def dependency_closure(package, repository, package_scripts):
+ """Include every local Python import, including package __init__ modules.
+
+ All package scripts are roots, also covering explicit importlib loading of
+ the producer and audited source. Only stdlib imports may be unresolved.
+ The sole external data read used by exact assembly is listed separately.
+ """
+ pending = [package / name for name in package_scripts]
+ seen, dependencies = set(), set(DATA_DEPENDENCIES)
+ while pending:
+ path = pending.pop().resolve()
+ if path in seen:
+ continue
+ seen.add(path)
+ imports = []
+ for node in ast.walk(ast.parse(path.read_text(), filename=str(path))):
+ if isinstance(node, ast.Import):
+ imports.extend((alias.name, 0) for alias in node.names)
+ elif isinstance(node, ast.ImportFrom) and node.module:
+ imports.append((node.module, node.level))
+ for name, level in imports:
+ parts = name.split('.')
+ if not level and parts[0] in sys.stdlib_module_names:
+ continue
+ found = None
+ bases = ((path.parent.parents[level-2] if level > 1 else path.parent),) if level else (package, repository / 'scripts')
+ for base in bases:
+ module = base.joinpath(*parts)
+ for candidate in (module.with_suffix('.py'), module / '__init__.py'):
+ if candidate.is_file():
+ found = candidate.resolve()
+ break
+ if found is not None:
+ pending.append(found)
+ if found.is_relative_to((repository / 'scripts').resolve()):
+ dependencies.add(str(found.relative_to(repository.resolve())))
+ parent = found.parent
+ while parent != (repository / 'scripts').resolve():
+ initializer = parent / '__init__.py'
+ if initializer.is_file():
+ pending.append(initializer)
+ dependencies.add(str(initializer.relative_to(repository)))
+ parent = parent.parent
+ break
+ require(found is not None, 'Unpinned non-stdlib Python import: ' + name)
+ return dependencies
+
+
+def create_manifest(package, repository, reflection_script, reflection_receipt):
+ scripts = sorted(path.name for path in package.glob('*.py'))
+ names = REQUIRED | set(scripts) | {reflection_script, reflection_receipt}
+ dependencies = dependency_closure(package, repository, scripts)
+ return dict(
+ schema=1,
+ scope='Frozen finite producer, profiles, exact assembly and reflection audit; inherited all-size transfer remains conditional.',
+ package_files={name: digest(safe_file(package, name)) for name in sorted(names)},
+ repository_files={name: digest(safe_file(repository, name)) for name in sorted(dependencies)},
+ reflection=dict(script=reflection_script, receipt=reflection_receipt),
+ provenance=dict(
+ base='https://github.com/CrocSwap/integer-mult-bounds/pull/110',
+ cyclic_strips='https://github.com/CrocSwap/integer-mult-bounds/pull/111',
+ saturated_base=dict(pull_request='https://github.com/CrocSwap/integer-mult-bounds/pull/114',
+ commit='7dfa16edfa5d6452f2b10dadcbef20d26222827e'),
+ scalar_dag=dict(pull_request='https://github.com/CrocSwap/integer-mult-bounds/pull/117',
+ commit='cbb05ce504d571546d9b7794c186a613c659c3bf',
+ file='inputs/complex-dag.json.gz', sha256=COMPLEX_DAG_PIN),
+ round7_repository='https://github.com/Swapnil-jain/integer-mult-kappa',
+ round7_commit='741e7aa078392553815df7926ee17ac5e25a8c38',
+ round7_sha256=BIT_PINS),
+ attribution='Avi Eisenberg / ikeboy (PR62 and PR110, Anthropic Claude assistance); Rohan Arun (PR111, Anthropic Claude assistance); Swapnil Jain (round-seven bit word); icekylinx (retained stopped-product, copied-center and finite assembly interfaces); Zhihao Chen and RaD (retained assembly). PR117 scalar DAG is separate upstream work by eumemic with Anthropic Claude assistance, retained byte for byte with its original attribution. Saturated deferred-frame integration and verification for eumemic with OpenAI Codex assistance. Shrunk-frame step by Joel Pulikkan with Anthropic Claude assistance (PR114 base). Original source notices remain authoritative.')
+
+
+def check_sources(package, repository, manifest=None):
+ manifest = manifest or json.loads((package / 'SOURCE.json').read_text())
+ require(manifest['schema'] == 1, 'Unsupported source-manifest schema')
+ names = set(manifest['package_files'])
+ reflection = manifest['reflection']
+ require(REQUIRED | {reflection['script'], reflection['receipt']} <= names,
+ 'Incomplete package source/finite-input closure')
+ for collection, base in ((manifest['package_files'], package),
+ (manifest['repository_files'], repository)):
+ for name, expected in collection.items():
+ require(digest(safe_file(base, name)) == expected, 'Source hash mismatch: ' + name)
+ scripts = sorted(name for name in names if name.endswith('.py'))
+ expected = dependency_closure(package, repository, scripts)
+ require(set(manifest['repository_files']) == expected,
+ 'Incomplete or stale transitive repository dependency closure')
+ for name, expected in BIT_PINS.items():
+ require(manifest['package_files']['inputs/' + name] == expected,
+ 'Round-seven provenance digest mismatch: ' + name)
+ require(manifest['package_files']['inputs/complex-dag.json.gz'] == COMPLEX_DAG_PIN,
+ 'PR117 scalar-DAG provenance digest mismatch')
+ return manifest
+
+
+def validate_profile(profile, label):
+ fields = ('h', 'v', 'R', 'm', 'N', 'W', 'L', 'total_rank', 'deficit', 'maxchild')
+ require(all(type(profile[key]) is int and profile[key] > 0 for key in fields),
+ label + ': nonpositive or noninteger ledger value')
+ h, v, R, m, N, W, L = (profile[key] for key in fields[:7])
+ require(v == comb(h, 3) and m == h*h and N == v*v, label + ': dimensions')
+ require(W == 2*N + 2*v*R and L == 2*v*h*(h-1), label + ': physical ledger')
+ rows = {int(t): count for t, count in profile['child_multiplicities'].items()}
+ require(len(rows) == len(profile['child_multiplicities']), label + ': duplicate child widths')
+ require(all(0 < t < m and type(count) is int and count > 0 for t, count in rows.items()),
+ label + ': invalid recursive child')
+ require(sum(t*count for t, count in rows.items()) == profile['total_rank'] == W*m-N+L,
+ label + ': rank mass')
+ require(profile['deficit'] == N-L and profile['maxchild'] == max(rows),
+ label + ': deficit or maximum child')
+ require(rows.get((h-1)**2) == 2*N and rows.get(1, 0) >= N,
+ label + ': omitted data projector or endpoint charge')
+ if label == 'complex':
+ require(R == profile['additions']+profile['roots']-profile['links'],
+ 'complex: addition/roots/matching role ledger')
+ require(sum(profile['deferred_dims'].values()) == profile['deferred_roles'],
+ 'complex: deferral inventory')
+ return rows
+
+
+def compare_json(actual, expected):
+ require(json.loads(actual.read_text()) == json.loads(expected.read_text()),
+ 'Frozen generated record mismatch: ' + expected.name)
+
+
+def snapshot(package, repository, manifest):
+ return {
+ **{'package:' + n: digest(package / n) for n in manifest['package_files']},
+ **{'repository:' + n: digest(repository / n) for n in manifest['repository_files']},
+ 'manifest': digest(package / 'SOURCE.json'),
+ }
+
+
+def verify(package, repository):
+ manifest = check_sources(package, repository)
+ before = snapshot(package, repository, manifest)
+ for label in ('bit', 'complex'):
+ validate_profile(json.loads((package / (label + '-profile.json')).read_text()), label)
+ environment = dict(os.environ, PYTHONDONTWRITEBYTECODE='1')
+ environment.pop('PYTHONPATH', None)
+ with tempfile.TemporaryDirectory(prefix='shrunk-frames-verify-') as directory:
+ root = Path(directory)
+ target = root / 'research/shrunk-frames'
+ for collection, source, destination in (
+ (manifest['package_files'], package, target),
+ (manifest['repository_files'], repository, root)):
+ for name in collection:
+ out = destination / name
+ out.parent.mkdir(parents=True, exist_ok=True)
+ shutil.copyfile(source / name, out)
+ shutil.copyfile(package / 'SOURCE.json', target / 'SOURCE.json')
+
+ def run(script, *arguments):
+ subprocess.run([sys.executable, str(target / script), *map(str, arguments)],
+ cwd=root, env=environment, check=True)
+
+ run('bit_round7.py', target / 'inputs')
+ compare_json(target / 'bit-profile.json', package / 'bit-profile.json')
+ print('PASS pinned round-seven bit ledger regenerated', flush=True)
+ run('complex_deferred.py')
+ compare_json(target / 'complex-profile.json', package / 'complex-profile.json')
+ print('PASS complete complex producer and deferred profile regenerated', flush=True)
+ run('certificate.py')
+ reflection = manifest['reflection']
+ actual_reflection = root / 'actual-reflection.json'
+ run(reflection['script'], '--source', target / 'complex_deferred.py',
+ '--output', actual_reflection)
+ compare_json(actual_reflection, package / reflection['receipt'])
+ print('PASS independent literal reflection and scalar-charge audit', flush=True)
+ run('test_controls.py', '--repository-root', root)
+ require(snapshot(package, repository, manifest) == before,
+ 'Verification changed the frozen package or a dependency')
+ print('PASS read-only finite package verification; inherited transfer remains conditional', flush=True)
+
+
+def main():
+ parser = argparse.ArgumentParser(description=__doc__)
+ parser.add_argument('--repository-root', type=Path, default=HERE.parents[1])
+ parser.add_argument('--freeze-manifest', action='store_true',
+ help='Explicit authoring operation: replace SOURCE.json from reviewed files')
+ parser.add_argument('--reflection-script', default='reflection_audit.py')
+ parser.add_argument('--reflection-receipt', default='reflection-audit.json')
+ args = parser.parse_args()
+ repository = args.repository_root.resolve()
+ if args.freeze_manifest:
+ manifest = create_manifest(HERE, repository, args.reflection_script, args.reflection_receipt)
+ (HERE / 'SOURCE.json').write_text(json.dumps(manifest, indent=2, sort_keys=True) + '\n')
+ print('Frozen source manifest; this operation does not certify the package')
+ else:
+ verify(HERE, repository)
+
+
+if __name__ == '__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/audit_short_guards.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/audit_short_guards.py
new file mode 100644
index 0000000000..e5c52c8afe
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/audit_short_guards.py
@@ -0,0 +1,183 @@
+#!/usr/bin/env python3
+"""Short working guards and an explicit, still-unproved gathering target.
+
+The packed gadget and address permutation are checked exactly. No fast tape
+implementation of gathering is claimed; independent window moves are linear
+in the number of windows and do not achieve the required saving.
+"""
+from fractions import Fraction as Q
+from pathlib import Path
+import json
+
+from certify import require, verify_sources
+from prepare_layers import serializable, scenarios
+
+ROOT=Path(__file__).resolve().parents[1]
+ROTATIONS=(('y',-1,0),('z',-1,0),('y',1,0),('z',1,0),
+ ('z',1,1),('y',1,1),('z',-1,1),('y',-1,1))
+
+
+def guard_width(p):
+ require(isinstance(p,int) and p>=2,'Integer p>=2 required')
+ return 4*(p-1).bit_length()+6
+
+
+def gather_order(f,K,rho,g):
+ """Input bit indices in output low-to-high order for one slot.
+
+ Gather the first f-1 windows into the most significant contiguous field.
+ Keep the remaining coordinates in relative order in a spectator field.
+ The highest selected bit is omitted and handled separately after undo.
+ """
+ require(f>=1 and K>=1 and 0<=rho>source)&1)<>target)&1)<>(j*g))&1)<<(j*g) for j in range(n))
+
+
+def rotate_gadget(x,y,z,n,g,*,inverse=False):
+ """Eight modular rotations on compact n*g-bit slots, omitting the top bit."""
+ require(n>=1 and g>=1,'Nonempty compact slots required')
+ modulus=1<<(n*g)
+ state={'y':y,'z':z}
+ operations=reversed(ROTATIONS) if inverse else ROTATIONS
+ for target,sign,test in operations:
+ other=state['z' if target=='y' else 'y']
+ offset=sum(1<<(j*g) for j in range(n-1)
+ if x>>(j*g)&1 and (other>>(j*g)&1)==test)
+ state[target]=(state[target]+(-sign if inverse else sign)*offset)%modulus
+ return x,state['y'],state['z']
+
+
+def exceptional(y,z,n,g):
+ mask=(1<>(j*g))&mask)//2<=maximum
+ for slot in (y,z) for j in range(n-1))
+
+
+def compact_add(x,y,z,n,g):
+ """Exact address map, including the existing exceptional-set correction.
+
+ This simulates addresses, not a tape implementation or its running time.
+ For g<6 every guard may be exceptional; those cases are finite controls.
+ """
+ out=rotate_gadget(x,y,z,n,g)
+ if exceptional(out[1],out[2],n,g):
+ original=rotate_gadget(*out,n,g,inverse=True)
+ out=(original[0],original[1]^active_mask(original[0],n-1,g),original[2])
+ # Supply the most significant selected bit omitted by the rotations.
+ top=(n-1)*g
+ return out[0],out[1]^(((out[0]>>top)&1)<>rho)&1)<>spectator_width for v in packed]
+ updated=compact_add(*data,n,g)
+ result=[ungather((new<>top)&1)<= 64*p**4,'Short guard inequality failed')
+ # Before inserting A<=C*p and R superpolynomial, the bad fraction is
+ # bounded by 80*f*2^-g <= (5/4)*p^-3. This deliberately overcounts.
+ fraction=Q(80*f,1<0 and
+ 0=0,'Invalid exponent hypothesis')
+ gathering=r+theta*c+(1-beta)*max(sigma-r,Q(0))
+ compact=tau+(1-beta)*max(sigma-tau,Q(0))
+ leaf=sigma+beta*(1-sigma)
+ return dict(gathering=gathering,compact_gadget=compact,leaf=leaf,
+ layer=max(gathering,compact,leaf),
+ status='IMPLICATION OF AN UNPROVED GATHERING BOUND')
+
+
+def monotone_lengths(permutation):
+ """Small exact LIS/LDS control; no inference about unrestricted tape time."""
+ inc=[1]*len(permutation);dec=[1]*len(permutation)
+ for i,x in enumerate(permutation):
+ for j in range(i):
+ if permutation[j]x:dec[i]=max(dec[i],dec[j]+1)
+ return max(inc,default=0),max(dec,default=0)
+
+
+def monotone_stream_obstruction(guard_bits,active_bits):
+ """A restricted transpose inside an extreme-field gathering permutation.
+
+ For A guard values and B active values, any global monotone output stream
+ contains at most A+B-1 of the AB selected records. This only rules out a
+ bounded number of one-shot global monotone streams; nested local reversals
+ and coded tape algorithms are outside this model.
+ """
+ require(guard_bits>=1 and active_bits>=1,'Need two nonempty variable fields')
+ A,B=1<= 20, "C1 must cover the upstream guard bound")
+ else:
+ # Caller must also certify m>=3 and 2<=s_c= 2 and p.beta >= Q(9, 10),
+ "Stopping guard requires C1>=2 and beta>=9/10")
+ slacks = constraints(p, layout_model=layout_model, assembly_model=assembly_model)
+ for name, slack in slacks.items():
+ require(slack > 0, f"Failed strict constraint: {name} ({slack})")
+ gs = margins(p, layout_model=layout_model, assembly_model=assembly_model)
+ if strict_margin:
+ require(min(gs.values()) > p.kappa, "Need a positive absorption gap")
+ else:
+ require(min(gs.values()) >= 2*p.kappa,
+ "The proposed patch requires every g_i >= 2*kappa")
+ result = {"parameters": {k: str(v) for k, v in vars(p).items()},
+ "constraint_slacks": {k: str(v) for k, v in slacks.items()},
+ "margins": {k: str(v) for k, v in gs.items()},
+ "minimum_margin": str(min(gs.values())),
+ "limiting_margins": [k for k, v in gs.items() if v == min(gs.values())],
+ "all_margins_at_least_twice_kappa": min(gs.values()) >= 2*p.kappa,
+ "absorption_gap": str(min(gs.values())-p.kappa),
+ "slack_rule": "strict" if strict_margin else "half",
+ "generalized_beta": generalized_beta}
+ if assembly_model != "original" or guard_model != "original":
+ result.update(assembly_model=assembly_model, guard_model=guard_model)
+ return result
+
+
+def network(h):
+ """Generalized counts only; these do not prove the network interface."""
+ require(h > 6 and h != 9, "Need spare coordinates and nondegenerate rational form")
+ v, m = comb(h, 3), h**3
+ N, I = v**3, 3*v**2
+ zb, zc = 3*comb(h-3, 2), comb(h-3, 3)+3*(h-3)
+ Wb, Wc = 2*N+I*(v*zb+h), 2*N+I*(v*zc+h+1)
+ Lb, Lc = I*h*h, I*(h+1)*h
+ sb, sc = Wb*m-N+2*Lb, Wc*m-2*N+2*Lc
+ eb, ec = Q(Wb*m-sb, Wb*m), Q(Wc*m-sc, Wc*m)
+ E = 64*(Wc+m+1)**3
+ B = sc+E
+ nu = 1
+ while m**nu < B:
+ nu += 1
+ return dict(h=h, v=v, m=m, N=N, I=I, zb=zb, zc=zc,
+ Wb=Wb, Wc=Wc, Lb=Lb, Lc=Lc, sb=sb, sc=sc,
+ eta_b=eb, eta_c=ec, B=B, nu=nu, C1=max(20, nu+3))
+
+
+def certify_network(h, k, log_bound):
+ n = network(h)
+ # A positive Taylor partial sum below exp(log_bound) proves m n["m"], "Could not certify the logarithm bound")
+ for key in ("eta_b", "eta_c"):
+ require(n[key] > log_bound*dyadic(k), f"Insufficient deficit: {key}")
+ require(2*n["Lb"] < n["N"] and 2*n["Lc"] < n["N"],
+ "The generalized residual lemma requires L A*LOG_BOUND for key in ("eta_b", "eta_c")),
+ "Rank deficit does not support the requested rational saving")
+ certify_network(46, 36, 12) # Residual and guard conditions.
+ return {"h": 46, "saving": str(A), "log_bound": str(LOG_BOUND),
+ "log_lower": str(lo), "log_upper": str(hi),
+ "deficit_slacks": {k: str(n[k]-A*LOG_BOUND) for k in ("eta_b", "eta_c")}}
+
+
+def certificates():
+ return {
+ "upstream_commit": verify_sources(),
+ "scope": "Exact numerical certificates, conditional on the upstream proof interfaces",
+ "cases": {name: certify_parameters(p) for name, p in {
+ "baseline_182": BASELINE, "frozen_154": proposed(50),
+ "same_network_130": proposed(42), "h46_112": proposed(36),
+ "balanced_frozen_153": balanced(50),
+ "balanced_same_network_129": balanced(42),
+ "balanced_h46_111": balanced(36),
+ "near_supremum_frozen": near_supremum(50),
+ "near_supremum_same_network": near_supremum(42),
+ "near_supremum_h46": near_supremum(36),
+ }.items()} | {
+ f"pushed_{v}": certify_parameters(pushed(v), generalized_beta=v != "109",
+ strict_margin=True)
+ for v in ("109", "108", "rational")
+ },
+ "networks": {
+ "baseline_h100": certify_network(100, 50, 20),
+ "improved_h100": certify_network(100, 42, 14),
+ "improved_h46": certify_network(46, 36, 12),
+ "rational_h46": certify_rational_network(),
+ },
+ }
+
+
+if __name__ == "__main__":
+ result = certificates()
+ out = ROOT / "certificates/parameters.json"
+ out.parent.mkdir(exist_ok=True)
+ out.write_text(json.dumps(result, indent=2, sort_keys=True) + "\n")
+ for name, case in result["cases"].items():
+ print(f"PASS {name}: minimum {case['minimum_margin']} ({', '.join(case['limiting_margins'])})")
+ print(f"Wrote {out.relative_to(ROOT)}")
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/compact_control_layer.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/compact_control_layer.py
new file mode 100644
index 0000000000..11b2e751bf
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/compact_control_layer.py
@@ -0,0 +1,156 @@
+#!/usr/bin/env python3
+"""Exact accounting for the written compact-control layer extension.
+
+Arithmetic checks accompany, and do not replace, the fixed-tape construction
+and proof. Historical witnesses and pinned upstream files are unchanged.
+"""
+from fractions import Fraction as Q
+from pathlib import Path
+import hashlib
+import json
+
+from certify import Parameters,constraints,margins,network,require,verify_sources
+from paired_network import BIT_SAVING
+from prepare_layers import guard,packed_exponents,complex_saving_bounds,serializable
+from search_network import log_integer_bounds
+from audit_short_guards import guard_width
+
+ROOT=Path(__file__).resolve().parents[1]
+COMPLEX_H=25
+COMPLEX_SAVING=Q(418,10**12)
+KAPPA=Q(83,10**12)
+
+
+def ceil_log(n,base):
+ require(n>=1 and base>=2,'Invalid logarithm')
+ j=0;power=1
+ while power=1 and min(m,W)>=2,'Invalid dimensions')
+ q0=ceil_log(W,2)*ceil_log(2*d,m)
+ k0=ceil_log(d,m)
+ H=d*G
+ front=(2*H+K-1)//K;back=(H+K-1)//K
+ reserved=q0+front+back
+ require(q0*K>=k0*ceil_log(W,2),'Insufficient row divisor capacity')
+ require(front*K>=2*H and back*K>=H,'Insufficient compact fields')
+ return dict(d=d,D=D,K=K,G=G,compact_capacity=H,row_chunks=q0,
+ front_chunks=front,back_chunks=back,reserved_chunks=reserved,
+ recursion_depth_cap=k0,row_bits=q0*K,
+ mode='individual' if D<=reserved else 'recursive',
+ active_chunks=max(0,D-reserved),
+ preprocessed_chunks=min(D,reserved),
+ front_slack_bits=front*K-2*H,back_slack_bits=back*K-H)
+
+
+def repair_bound(p,n,K):
+ require(p>=2 and 0<=n<=p,'Invalid repair family')
+ G=guard_width(p);ell=(p-1).bit_length()
+ require(K>=G+4*ell+10,'Use the common eventual cutoff')
+ delta=Q(2*n,1<0,'Positive spacing growth required')
+ e=packed_exponents(tau,sigma,beta,c,theta=Q(0))
+ return dict(internal=e['internal'],leaf=e['leaf'],
+ preprocessing=max(Q(0),1-c),
+ layer=max(e['internal'],e['leaf'],1-c,Q(0)))
+
+
+def parameters():
+ return Parameters(tau=1-BIT_SAVING,sigma=1-COMPLEX_SAVING,
+ epsilon=Q(1999,10000),c=Q(1,5),
+ lam=1-Q(1671,4*10**12),lamp=1-Q(167,4*10**11),
+ kappa=KAPPA,beta=Q(1,1000),delta=Q(1,10**6),C1=Q(49961,10000))
+
+
+def check(p,h=COMPLEX_H,zeta=Q(1,10000)):
+ require(0<1-p.tau<=BIT_SAVING,'Bit exponent exceeds retained witness')
+ n=network(h);lo,hi=complex_saving_bounds(h)
+ require(0<1-p.sigma0,'Compact-control constraint: '+name)
+ gs=margins(p,layout_model='nonadjacent',assembly_model='tight-gaussian')
+ require(min(gs.values())>p.kappa,'No final absorption gap')
+ require(Q(1,2**34)0 for v in cs.values()),'Milestone constraint failed')
+ gs=margins(p,layout_model='nonadjacent',assembly_model='tight-gaussian')
+ require(min(gs.values())>p.kappa,'Milestone has no absorption gap')
+ return dict(parameters=vars(p),guard=g,recurrence=e,constraint_slacks=cs,
+ minimum_margin=min(gs.values()),absorption_gap=min(gs.values())-p.kappa)
+
+
+def certificate():
+ from prepare_layers import scenarios
+ p=parameters();main=check(p);n=network(COMPLEX_H)
+ _,log_hi=log_integer_bounds(n['m'])
+ require(n['eta_c']>COMPLEX_SAVING*log_hi,'Simple exponential comparison failed')
+ targets={}
+ for key,h in (('hypothetical_39',50),('hypothetical_34',25)):
+ old=scenarios()[key]
+ targets[key.replace('hypothetical_','target_')]=milestone(Parameters(**old['parameters']),h)
+ hi=complex_saving_bounds(COMPLEX_H)[1]
+ # The Gaussian margin enforces epsilon<1/5; the leaf margin limits
+ # 1-lambda' to (1-beta)*a_c 2^-34; proof review required.')
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_circuit.py
new file mode 100644
index 0000000000..9e83a1065c
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_circuit.py
@@ -0,0 +1,454 @@
+#!/usr/bin/env python3
+"""Compressed side correction for the complex network, with binary frames.
+
+Target S must receive (1/2) * sum{x_T : T disjoint from S}
+minus (1/2) * sum{x_T : |S cap T| = 2}. Both sums are computed by
+cancellation-free addition graphs and injected as pieces with those weights.
+
+Labels are subspaces of F2^h with the dot product. A disjoint-sum node carries
+the coordinate space of its covered points; a pair-star node carries the span
+of its triple indicators, which is orthonormal. An injected piece must leave a
+point outside S uncovered: the residual up to t_S^perp then contains an odd
+coordinate vector. A disjoint piece covering every point outside S would have
+the alternating residual , so the disjoint sum is split.
+"""
+from fractions import Fraction as Q
+from itertools import combinations
+
+EMPTY = frozenset()
+
+
+def subsets(points, k):
+ return [frozenset(c) for j in range(min(k, len(points))+1)
+ for c in combinations(points, j)]
+
+
+class ComplexSideCircuit:
+ def __init__(self, h):
+ assert h >= 8, 'Need at least four points outside every target'
+ self.h = h
+ self.triples = list(combinations(range(h), 3))
+ self.index = {t: i for i, t in enumerate(self.triples)}
+ self.support = [0]; self.args = [None]; self.kind = [None]
+ self.lookup = {}; self.input = {}
+ for i, t in enumerate(self.triples):
+ self.input[t] = len(self.support)
+ self.support.append(1 << i); self.args.append(None); self.kind.append('in')
+ self.points = {} # covered point masks, filled lazily
+ self.pieces = [] # (target, node, coefficient)
+ self.build_disjoint()
+ self.build_pair_stars()
+ self.prune()
+
+ # -- node store -------------------------------------------------------
+ def x(self, *pts):
+ return self.input[tuple(sorted(pts))]
+
+ def add(self, a, b, kind):
+ if not a: return b
+ if not b: return a
+ sa, sb = self.support[a], self.support[b]
+ assert not sa & sb, 'Cancellation is forbidden'
+ key = (kind, sa | sb)
+ node = self.lookup.get(key)
+ if node is None:
+ node = len(self.support)
+ self.lookup[key] = node
+ self.support.append(sa | sb); self.args.append((a, b)); self.kind.append(kind)
+ return node
+
+ def total(self, nodes, kind):
+ nodes = [x for x in nodes if x]
+ while len(nodes) > 1:
+ nodes = [self.add(nodes[i], nodes[i+1], kind) if i+1 < len(nodes) else nodes[i]
+ for i in range(0, len(nodes), 2)]
+ return nodes[0] if nodes else 0
+
+ # -- disjoint sums ----------------------------------------------------
+ def vec(self, items, k):
+ """{E: sum of item nodes whose points avoid E}, |E| <= k."""
+ if not items: return {EMPTY: 0}
+ if len(items) == 1:
+ p, node = items[0]
+ return {EMPTY: node, frozenset([p]): 0} if k else {EMPTY: node}
+ half = len(items)//2
+ A = self.vec(items[:half], k); B = self.vec(items[half:], k)
+ return {ea | eb: self.add(xa, xb, 'd0') for ea, xa in A.items()
+ for eb, xb in B.items() if len(ea)+len(eb) <= k}
+
+ def pairs(self, pts, weight, k):
+ """{E: sum of weight(u,v) over pairs avoiding E}, |E| <= k."""
+ if len(pts) < 2: return {E: 0 for E in subsets(pts, k)}
+ half = len(pts)//2; L, R = pts[:half], pts[half:]
+ PL = self.pairs(L, weight, k); PR = self.pairs(R, weight, k)
+ rows = {u: self.vec([(r, weight(u, r)) for r in R], k) for u in L}
+ cross = {}
+ for ER in subsets(R, k):
+ for EL, node in self.vec([(u, rows[u][ER]) for u in L], k-len(ER)).items():
+ cross[EL, ER] = node
+ return {EL | ER: self.total([xl, xr, cross[EL, ER]], 'd0')
+ for EL, xl in PL.items() for ER, xr in PR.items() if len(EL)+len(ER) <= k}
+
+ def tri_parts(self, pts, k):
+ """Recursive halves and the two mixed families, before combination."""
+ half = len(pts)//2; L, R = pts[:half], pts[half:]
+ TL = self.tri(L, k); TR = self.tri(R, k)
+ PR = {r: self.pairs(L, lambda u, v, r=r: self.x(u, v, r), k) for r in R}
+ PL = {u: self.pairs(R, lambda a, b, u=u: self.x(u, a, b), k) for u in L}
+ return L, R, TL, TR, PR, PL
+
+ def tri(self, pts, k):
+ """{E: sum of triples inside pts avoiding E}, |E| <= k."""
+ if len(pts) < 3: return {E: 0 for E in subsets(pts, k)}
+ L, R, TL, TR, PR, PL = self.tri_parts(pts, k)
+ c21 = {}; c12 = {}
+ for EL in subsets(L, k):
+ for ER, node in self.vec([(r, PR[r][EL]) for r in R], k-len(EL)).items():
+ c21[EL, ER] = node
+ for ER in subsets(R, k):
+ for EL, node in self.vec([(u, PL[u][ER]) for u in L], k-len(ER)).items():
+ c12[EL, ER] = node
+ return {EL | ER: self.total([xl, xr, c21[EL, ER], c12[EL, ER]], 'd0')
+ for EL, xl in TL.items() for ER, xr in TR.items() if len(EL)+len(ER) <= k}
+
+ def build_disjoint(self):
+ """Six pieces per target, each leaving an outside point uncovered."""
+ pts = list(range(self.h))
+ L, R, TL, TR, PR, PL = self.tri_parts(pts, 3)
+ R1, R2 = R[:len(R)//2], R[len(R)//2:]
+ L1, L2 = L[:len(L)//2], L[len(L)//2:]
+ for S in self.triples:
+ E = frozenset(S); EL = E & frozenset(L); ER = E & frozenset(R)
+ pieces = [TL[EL], TR[ER]]
+ for half in (R1, R2):
+ pieces.append(self.vec([(r, PR[r][EL]) for r in half], 3-len(EL))[ER & frozenset(half)])
+ for half in (L1, L2):
+ pieces.append(self.vec([(u, PL[u][ER]) for u in half], 3-len(ER))[EL & frozenset(half)])
+ for node in pieces: self.emit(S, node, Q(1, 2))
+
+ # -- pair stars -------------------------------------------------------
+ def build_pair_stars(self):
+ """Prefix and suffix pair-star sums around each excluded third point."""
+ h = self.h
+ for a, b in combinations(range(h), 2):
+ others = [u for u in range(h) if u not in (a, b)]
+ n = len(others)
+ pre = [0]
+ for u in others: pre.append(self.add(pre[-1], self.x(a, b, u), 'd2'))
+ suf = [0]*(n+1)
+ for i in range(n-1, -1, -1): suf[i] = self.add(self.x(a, b, others[i]), suf[i+1], 'd2')
+ for i, c in enumerate(others):
+ S = tuple(sorted((a, b, c)))
+ self.emit(S, pre[i], Q(-1, 2)); self.emit(S, suf[i+1], Q(-1, 2))
+
+ def emit(self, S, node, coef):
+ """Inject a piece, splitting it until it leaves a point outside S uncovered."""
+ if not node: return
+ if self.cover(node) | sum(1 << p for p in S) == (1 << self.h)-1:
+ a, b = self.args[node]
+ self.emit(S, a, coef); self.emit(S, b, coef)
+ else:
+ self.pieces.append((S, node, coef))
+
+ # -- bookkeeping ------------------------------------------------------
+ def prune(self):
+ self.active = set(); stack = [node for _, node, _ in self.pieces]
+ while stack:
+ node = stack.pop()
+ if node in self.active: continue
+ self.active.add(node)
+ if self.args[node]: stack.extend(self.args[node])
+ self.additions = sum(self.args[n] is not None for n in self.active)
+ self.roles = self.additions + len(self.pieces)
+
+ def cover(self, node):
+ """Mask of ground points covered by the node's source triples."""
+ if node not in self.points:
+ s = self.support[node]; mask = 0
+ while s:
+ low = s & -s; mask |= sum(1 << p for p in self.triples[low.bit_length()-1]); s ^= low
+ self.points[node] = mask
+ return self.points[node]
+
+ def stats(self):
+ v = len(self.triples)
+ return dict(h=self.h, v=v, additions=self.additions, injections=len(self.pieces),
+ roles=self.roles, roles_per_target=round(self.roles/v, 3),
+ disjoint_additions=sum(self.kind[n] == 'd0' for n in self.active),
+ pair_star_additions=sum(self.kind[n] == 'd2' for n in self.active))
+
+
+# -- binary linear algebra on F2^h, vectors as integer masks ---------------
+def echelon(vectors):
+ """Reduced basis {pivot bit: vector}; raises on dependence."""
+ basis = {}
+ for x in vectors:
+ for bit, b in basis.items():
+ if x & bit: x ^= b
+ assert x, 'Dependent label vectors'
+ bit = x & -x
+ for other in basis:
+ if basis[other] & bit: basis[other] ^= x
+ basis[bit] = x
+ return basis
+
+
+def reduce(basis, x):
+ for bit, b in basis.items():
+ if x & bit: x ^= b
+ return x
+
+
+def dot(x, y):
+ return (x & y).bit_count() & 1
+
+
+def rank(rows):
+ rows = list(rows); r = 0
+ for col in range(max((x.bit_length() for x in rows), default=0)):
+ bit = 1 << col
+ pivot = next((i for i in range(r, len(rows)) if rows[i] & bit), None)
+ if pivot is None: continue
+ rows[r], rows[pivot] = rows[pivot], rows[r]
+ for i in range(len(rows)):
+ if i != r and rows[i] & bit: rows[i] ^= rows[r]
+ r += 1
+ return r
+
+
+class Label:
+ """A binary subspace with a canonical basis."""
+ def __init__(self, vectors):
+ self.basis = echelon(vectors); self.dim = len(self.basis)
+ self.key = tuple(sorted(self.basis.values()))
+
+ def contains(self, other):
+ return all(not reduce(self.basis, x) for x in other.basis.values())
+
+ def nondegenerate(self):
+ vs = list(self.basis.values())
+ return rank([sum(dot(a, b) << j for j, b in enumerate(vs)) for a in vs]) == len(vs)
+
+ def complement_in(self, other):
+ """Basis of other ∩ self^perp, assuming self ⊆ other."""
+ vs = list(other.basis.values()); us = list(self.basis.values()); k = len(us)
+ rows = [sum(dot(v, u) << j for j, u in enumerate(us)) | 1 << (k+i)
+ for i, v in enumerate(vs)]
+ r = 0
+ for col in range(k):
+ bit = 1 << col
+ piv = next((i for i in range(r, len(rows)) if rows[i] & bit), None)
+ if piv is None: continue
+ rows[r], rows[piv] = rows[piv], rows[r]
+ for i in range(len(rows)):
+ if i != r and rows[i] & bit: rows[i] ^= rows[r]
+ r += 1
+ out = []
+ for row in rows[r:]:
+ assert not row & ((1 << k)-1)
+ x = 0
+ for i, v in enumerate(vs):
+ if row >> (k+i) & 1: x ^= v
+ out.append(x)
+ return out
+
+
+def odd(vectors):
+ return any(x.bit_count() & 1 for x in vectors)
+
+
+# -- exact checks -----------------------------------------------------------
+def tmask(t):
+ return sum(1 << p for p in t)
+
+
+class Checks:
+ """Exact verification of the side map, labels and compiled roles."""
+ def __init__(self, c):
+ self.c = c; self.h = c.h; self.cache = {}; self.verdicts = {}
+ self.everything = Label([1 << p for p in range(c.h)])
+
+ def label(self, node):
+ if node in self.cache: return self.cache[node]
+ c = self.c; kind = c.kind[node]
+ if kind == 'in':
+ vectors = [tmask(c.triples[node-1])]
+ elif kind == 'd0':
+ m = c.cover(node); vectors = [1 << p for p in range(self.h) if m >> p & 1]
+ else:
+ s = c.support[node]; ts = []
+ while s:
+ low = s & -s; ts.append(c.triples[low.bit_length()-1]); s ^= low
+ common = set(ts[0]).intersection(*ts)
+ assert len(common) >= 2, 'Pair-star node without a common pair'
+ vectors = [tmask(t) for t in ts]
+ lab = Label(vectors); self.cache[node] = lab
+ return lab
+
+ def target_frame(self, S):
+ t = tmask(S)
+ key = ('perp', S)
+ if key not in self.cache:
+ self.cache[key] = Label([x for x in (1 << p for p in range(self.h))
+ if not dot(x, t)] + [tmask((S[0], S[1])), tmask((S[1], S[2]))])
+ return self.cache[key]
+
+ def residual_ok(self, small, big):
+ """small ⊆ big and big ⊖ small is zero or has an odd vector."""
+ key = (small.key, big.key)
+ if key not in self.verdicts:
+ res = small.complement_in(big) if big.contains(small) else None
+ self.verdicts[key] = res is not None and (not res or odd(res))
+ return self.verdicts[key]
+
+ def label_ok(self, lab):
+ """Nondegenerate, contains an odd vector, and its complement is zero or does."""
+ key = ('label', lab.key)
+ if key not in self.verdicts:
+ perp = lab.complement_in(self.everything)
+ self.verdicts[key] = (lab.nondegenerate() and odd(lab.basis.values())
+ and (not perp or odd(perp)))
+ return self.verdicts[key]
+
+ def verify_map(self):
+ c = self.c
+ for node in c.active:
+ if c.args[node]:
+ a, b = c.args[node]
+ assert a < node and b < node and not c.support[a] & c.support[b]
+ assert c.support[node] == c.support[a] | c.support[b]
+ got = {}
+ for S, node, coef in c.pieces:
+ assert coef in (Q(1, 2), Q(-1, 2))
+ key = (S, coef)
+ assert not got.get(key, 0) & c.support[node], 'Overlapping pieces'
+ got[key] = got.get(key, 0) | c.support[node]
+ nonzero = 0
+ for S in c.triples:
+ zero = sum(1 << i for i, T in enumerate(c.triples) if not set(S) & set(T))
+ two = sum(1 << i for i, T in enumerate(c.triples) if len(set(S) & set(T)) == 2)
+ assert got.get((S, Q(1, 2)), 0) == zero and got.get((S, Q(-1, 2)), 0) == two
+ nonzero += zero.bit_count()+two.bit_count()
+ return dict(targets=len(c.triples), nonzero_coefficients=nonzero,
+ side_map_exact=True, coefficients='+1/2 disjoint, -1/2 intersection two')
+
+ def verify_labels(self):
+ c = self.c; checked = 0
+ for node in sorted(c.active):
+ lab = self.label(node)
+ assert self.label_ok(lab), node # includes the exit to the full space
+ if c.args[node]:
+ for child in c.args[node]:
+ assert self.residual_ok(self.label(child), lab), (node, child)
+ checked += 1
+ for S, node, coef in c.pieces:
+ assert self.residual_ok(self.label(node), self.target_frame(S)), (S, node)
+ checked += 1
+ return dict(active_nodes=len(c.active), checked_inclusions=checked,
+ all_labels_nondegenerate=True, all_residuals_have_odd_vectors=True)
+
+
+def compile_roles(c):
+ """Reversible roles: one per addition plus one per injected piece."""
+ users = {x: [] for x in c.active}
+ for node in sorted(c.active):
+ if c.args[node]:
+ for pos, x in enumerate(c.args[node]): users[x].append(('gate', node, pos))
+ for i, (_, node, _) in enumerate(c.pieces): users[node].append(('output', i))
+ edge = {}; sources = {}; outputs = {}; gates = []; size = 0
+ for node in sorted(c.active):
+ if c.args[node]:
+ ins = (edge[node, 0], edge[node, 1]); pivot = ins[0]
+ else:
+ pivot = size; size += 1; ins = (pivot,); sources[c.triples[node-1]] = pivot
+ assert users[node]
+ outs = (pivot,)+tuple(range(size, size+len(users[node])-1))
+ size += len(users[node])-1
+ assert len(set(ins)) == len(ins) and set(ins) & set(outs) == {pivot}
+ gates.append((node, ins, outs))
+ for user, slot in zip(users[node], outs):
+ if user[0] == 'gate': edge[user[1], user[2]] = slot
+ else: outputs[user[1]] = slot
+ assert size == c.roles
+ return dict(roles=size, gates=gates, sources=sources, outputs=outputs)
+
+
+def verify_role_frames(c, checks, code=None):
+ """Follow every physical role in both directions through its frames."""
+ code = code or compile_roles(c)
+ def step(small, big): assert checks.residual_ok(small, big)
+ frames = [None]*code['roles']
+ for T, slot in code['sources'].items(): frames[slot] = checks.label(c.input[T])
+ for node, ins, outs in code['gates']:
+ lab = checks.label(node)
+ for slot in set(ins+outs):
+ if frames[slot] is None: assert checks.label_ok(lab) # entry from D0
+ else: step(frames[slot], lab)
+ frames[slot] = lab
+ for i, slot in code['outputs'].items():
+ S = c.pieces[i][0]; J = checks.target_frame(S)
+ step(frames[slot], J); frames[slot] = J
+ for lab in frames:
+ assert checks.label_ok(lab) # includes the exit residual to D1
+ # Reverse stage: complements, traversed backward. U^perp grows iff U shrinks.
+ # Its entries and exits have the forward residuals U^perp and U, checked above.
+ back = [None]*code['roles']
+ for i, slot in code['outputs'].items(): back[slot] = ('line', c.pieces[i][0])
+ for node, ins, outs in reversed(code['gates']):
+ lab = checks.label(node)
+ for slot in set(ins+outs):
+ prev = back[slot]
+ if prev is None:
+ assert checks.label_ok(lab) # reverse entry residual is lab^perp
+ elif prev[0] == 'line': # ⊆ U^perp iff U ⊆ t_S^perp
+ step(lab, checks.target_frame(prev[1]))
+ else:
+ step(lab, prev[1]) # prev^perp ⊆ lab^perp iff lab ⊆ prev
+ back[slot] = ('node', lab)
+ for T, slot in code['sources'].items():
+ assert back[slot][1].key == checks.label(c.input[T]).key # ends at t_T^perp
+ return dict(roles=code['roles'], forward_frames_nested=True,
+ reverse_complement_frames_nested=True)
+
+
+def simulate_invocation(c, code, x, y, side, center, inverse=False):
+ """Scalar invocation over Q with arbitrary scratch; returns the new state.
+
+ Forward: L,-J,L^-1,-R,V,G,R,L,J,L^-1,G^-1,V^-1 gives y <- y + x.
+ inverse=True runs the inverted schedule, giving x <- x - y.
+ """
+ h = c.h; T = c.triples
+ side = list(side); center = dict(center); x = dict(x); y = dict(y)
+ def L(sign=1):
+ order = code['gates'] if sign > 0 else list(reversed(code['gates']))
+ for node, ins, outs in order:
+ if sign > 0:
+ if len(ins) == 2: side[ins[0]] += side[ins[1]]
+ for o in outs[1:]: side[o] += side[outs[0]]
+ else:
+ for o in outs[1:]: side[o] -= side[outs[0]]
+ if len(ins) == 2: side[ins[0]] -= side[ins[1]]
+ def J(target, sign):
+ for i, slot in code['outputs'].items():
+ S, _, coef = c.pieces[i]; target[S] += sign*coef*side[slot]
+ def V(source, sign):
+ for t, slot in code['sources'].items(): side[slot] += sign*source[t]
+ def G(source, sign):
+ for i in range(h): center[i] += sign*sum(source[t] for t in T if i in t)
+ center['*'] += sign*sum(source.values())
+ def R(target, sign):
+ for t in T: target[t] += sign*(sum(center[i] for i in t)-center['*'])/2
+ if not inverse:
+ L(); J(y, -1); L(-1); R(y, -1); V(x, 1); G(x, 1); R(y, 1)
+ L(); J(y, 1); L(-1); G(x, -1); V(x, -1)
+ else: # inverse schedule with logical source y and target x
+ V(y, 1); G(y, 1); L(); J(x, -1); L(-1); R(x, -1); G(y, -1); V(y, -1)
+ R(x, 1); L(); J(x, 1); L(-1)
+ return x, y, side, center
+
+
+if __name__ == '__main__':
+ import sys, time
+ for h in map(int, sys.argv[1:] or ['10', '12', '16']):
+ t = time.time(); c = ComplexSideCircuit(h)
+ print(c.stats(), f'{time.time()-t:.1f}s', flush=True)
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_network.py
new file mode 100644
index 0000000000..af9bb6d7b3
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/complex_network.py
@@ -0,0 +1,120 @@
+#!/usr/bin/env python3
+"""Conditional 59/10^11 witness: a compressed complex side circuit.
+
+The compact-control witness was limited by the original complex motif, whose
+v*z_c side wires per invocation dilute its rank deficit. The new side circuit
+computes the same correction with shared sums, binary coordinate and pair-star
+labels, and the bit network's transparent twelve-operation schedule. The bit
+network, compact-control movement and assembly recipe are unchanged.
+"""
+from fractions import Fraction as Q
+from math import comb
+from pathlib import Path
+import json
+
+from certify import Parameters, constraints, margins, require, verify_sources
+from compact_control_layer import layer_exponents
+from complex_circuit import ComplexSideCircuit, Checks, compile_roles, verify_role_frames
+from paired_network import BIT_SAVING
+from prepare_layers import serializable
+from search_network import log_integer_bounds
+
+ROOT = Path(__file__).resolve().parents[1]
+H = 25
+COMPLEX_SAVING = Q(14, 10**9)
+LOG_BOUND = Q(966, 100)
+KAPPA = Q(59, 10**11)
+
+
+def counts(c):
+ h = c.h; v = comb(h, 3); m = h**3; N = v**3; I = 3*v*v
+ R = c.roles; W = 2*N+I*(R+h+1); L = I*(h+1)*h
+ s = W*m-2*N+2*L
+ require(L < N, 'Complex deficit is not positive')
+ return dict(h=h, v=v, m=m, N=N, I=I, side_roles_per_invocation=R,
+ central_roles=h+1, W=W, L=L, s=s, deficit=W*m-s, eta=Q(W*m-s, W*m),
+ original_side_wires_per_invocation=v*(comb(h-3, 3)+3*(h-3)))
+
+
+def gate_count(c, n):
+ """Per invocation: four mixer passes, two copies, two injections, four central gates."""
+ per = 4*len(c.active)+4*n['v']+4
+ require(n['I']*per <= 12*n['W'], 'The 12W gate bound behind E=64(W+m+1)^3 failed')
+ return dict(gates_per_invocation=per, total_gates=n['I']*per, twelve_W=12*n['W'])
+
+
+def guard(n, beta, zeta):
+ """Generalized stopped-depth guard with the new complex constants."""
+ m, s, W = n['m'], n['s'], n['W']
+ E = 64*(W+m+1)**3; B = s+E
+ require(m >= 3 and 2 <= s < m**5, 'Unverified coefficient-depth hypothesis')
+ require(s*(8+E) <= 9*B*B, 'One-piece constant failed')
+ C1 = 5-4*beta+zeta
+ raw = max(Q(128*m*B*B), 18*m*B*B*(1+1/zeta))
+ C0 = -(-raw.numerator//raw.denominator)
+ require(9*m*B*B*(1+1/zeta)+18 <= C0, 'Whole-layer constant failed')
+ return dict(m=m, s=s, E=E, B=B, beta=beta, zeta=zeta, C0=C0, C1=C1)
+
+
+def parameters():
+ return Parameters(tau=1-BIT_SAVING, sigma=1-COMPLEX_SAVING,
+ epsilon=Q(19999, 100000), c=Q(999, 1000),
+ lam=1-Q(2958, 10**12), lamp=1-Q(2956, 10**12),
+ kappa=KAPPA, beta=Q(1, 1000), delta=Q(1, 10**6),
+ C1=Q(49961, 10000))
+
+
+def witness(p, n):
+ g = guard(n, p.beta, Q(1, 10000))
+ require(p.C1 == g['C1'], 'Guard mismatch')
+ e = layer_exponents(p.tau, p.sigma, p.beta, p.c)
+ slacks = constraints(p, layout_model='nonadjacent', assembly_model='tight-gaussian')
+ slacks['packed_overhead'] = p.lam-e['internal'] # compact control: internal = max exponent
+ slacks['reserved_axes'] = p.lamp-e['preprocessing']
+ for name, slack in slacks.items(): require(slack > 0, 'Constraint failed: '+name)
+ gs = margins(p, layout_model='nonadjacent', assembly_model='tight-gaussian')
+ require(min(gs.values()) > p.kappa, 'No final absorption gap')
+ return dict(parameters=vars(p), guard=g, recurrence=e, constraint_slacks=slacks,
+ margins=gs, minimum_margin=min(gs.values()),
+ limiting_margins=[k for k, v in gs.items() if v == min(gs.values())],
+ absorption_gap=min(gs.values())-p.kappa)
+
+
+def witness_only():
+ """Counts and parameter witness without the full finite checks (for the patch)."""
+ n = counts(ComplexSideCircuit(H))
+ require(n['eta'] > COMPLEX_SAVING*LOG_BOUND, 'Complex saving failed')
+ return witness(parameters(), n)
+
+
+def certificate():
+ c = ComplexSideCircuit(H); checks = Checks(c); code = compile_roles(c)
+ side = checks.verify_map(); labels = checks.verify_labels()
+ roles = verify_role_frames(c, checks, code)
+ n = counts(c)
+ lo, hi = log_integer_bounds(n['m'])
+ require(hi < LOG_BOUND, 'Logarithm enclosure failed')
+ require(n['eta'] > COMPLEX_SAVING*LOG_BOUND, 'Complex saving failed')
+ p = parameters(); w = witness(p, n)
+ require(Q(1, 2**31) < KAPPA < Q(1, 2**30), 'Unexpected dyadic scale')
+ # With the bit exponent fixed, g3 <= epsilon*(1-lambda) < epsilon*a_b < a_b/5.
+ ceiling = BIT_SAVING/5
+ require(ceiling < Q(1, 2**30), 'This bit network could cross 2^-30')
+ return dict(status='CONDITIONAL 59/10^11 WITNESS; COMPRESSED COMPLEX SIDE CIRCUIT; NOT FORMAL VERIFICATION',
+ upstream_commit=verify_sources(), circuit=c.stats(), side_map=side,
+ labels=labels, role_frames=roles, gates=gate_count(c, n),
+ complex_counts=n, complex_saving=COMPLEX_SAVING, log_m_upper=LOG_BOUND,
+ log_enclosure=(lo, hi), complex_deficit_slack=n['eta']-COMPLEX_SAVING*LOG_BOUND,
+ bit_saving=BIT_SAVING, witness=w,
+ improvement_over_compact_control=KAPPA/Q(83, 10**12),
+ scoped_ceiling=dict(upper=ceiling, below_2_to_minus_30=True,
+ scope='Published h=50 paired bit network and retained Gaussian margin; not a bound on other networks or algorithms.'),
+ scope='Conditional on the pinned upstream interfaces, the compact-control movement and guard proofs, the paired bit network, and the written binary-frame transfer for this complex side circuit. Exact arithmetic and finite checks are not formal verification.')
+
+
+if __name__ == '__main__':
+ result = serializable(certificate())
+ (ROOT/'certificates/complex-network.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+ print('PASS conditional', KAPPA, '> 2^-31; minimum margin', result['witness']['minimum_margin'])
+ print('Side roles per invocation', result['complex_counts']['side_roles_per_invocation'],
+ 'vs original', result['complex_counts']['original_side_wires_per_invocation'])
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/__init__.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/__init__.py
new file mode 100644
index 0000000000..e0758c53ca
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/__init__.py
@@ -0,0 +1 @@
+"""Copied-center incremental certificates, copyright 2026 icekylinx."""
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/corners.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/corners.py
new file mode 100644
index 0000000000..80fc438270
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/corners.py
@@ -0,0 +1,142 @@
+"""Exact selected PR31/PR33 corner witness and zero-minor verification.
+
+Original corner and incidence methods: Rohan Arun, PR31, commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305 (Apache-2.0; OpenAI Codex assistance).
+Parameterization: Dominik Scholz, PR33, commit
+a499a345c040aa15b68e984a0904eadc485c7a7e (Apache-2.0; recorded Anthropic
+Claude Opus 5.5 and OpenAI GPT-6 Astra/Codex assistance).
+Modification copyright 2026 icekylinx, Apache-2.0, with OpenAI GPT-6 Astra
+and Codex assistance: verify the selected (25,23) saved partitions directly;
+omit exploratory matroid search and unrelated historical dimensions.
+See repository NOTICE, LICENSE and SOURCES.json for retained notices.
+"""
+from fractions import Fraction as Q
+from functools import reduce
+from math import gcd
+
+
+def require(condition, message):
+ if not condition:
+ raise ValueError(message)
+
+
+def integer_rank(matrix):
+ """PR31 exact rank by integer row operations and gcd reduction."""
+ matrix = [row[:] for row in matrix]
+ height = len(matrix)
+ width = len(matrix[0]) if height else 0
+ rank = 0
+ for col in range(width):
+ pivot = next((r for r in range(rank,height) if matrix[r][col]),None)
+ if pivot is None:
+ continue
+ matrix[rank],matrix[pivot] = matrix[pivot],matrix[rank]
+ for row in range(rank+1,height):
+ if not matrix[row][col]:
+ continue
+ d = gcd(matrix[rank][col],matrix[row][col])
+ u,v = matrix[rank][col]//d,matrix[row][col]//d
+ matrix[row] = [u*x-v*y for x,y in zip(matrix[row],matrix[rank])]
+ common = reduce(gcd,matrix[row],0)
+ if common:
+ matrix[row] = [x//common for x in matrix[row]]
+ rank += 1
+ if rank == height:
+ break
+ return rank
+
+
+def incidence(edges, mask, constant):
+ bits = []
+ while mask:
+ bit = mask & -mask
+ bits.append(bit)
+ mask ^= bit
+ return [[int(bit == constant or bit == 1 << u or bit == 1 << v)
+ for bit in bits] for u,v in edges]
+
+
+def verify(certificate):
+ a,b = 25,23
+ m,d = a*b,a+b-1
+ rows = (list(range(a))+list(range(1,a))+[0])[:d]
+ cols = ([a-1]+list(range(a-1))+list(range(a)))[-d:]
+ require(certificate['dimensions'] == [a,b] and certificate['m'] == m
+ and certificate['d'] == d, 'Wrong selected corner dimensions')
+ require(certificate['R'] == rows and certificate['C'] == cols,
+ 'Wrong controlled boundary prescription')
+ require(certificate['gamma_offset'] == (m-d)%b, 'Wrong column residue offset')
+ left = [Q((r+1)**2,sum(s*s for s in range(1,a+1))) for r in range(a)]
+ right = [Q((t+1)**3,sum(s**3 for s in range(1,b+1))) for t in range(b)]
+ witness = certificate['witness']
+ require(list(map(Q,witness['left_weights'])) == left and
+ list(map(Q,witness['right_weights'])) == right,
+ 'Wrong rational witness weights')
+ require(sum(left) == sum(right) == 1 and all(left) and all(right),
+ 'Degenerate normalized witness')
+ matrix = [[Q(rows[i]==cols[j])/left[rows[i]]
+ +Q(i%b==(m-d+j)%b)/right[i%b]-1
+ for j in range(d)] for i in range(d)]
+ available = list(range(d))
+ pivots = []
+ require(len(witness['pivots']) == d, 'Incomplete rational pivot certificate')
+ for row,(saved_row,saved_col,saved_value) in enumerate(witness['pivots']):
+ col = next((j for j in reversed(available) if matrix[row][j]),None)
+ require(saved_row == row and col == saved_col and col is not None,
+ 'Wrong rightmost rational pivot')
+ value = matrix[row][col]
+ require(value == Q(saved_value) and value != 0, 'Wrong rational pivot value')
+ pivots.append((row,col))
+ available.remove(col)
+ for r in range(row+1,d):
+ if matrix[r][col]:
+ ratio = matrix[r][col]/value
+ for c in available:
+ matrix[r][c] -= ratio*matrix[row][c]
+ matrix[r][col] = 0
+ runs = []
+ for row,col in pivots:
+ if runs and row == runs[-1][-1][0]+1 and col == runs[-1][-1][1]+1:
+ runs[-1].append([row,col])
+ else:
+ runs.append([[row,col]])
+ require(certificate['runs'] == runs, 'Wrong contiguous pivot runs')
+ profile = dict(singletons=sum(len(run)==1 for run in runs),
+ blocks=[len(run) for run in runs if len(run)>1]+[m-2*d],
+ rank=m-d)
+ require(profile == certificate['data_profile'] ==
+ dict(singletons=11,blocks=[21,15,481],rank=528),
+ 'Wrong selected data profile')
+ constant = 1 << (a+b)
+ full = (constant << 1)-1
+ zero_records = certificate['zero_minor_certificates']
+ require(len(zero_records) == 315, 'Wrong number of zero-minor certificates')
+ selected_rows,selected_cols = [],[]
+ position = 0
+ for row,pivot in pivots:
+ for col in range(pivot+1,d):
+ if col in selected_cols:
+ continue
+ require(position < len(zero_records), 'Missing rightmost-zero minor')
+ record = zero_records[position]
+ position += 1
+ require((record['row'],record['col'],record['size']) ==
+ (row,col,row+1), 'Wrong zero-minor coverage/order')
+ partition = record['partition']
+ require(isinstance(partition,int) and 0 <= partition <= full,
+ 'Invalid incidence partition')
+ row_edges = [(rows[i],a+i%b) for i in selected_rows+[row]]
+ col_edges = [(cols[j],a+(m-d+j)%b) for j in selected_cols+[col]]
+ r1 = integer_rank(incidence(row_edges,partition,constant))
+ r2 = integer_rank(incidence(col_edges,full^partition,constant))
+ require(r1 == record['row_rank'] and r2 == record['column_rank'],
+ 'Wrong exact partition ranks')
+ require(r1+r2 < row+1, 'Partition fails to force zero minor')
+ require(record['common_independent_size'] == r1+r2,
+ 'Inconsistent archived intersection rank')
+ selected_rows.append(row)
+ selected_cols.append(pivot)
+ require(position == len(zero_records), 'Unused or duplicated minor certificate')
+ return dict(dimensions=[a,b], rational_pivots=d, zero_minors=position,
+ integer_rank_checks=2*position, data_profile=profile,
+ exact=True, matroid_search_repeated=False)
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/physical.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/physical.py
new file mode 100644
index 0000000000..31d0083382
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers/physical.py
@@ -0,0 +1,31 @@
+"""Exact copied-retained-total physical histogram replacement.
+
+Copyright 2026 icekylinx, Apache-2.0; developed with OpenAI GPT-6 Astra and
+Codex assistance. The copied-stream interface is credited to Aurel Prosz
+(Paureel); this application to retained-total reads is icekylinx's work.
+"""
+from .corners import require
+
+
+def copied_histogram(record):
+ """Return H' from the unchanged selected scalar/matching record."""
+ h, roles = record['h'], record['R']
+ old = record['histogram']
+ loss = h*(h-1)
+ require(record['loss'] == loss, 'Every selected retained center must have rank h-1')
+ require(len(old) == h+1 and all(isinstance(n,int) and n>=0 for n in old),
+ 'Invalid original physical histogram')
+ require(sum(r*n for r,n in enumerate(old)) == h*roles+2*loss,
+ 'Original producer rank identity failed')
+ require(old[h] >= h, 'Missing retained-total rank-h cleanup children')
+ changed = list(old)
+ changed[1] += h
+ changed[h] -= h
+ require(sum(changed) == sum(old), 'Copied reads changed the charged call count')
+ require(changed[h-1] == old[h-1], 'Copied rank-(h-1) transforms were removed')
+ require(all(changed[r] == old[r] for r in range(h+1) if r not in (1,h)),
+ 'Copied read modified an unrelated residual')
+ mass = sum(r*n for r,n in enumerate(changed))
+ require(mass == h*roles+loss, 'Copied-total rank mass failed')
+ return dict(histogram=changed, rank_sum=mass, saved_rank=loss,
+ retained_total_uses=h, roles_unchanged=roles)
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers_network.py
new file mode 100644
index 0000000000..74796d6e15
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/copied_centers_network.py
@@ -0,0 +1,196 @@
+#!/usr/bin/env python3
+"""Exact selected copied-center moments and semantic assembly.
+
+Copyright 2026 icekylinx. Apache-2.0.
+Prepared with substantial OpenAI GPT-6 Astra and Codex assistance.
+Two-stage topology: Aurel Prosz (Paureel), through PR29 (Zhihao Chen).
+Corner method: Rohan Arun PR31, parameterized by Dominik Scholz PR33.
+Semantic assembly: Zhihao Chen PR23, building on RaD (hipotures).
+See SOURCES.json and references/copied-centers for pinned contributions.
+"""
+import argparse
+from collections import Counter
+from fractions import Fraction as Q
+from hashlib import sha256
+from math import comb
+from pathlib import Path
+import json
+import sys
+
+from certify import require
+from copied_centers.physical import copied_histogram as physical_histogram
+from partial_swap_network import moment
+from structured_bulk_assembly import assembly, halving, js
+
+ROOT = Path(__file__).resolve().parents[1]
+AB = Q(384599, 10**10)
+AC = Q(717, 10**7)
+KAPPA = Q(384569, 10**10)
+GRID = 1 << 100
+
+
+def copied_histogram(row):
+ require(row['v'] == comb(row['h'], 3), 'Triple count')
+ return physical_histogram(row)['histogram']
+
+
+def profile(rows, corner=None):
+ a, b = (row['h'] for row in rows)
+ m, N = a*b, rows[0]['v']*rows[1]['v']
+ B1, B2 = (N//row['v']*row['R'] for row in rows)
+ W = 2*N+B1+B2
+ L = sum(N//row['v']*row['loss'] for row in rows)
+ z = Counter()
+
+ def ordinary(h, r, n):
+ if 2*r > h:
+ z[2*r-h] += n
+ z[1] += (h-r)*n
+ else:
+ z[1] += r*n
+
+ if corner is not None:
+ require((a, b) == (25, 23), 'Selected bit dimensions')
+ require(corner['dimensions'] == [a, b] and corner['m'] == m, 'Corner dimensions')
+ cp = corner['data_profile']
+ require(cp['singletons'] == 11 and cp['blocks'] == [21, 15, 481], 'Selected data profile')
+ for h, count in ((a, B1), (b, B2)):
+ z[h] += count
+ z[m-2*h] += count
+ z[1] += cp['singletons']*2*N
+ for t in cp['blocks']:
+ z[t] += 2*N
+ else:
+ require((a, b) == (28, 28), 'Selected complex dimensions')
+ z[m-a] += B1
+ z[m-b] += B2
+ z[(a-1)*(b-1)] += 2*N
+
+ copied = []
+ for row in rows:
+ h, copies = row['h'], N//row['v']
+ hist = copied_histogram(row)
+ copied.append(dict(h=h, center_ranks=[h-1]*h, histogram=hist))
+ for r, n in enumerate(hist):
+ if corner is not None:
+ ordinary(h, r, copies*n)
+ elif r:
+ z[r] += copies*n
+ if corner is not None:
+ ordinary(h, h-1, 2*N)
+ else:
+ z[h-1] += 2*N
+ z[1] += N # Paid endpoint transform on the copied first output.
+ z = dict(sorted((t, n) for t, n in z.items() if t and n))
+ require(all(0 < t < m and n > 0 for t, n in z.items()), 'Child domains')
+ s = W*m-N+L
+ require(sum(t*n for t, n in z.items()) == s, 'Complete two-stage rank')
+ return dict(dimensions=[a,b], m=m, N=N, B1=B1, B2=B2, W=W, L=L,
+ total_rank=s, deficit=N-L, maxchild=max(z),
+ copied_center_circuits=copied, child_multiplicities=z)
+
+
+def grid_upper(x):
+ return Q((x.numerator*GRID+x.denominator-1)//x.denominator, GRID)
+
+
+def bit_moment(p):
+ def log_upper(x):
+ k = 0
+ while x >= 2:
+ x /= 2
+ k += 1
+ def small(y):
+ z = (y-1)/(y+1)
+ return 2*sum((z**(2*j+1)/(2*j+1) for j in range(24)), Q(0)) + 2*z**49/(49*(1-z*z))
+ return grid_upper(k*small(Q(2))+small(x))
+ total = Q(0)
+ logs = {}
+ for t, n in p['child_multiplicities'].items():
+ logs[t] = log_upper(Q(p['m'], t))
+ u = AB*logs[t]
+ require(0 < u < 3, 'Bit exponential enclosure')
+ total += n*t*grid_upper(1+u+u*u/(2*(1-u/3)))
+ upper = total/(p['W']*p['m'])
+ require(upper < 1, 'Strict bit moment')
+ return dict(saving=AB, exponent=1-AB, moment_upper=upper, strict_gap=1-upper,
+ logarithm_upper_bounds=logs, rounding_denominator=GRID,
+ enclosure='24-term atanh log with geometric tail; exp upper 1+u+u^2/(2(1-u/3)); upward 2^-100 rounding')
+
+
+def finite_bridge(bit, phase, rows):
+ m, W, s, N = (phase[k] for k in ('m', 'W', 'total_rank', 'N'))
+ terms = []
+ for row in rows:
+ h, v, c = (row[k] for k in ('h', 'v', 'c'))
+ local = 4*(c+v)+10*v+4*h*v+4*h*h+8*h+8
+ terms.append(dict(h=h, v=v, c=c, invocations=N//v,
+ local_group_upper=local, copied_center_extra_groups=2*h))
+ G = N+sum(t['invocations']*(t['local_group_upper']+t['copied_center_extra_groups']) for t in terms)
+ E = 64*(W+m+G+1)**3
+ charge = 2*G*W*W+8*s+4*W+4+32*m
+ B, r = s+E, phase['maxchild']
+ C0 = 32*m*B*B
+ require(charge < E and 2*B*(m-r) >= s+E and 2*B+18 < C0, 'Semantic induction')
+ db, dc = halving(bit['m'], bit['maxchild']), halving(m, r)
+ wb, wc = bit['W'].bit_length(), W.bit_length()
+ coeff = wb*db+wc*dc
+ degree = 1000*((coeff*51)//25000+1)
+ return dict(bit=dict(m=bit['m'], W=bit['W'], maxchild=bit['maxchild'], halving_degree=db, wire_bits=wb),
+ complex=dict(m=m, W=W, s=s, maxchild=r, halving_degree=dc, wire_bits=wc,
+ scalar_terms=terms, scalar_group_upper=G),
+ semantic=dict(E=E, literal_charge=charge, strict_literal_gap=E-charge, B=B,
+ C0=C0, C1=1, induction_gap=2*B*(m-r)-s-E),
+ rows=dict(coefficient=coeff, degree=degree, suffix_slope=4*degree,
+ degree_gap=Q(degree)-Q(coeff*51,25),
+ contract='W_complex^D_complex * W_bit^D_bit; one preceding prefix and padding; all temporary copies sequential'))
+
+
+def certificate():
+ require(not sys.flags.optimize, 'Run without -O')
+ def read(name):
+ return json.loads((ROOT/'certificates'/('copied-centers-'+name+'.json')).read_text())
+ axes, row, corner, expected = map(read, ('bit-axes', 'complex-input', 'corner-25-23', 'input'))
+ bit, phase = profile(axes, corner), profile([row, row])
+ for label, p in (('bit', bit), ('complex', phase)):
+ for key, value in expected[label].items():
+ require(js(p[key]) == value, label+' saved '+key)
+ bm = bit_moment(bit)
+ cm = moment(phase['m'], phase['W'], phase['child_multiplicities'], AC, True)
+ require(bm['strict_gap'] == Q(expected['bit_moment_gap']), 'Saved bit moment')
+ require(cm['strict_gap'] == Q(expected['complex_moment_gap']), 'Saved complex moment')
+ bridge = finite_bridge(bit, phase, [row, row])
+ assembled = assembly(AB, AC, bridge, KAPPA)
+ require(js(bridge) == expected['finite_bridge'], 'Saved finite bridge')
+ require(js(assembled) == expected['assembly'], 'Saved assembly')
+ require(len(assembled['strict_constraints']) == 47 and len(assembled['margins']) == 7, 'Complete assembly')
+ sources = sorted(p for p in (ROOT/'certificates').glob('copied-centers-*.json') if p.name != 'copied-centers-network.json')
+ sources += sorted((ROOT/'scripts').glob('copied_centers*.py'))
+ sources += sorted(p for p in (ROOT/'scripts/copied_centers').rglob('*') if p.is_file() and '__pycache__' not in p.parts)
+ sources += sorted((ROOT/'notes').glob('copied-centers-*.tex'))
+ sources += [ROOT/'scripts/structured_bulk_assembly.py', ROOT/'scripts/partial_swap_network.py']
+ manifest = json.loads((ROOT/'references/copied-centers/MANIFEST.json').read_text())
+ for name, digest in manifest['files'].items():
+ require(sha256((ROOT/'references/copied-centers'/name).read_bytes()).hexdigest() == digest, 'Adopted source hash: '+name)
+ sources += [ROOT/'references/copied-centers/MANIFEST.json']
+ return dict(status='Conditional copied-center multiplication witness', kappa=KAPPA,
+ bit=dict(counts=bit, **bm), complex=dict(counts=phase, **cm),
+ finite_bridge=bridge, assembly=assembled,
+ inherited_commit='0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52', adopted_sources=manifest,
+ source_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in sources},
+ scope='Exact finite moments and assembly; producer and corner certificates checked separately. '
+ 'Copied-stream scheduling, simultaneous basis existence, analytic and tape interfaces remain written proof dependencies.')
+
+
+def main():
+ parser = argparse.ArgumentParser(description=__doc__)
+ parser.add_argument('--output', type=Path, default=ROOT/'certificates/copied-centers-network.json')
+ args = parser.parse_args()
+ result = certificate()
+ args.output.write_text(json.dumps(js(result), indent=2, sort_keys=True)+'\n')
+ print('PASS kappa=384569/10000000000 = 3.84569e-5')
+ print('Both exact moments; copied-center rank budgets; C1=1; p^2000 row stock; 47 strict constraints')
+
+
+if __name__ == '__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/exclusion_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/exclusion_circuit.py
new file mode 100644
index 0000000000..aaa99986c4
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/exclusion_circuit.py
@@ -0,0 +1,184 @@
+#!/usr/bin/env python3
+"""Cancellation-free circuit for all pair sums avoiding two specified points.
+
+Every addition has disjoint input supports. Node interning shares equal sums;
+support tracking verifies the full linear map, not sampled input values.
+"""
+from itertools import combinations
+from hashlib import sha256
+import json
+
+
+class ExclusionCircuit:
+ def __init__(self,n):
+ assert n>=4
+ self.n=n
+ self.inputs=list(combinations(range(n),2))
+ self.support=[0]+[1<=1 holds eventually because 2eps<1.
+ """
+ s = constraints(p, layout_model='nonadjacent', assembly_model='tight-gaussian')
+ for key in ('gaussian_cost', 'dimension_upper_bound', 'alpha_below_sqrt_p', 'gamma_sublinear'):
+ del s[key]
+ s['gaussian_cost'] = 1-p.delta-2*p.epsilon
+ s['alpha_squared_theta_growth'] = 1-2*p.epsilon
+ return s
+
+
+def fast_margins(p):
+ g = margins(p, layout_model='nonadjacent', assembly_model='tight-gaussian')
+ g['g5'] = 1-p.delta-2*p.epsilon
+ return g
+
+
+def witness(p, n):
+ g = guard(n, p.beta, ZETA)
+ require(p.C1 == g['C1'], 'Guard mismatch')
+ e = layer_exponents(p.tau, p.sigma, p.beta, p.c)
+ slacks = fast_constraints(p)
+ slacks['packed_overhead'] = p.lam-e['internal']
+ slacks['reserved_axes'] = p.lamp-e['preprocessing']
+ for name, slack in slacks.items(): require(slack > 0, 'Constraint failed: '+name)
+ gs = fast_margins(p)
+ require(min(gs.values()) > p.kappa, 'No final absorption gap')
+ return dict(parameters=vars(p), guard=g, recurrence=e, constraint_slacks=slacks,
+ margins=gs, minimum_margin=min(gs.values()),
+ limiting_margins=[k for k, v in gs.items() if v == min(gs.values())],
+ absorption_gap=min(gs.values())-p.kappa)
+
+
+def witness_only():
+ """Counts and parameter witness without the finite checks (for the patch)."""
+ n = counts(ComplexSideCircuit(H))
+ require(n['eta'] > COMPLEX_SAVING*Q(966, 100), 'Complex saving failed')
+ return witness(parameters(), n)
+
+
+def nearest(x):
+ """Nearest integer with ties rounded up, as for q_j=floor(tj/s+1/2)."""
+ return floor(x+Q(1, 2))
+
+
+def step_inequality(s, t, H):
+ """Exact check of c(j,h) >= Phi(j+h)-Phi(j)+sigma h^2 for 0<=j= 0, 'Step inequality failed')
+ require(abs(beta(j+h)) <= Q(1, 2), 'Phase outside the half interval')
+ worst = excess if worst is None else min(worst, excess)
+ return worst
+
+
+def neumann_count(p_bits, alpha, theta):
+ """n_new=ceil((p+1)/(4 alpha^2)+1/theta) and the original count ceil(p/(alpha^2 theta)).
+
+ With L=log2(2.01)<101/100 and pi log2(e) > KAPPA0_LO, each extra power of E
+ gains at least KAPPA0_LO*alpha^2-L >= 4 alpha^2 bits, and the burn-in costs at
+ most KAPPA0_HI*alpha^2*(1/(4 theta)+1/2) bits.
+ """
+ a2 = alpha*alpha
+ require(alpha >= 2 and a2*theta >= 1 and theta < 1, 'Need alpha>=2, alpha^2 theta>=1, theta<1')
+ require(Q(201, 100)**100 < 2**101, 'log2(2.01)<101/100 failed')
+ require(KAPPA0_LO*a2-Q(101, 100) >= 4*a2, 'Per-step decay constant failed')
+ n_new = ceil(Q(p_bits+1, 4*a2)+1/theta)
+ require(4*a2*n_new >= p_bits+1+KAPPA0_HI*a2*(1/(4*theta)+Q(1, 2)), 'Neumann count failed')
+ n_hvdh = ceil(Q(p_bits)/(a2*theta))
+ return dict(n_new=n_new, n_hvdh=n_hvdh, n=min(n_new, n_hvdh))
+
+
+def application_counts(d, b):
+ """Counts at given (d,b): alpha=floor(sqrt(b/(8d))), theta>1/(4d)."""
+ from math import isqrt
+ alpha = isqrt(b//(8*d))
+ while 8*d*(alpha+1)**2 <= b: alpha += 1
+ while 8*d*alpha**2 > b: alpha -= 1
+ gamma = 2*d*alpha*alpha
+ theta = Q(1, 4*d)
+ require(gamma*4 <= b, 'gamma exceeds b/4')
+ return dict(d=d, b=b, alpha=alpha, gamma=gamma, **neumann_count(6*b, alpha, theta))
+
+
+def certificate():
+ c = ComplexSideCircuit(H); n = counts(c)
+ require(n['eta'] > COMPLEX_SAVING*Q(966, 100), 'Complex saving failed')
+ p = parameters(); w = witness(p, n)
+ require(Q(1, 2**30) < KAPPA < Q(1, 2**29), 'Unexpected dyadic scale')
+ steps = {f'{s}/{t}': str(step_inequality(s, t, 6)) for s, t in ((7, 8), (31, 32), (61, 64), (97, 101), (251, 256))}
+ samples = [application_counts(d, b) for d, b in ((8, 2**20), (64, 2**30), (1000, 2**40))]
+ for x in samples: require(x['n_new'] <= 30*x['d'], 'Neumann count exceeds 30d')
+ # Under the retained Gaussian margin the same networks are capped below a_b/5.
+ return dict(status='CONDITIONAL 1479/10^12 WITNESS; FAST GAUSSIAN RESAMPLING; NOT FORMAL VERIFICATION',
+ upstream_commit=verify_sources(), complex_counts=dict(h=n['h'], W=n['W'], s=n['s'], eta=n['eta']),
+ bit_saving=BIT_SAVING, complex_saving=COMPLEX_SAVING, witness=w,
+ step_inequality_minimum_excess=steps, neumann_samples=samples,
+ gaussian_cost_power='2*epsilon+delta (was 3/4+delta+5*epsilon/4)',
+ improvement_over_compressed_complex=KAPPA/Q(59, 10**11),
+ improvement_over_compact_control=KAPPA/Q(83, 10**12),
+ scoped_ceiling=dict(upper=BIT_SAVING/2, below_2_to_minus_29=BIT_SAVING/2 < Q(1, 2**29),
+ scope='g2,g3,g4 <= a_b*min(eps,1-eps); published h=50 paired bit network only.'),
+ scope='Conditional on the pinned upstream interfaces, the compact-control movement and guard, '
+ 'the compressed complex network, and the written fast resampling lemmas. '
+ 'Exact arithmetic and finite checks are not formal verification.')
+
+
+if __name__ == '__main__':
+ result = serializable(certificate())
+ (ROOT/'certificates/fast-gaussian.json').write_text(json.dumps(result, indent=2, sort_keys=True)+'\n')
+ print('PASS conditional', KAPPA, '> 2^-30; minimum margin', result['witness']['minimum_margin'],
+ 'limiting', result['witness']['limiting_margins'])
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_exclusion_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_exclusion_circuit.py
new file mode 100644
index 0000000000..36d1fa2c02
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_exclusion_circuit.py
@@ -0,0 +1,41 @@
+#!/usr/bin/env python3
+"""Cancellation-free pair exclusion with recursively aggregated vertex weights.
+
+At each level group vertices in pairs. Internal edges become vertex weights
+in the smaller graph. Keeping those weights in the recursion avoids a separate
+leave-two-out circuit for each level. All coefficients are checked exactly.
+"""
+from exclusion_circuit import ExclusionCircuit
+from itertools import combinations
+class PairedExclusionCircuit(ExclusionCircuit):
+ def pair(self,points):return self.block(points,{(a,b):self.variables[a,b] for a,b in combinations(points,2)},{a:0 for a in points})
+ def grouping(self,points):return [points[i:i+2] for i in range(0,len(points),2)]
+ def block(self,points,edges,weights):
+ if len(points)<=4:
+ total=lambda omit:self.total([x for p,x in edges.items() if not set(p)&set(omit)]+[x for p,x in weights.items() if p not in omit])
+ return total(()),{a:total((a,)) for a in points},{(a,b):total((a,b)) for a,b in combinations(points,2)}
+ groups=self.grouping(points);ng=len(groups);e=lambda a,b:edges[tuple(sorted((a,b)))]
+ coarse={(i,j):self.total([e(a,b) for a in groups[i] for b in groups[j]]) for i,j in combinations(range(ng),2)}
+ wt={i:self.total([weights[a] for a in g]+[e(a,b) for a,b in combinations(g,2)]) for i,g in enumerate(groups)}
+ total,outside,far=self.block(list(range(ng)),coarse,wt)
+ strips={};sums={}
+ for i,g in enumerate(groups):
+ other=[j for j in range(ng) if j!=i]
+ for a in g:
+ carry=self.total([weights[u] for u in g if u!=a])
+ vals=[self.total([e(u,v) for u in g if u!=a for v in groups[j]]) for j in other]
+ st,one,_=self.vector([carry]+vals,False)
+ strips[a]={j:z for j,z in zip(other,one[1:])};sums[a]=st
+ out={};single={a:self.add(outside[i],sums[a]) for i,g in enumerate(groups) for a in g}
+ for i,g in enumerate(groups):
+ for a,b in combinations(g,2):out[a,b]=outside[i]
+ for i,j in combinations(range(ng),2):
+ for a in groups[i]:
+ left=self.add(far[i,j],strips[a][j])
+ for b in groups[j]:
+ cross=self.total([e(u,v) for u in groups[i] if u!=a for v in groups[j] if v!=b])
+ out[a,b]=self.add(left,self.add(strips[b][i],cross))
+ return total,single,out
+if __name__=='__main__':
+ for n in (15,25,45,49):
+ c=PairedExclusionCircuit(n);print(n,c.verify(),flush=True)
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_network.py
new file mode 100644
index 0000000000..910449dd51
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/paired_network.py
@@ -0,0 +1,91 @@
+#!/usr/bin/env python3
+"""Conditional 2^-59 certificate: paired sums, stopped guard, tighter Gaussian width."""
+from fractions import Fraction as Q
+from pathlib import Path
+import json
+
+from certify import Parameters,certify_parameters,network,require,verify_sources
+from shared_point_circuit import SharedPointCircuit
+from shared_point_network import counts
+from paired_exclusion_circuit import PairedExclusionCircuit
+from search_network import log_integer_bounds
+
+ROOT=Path(__file__).resolve().parents[1]
+H=50
+BIT_SAVING=Q(296,10**11)
+COMPLEX_SAVING=Q(1,10**11)
+LOG_BOUND=Q(11737,1000)
+KAPPA=Q(1,2**59)
+
+
+def circuit(h=H):return SharedPointCircuit(h,PairedExclusionCircuit(h-1))
+
+
+def parameters():
+ a=BIT_SAVING;b=Q(999,1000)
+ return Parameters(1-a,1-COMPLEX_SAVING,Q(199,1000),b*a,
+ 1-(1+b)*a*a/2,1-b*a*a,KAPPA,beta=b,
+ delta=Q(1,10000),C1=2)
+
+
+def guard_certificate(h=H,beta=Q(999,1000)):
+ n=network(h);m=n['m'];s=n['sc'];E=n['B']-s;B=n['B']
+ require(m>=3 and 2<=sBIT_SAVING*LOG_BOUND,'Bit saving failed')
+ require(old['eta_c']>COMPLEX_SAVING*LOG_BOUND,'Complex saving failed')
+ require(2*old['Lc']=2^40 cutoff failed')
+ witness=certify_parameters(p,generalized_beta=True,strict_margin=True,
+ layout_model='nonadjacent',guard_model='stopping',assembly_model='tight-gaussian')
+ require(Q(witness['minimum_margin'])==p.epsilon*p.beta*BIT_SAVING**2,'Wrong limiting margin')
+ a_upper=n['eta']/((1-n['eta'])*lo)
+ ceiling=a_upper*a_upper/(5*(1-a_upper))
+ require(ceiling= 1, 'Log argument below one')
+ power = 0
+ while value > 2:
+ value /= 2
+ power += 1
+ def series(x):
+ z = (x-1)/(x+1)
+ return 2*sum((z**(2*j+1)/(2*j+1) for j in range(24)), Q(0)) + 2*z**49/(49*(1-z*z))
+ scaled = (power*series(Q(2)) + series(value))*10**12
+ return Q(-(-scaled.numerator//scaled.denominator), 10**12)
+
+
+def moment(m, W, rows, saving, sharp):
+ upper = Q(0)
+ logs = {}
+ for t, count in sorted(rows.items()):
+ require(0 < t < m and count >= 0, 'Invalid recursive child')
+ ell = log_upper(Q(m, t))
+ u = saving*ell
+ require(0 <= u < 1, 'Exponential enclosure outside range')
+ bound = 1+u+u*u/(2*(1-u/3)) if sharp else 1/(1-u)
+ upper += Q(count*t, W*m)*bound
+ logs[str(t)] = ell
+ require(upper < 1, 'Characteristic moment does not contract')
+ return dict(saving=saving, exponent=1-saving, moment_upper=upper,
+ strict_gap=1-upper, logarithm_upper_bounds=logs,
+ child_width_multiplicities=sorted(rows.items()),
+ enclosure='1+u+u^2/(2(1-u/3))' if sharp else '1/(1-u)')
+
+
+def bit_counts(d):
+ dims = (25, 23, 57)
+ ps = d['producers']
+ v = [comb(h, 3) for h in dims]
+ N, m = prod(v), prod(dims)
+ banks = [N//vi*ps[str(h)]['roles'] for h, vi in zip(dims, v)]
+ B1, B2, B3 = banks
+ E = B3-B1
+ require(E >= 0, 'Stage-three bank must accommodate stage one')
+ W = 2*N+B2+B3
+ L = N*sum((Q(6, h-2) for h in dims), Q(0))
+ require(L.denominator == 1, 'Nonintegral retained loss')
+ L = int(L)
+ s = W*m-2*N+2*L
+ rows = Counter()
+ profiles = [(B1, (25,7,25,25,32611)), (E,(57,32661)),
+ (B2,(575,31625)), (B2,(23,529)),
+ (2*N,(55,463,31513)), (2*N,(481,)),
+ (2*N,(1,23)), (2*N,(1,21)), (2*N,(1,55))]
+ rows[1] += 2*N*(113+47)
+ for count, profile in profiles:
+ for t in profile:
+ rows[t] += count
+ for h, vi in zip(dims, v):
+ p = ps[str(h)]
+ require(p['v'] == vi and p['outputs'] == 3*vi+h, 'Producer dimensions')
+ require(p['roles'] == p['additions']+p['outputs']-p['matches'], 'Role count')
+ require(p['loss'] == h*(h-1), 'Producer retained loss')
+ hist = p['histogram']
+ require(len(hist) == h+1 and all(n >= 0 for n in hist), 'Histogram range')
+ require(sum(r*n for r,n in enumerate(hist)) == h*p['roles']+2*h*(h-1), 'Internal rank mass')
+ for r,n in enumerate(hist):
+ copies = N//vi*n
+ block = max(0, 2*r-h)
+ rows[1] += copies*(r-block)
+ if block:
+ rows[block] += copies
+ computed = dict(m=m,N=N,B1=B1,B2=B2,B3=B3,E=E,W=W,L=L,s=s,
+ deficit=W*m-s,eta=Q(W*m-s,W*m),singletons=rows[1])
+ for name,value in computed.items():
+ require(value == Q(d['parameters'][name]), 'Recorded bit count differs: '+name)
+ require(sorted((t,n) for t,n in rows.items() if t>1) == [tuple(x) for x in d['bit_bulk_width_multiplicities']], 'Recorded bit multiset differs')
+ require(sum(t*n for t,n in rows.items()) == s, 'Complete bit rank mass')
+ return computed, rows
+
+
+def complex_counts(d):
+ p = d['complex']
+ h=28; v=comb(h,3); m=h**3; N=v**3
+ B=v*v*(93838+h+1); W=2*N+2*B
+ s=W*m-2*N+6*v*v*h*(h+1)
+ macros=[(m-2*h,B),(m-h*h,B),((h*h-1)*(h-1),2*N),
+ (h*(h-1),B-N),((h-1)**2,3*N)]
+ require(macros == [tuple(x) for x in p['macro_width_multiplicities']], 'Complex macro profiles')
+ hist=p['histogram']
+ require(sum(r*n for r,n in enumerate(hist)) == h*(93838+h+1)+2*h*(h+1), 'Complex internal rank mass')
+ rows=Counter(dict(macros))
+ for r,n in enumerate(hist):
+ if r>=2:
+ rows[r] += 3*v*v*n
+ # The remaining physical and macro singleton transitions are fixed by the
+ # retained full rank budget; the internal histogram is regenerated separately.
+ rows[1]=s-sum(t*n for t,n in rows.items())
+ counts=dict(h=h,v=v,m=m,N=N,B=B,W=W,s=s,singletons=rows[1])
+ for name,value in counts.items():
+ require(value == int(p[name]), 'Recorded complex count differs: '+name)
+ return counts, rows
+
+
+def guard(n):
+ m=n['m']; W=n['W']; h=n['h']; q=m+6*h
+ rho=Q(6,5); gamma=Q(4999,5000); lower=160000
+ require(lower**5 < m**6 and 28 < 2**5 and 756 < 4**5, 'Guard power bounds')
+ t=Q(56,m)
+ # Taylor integral remainder: (1-t)^(6/5) <= 1-6t/5+3t²/[25(1-t)].
+ power=1-Q(6,5)*t+Q(3,25)*t*t/(1-t)
+ bounds=dict(largest=power+Q(2*(q-(m-56)),lower),
+ other_large=Q(27,28)+Q(4*979,lower),
+ no_large=Q(4*q,lower))
+ require(all(2*r>q for r in (21896,21168,21141)), 'Two large edges on a path')
+ require(q-21896 < 729, 'Largest-edge remainder admits medium edge')
+ require(max(bounds.values()) < gamma, 'Precision path does not contract')
+ E=64*(W+m+1)**3
+ require(36*W**3+4*n['s']+4*W+8*m+4 < E, 'Local coefficient allowance')
+ dep=5000*(E+16*m+1)
+ beta=Q(1,1000); zeta=Q(1,10000)
+ raw=128*m*(1+1/zeta)*dep
+ C0=-(-raw.numerator//raw.denominator)
+ require(dep*(1-gamma)>=E and dep>=16*m, 'Depth induction allowance')
+ require(m*(1+1/zeta)*dep+18<=C0, 'Layer allowance')
+ return dict(q=q,rho=rho,gamma=gamma,path_moment_upper=bounds,
+ strict_gap=gamma-max(bounds.values()),E=E,dependency_constant=dep,
+ C0=C0,C1=rho-(rho-1)*beta+zeta)
+
+
+def parameters():
+ tau=1-BIT_SAVING
+ return Parameters(tau=tau,sigma=1-COMPLEX_SAVING,
+ epsilon=1/(2+BIT_SAVING),c=Q(1),beta=Q(1,1000),delta=Q(1,10**16),
+ lam=tau+Q(1,10**20),lamp=tau+Q(2,10**20),C1=Q(11999,10000),kappa=KAPPA)
+
+
+def assembly(p=None):
+ p=parameters() if p is None else p
+ ex=layer_exponents(p.tau,p.sigma,p.beta,p.c)
+ cs=fast_constraints(p)
+ cs['packed_overhead']=p.lam-ex['internal']
+ cs['reserved_axes']=p.lamp-ex['preprocessing']
+ require(len(cs)==29 and all(v>0 for v in cs.values()), 'Strict assembly constraint')
+ margins=fast_margins(p)
+ require(len(margins)==7 and min(margins.values())>p.kappa, 'Strict assembly absorption')
+ return dict(parameters=asdict(p),recurrence=ex,constraints=cs,margins=margins,
+ minimum_margin=min(margins.values()),absorption_gap=min(margins.values())-p.kappa)
+
+
+def basis_combinatorics():
+ a,b,k=25,23,57; H=a*b; size=k+a
+ R=list(range(a))+list(range(7))+list(range(a))*2
+ C=list(range(a))*2+list(range(7))+list(range(a))
+ completions=[]
+ for beta in range(b):
+ prescribed={}
+ def set_entry(row,col):
+ require(row not in prescribed or prescribed[row]==col, 'Conflicting prescribed row')
+ require(col not in prescribed.values() or prescribed.get(row)==col, 'Conflicting prescribed column')
+ prescribed[row]=col
+ for i,label in enumerate(R):
+ if i%b==beta: set_entry(i//b,label)
+ for j,label in enumerate(C):
+ i=H-size+j
+ if i%b==beta: set_entry(i//b,label)
+ unused=iter(c for c in range(a) if c not in prescribed.values())
+ completions.append([prescribed[r] if r in prescribed else next(unused) for r in range(a)])
+ forward=[(0,23),(1,24)]+[((j+2)%23,j) for j in range(7)]+[((j+9)%23,j) for j in range(15)]
+ dual=[(23,0),(24,1)]+[(2+((-9+j)%23),j) for j in range(7)]+[(2+((-11+j)%23),j) for j in range(10,25)]
+ for edges in (forward,dual):
+ require(len(edges)==24, 'Tree edge count')
+ seen={0}
+ while True:
+ expanded=seen|{y for x,y in edges if x in seen}|{x for x,y in edges if y in seen}
+ if expanded==seen:break
+ seen=expanded
+ require(seen==set(range(25)), 'A5 incidence graph disconnected')
+ return dict(row_labels=R,inverse_column_labels=C,permutation_completions=completions,
+ A5_forward_tree=forward,A5_dual_tree=dual,
+ scope='Prescription compatibility and A5 trees; remaining generic minors are proved in the note.')
+
+
+def certificate():
+ d=json.loads(INPUT.read_text())
+ bn,br=bit_counts(d); cn,cr=complex_counts(d)
+ bit=moment(bn['m'],bn['W'],br,BIT_SAVING,True)
+ comp=moment(cn['m'],cn['W'],cr,COMPLEX_SAVING,False)
+ require(bit['strict_gap']>Q(617,10**16), 'Bit gap lower bound')
+ require(comp['strict_gap']>Q(23982,10**15), 'Complex gap lower bound')
+ a=assembly(); g=guard(cn)
+ require(g['C1']==a['parameters']['C1'], 'Guard exponent mismatch')
+ require(a['absorption_gap']>Q(44822,10**17), 'Assembly gap lower bound')
+ sources=[INPUT,Path(__file__).resolve(),ROOT/'scripts/partial_swap_producer.py']
+ sources += sorted(p for p in (ROOT/'scripts/partial_swap').iterdir() if p.is_file())
+ sources += sorted((ROOT/'notes').glob('partial-swap-*.tex'))
+ return dict(status='Conditional partial-swap integer-multiplication witness',
+ kappa=KAPPA,bit=dict(counts=bn,**bit),complex=dict(counts=cn,**comp),
+ basis_combinatorics=basis_combinatorics(),guard=g,assembly=a,
+ source_sha256={str(p.relative_to(ROOT)):sha256(p.read_bytes()).hexdigest() for p in sources},
+ inherited_PR10_commit='62691e395a0458ce089a1c7b5d89e74291e95e29',
+ scope='Exact finite arithmetic and basis combinatorics. Producer regeneration is separate. '
+ 'The common-basis, recursion, and retained analytic/tape arguments remain written proofs.')
+
+
+def main():
+ parser=argparse.ArgumentParser(description=__doc__)
+ parser.add_argument('--output',type=Path,default=ROOT/'certificates/partial-swap-network.json')
+ args=parser.parse_args()
+ result=certificate()
+ args.output.write_text(json.dumps(serializable(result),indent=2,sort_keys=True)+'\n')
+ print('PASS partial-swap kappa='+str(KAPPA)+' = 1.884586e-6')
+ print('29 strict constraints; 7 strict assembly margins; bit/complex moments and precision guard')
+
+if __name__=='__main__':
+ main()
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/prepare_layers.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/prepare_layers.py
new file mode 100644
index 0000000000..8e17b52f95
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/prepare_layers.py
@@ -0,0 +1,163 @@
+#!/usr/bin/env python3
+"""Reusable layer estimates and complex-family screen, not a new headline bound.
+
+The sparse-cost examples are implications of an UNPROVED primitive. They are
+kept explicitly separate from estimates for the existing machine routine.
+"""
+from fractions import Fraction as Q
+from pathlib import Path
+import json
+
+from certify import Parameters, constraints, margins, network, require, verify_sources
+from search_network import log_integer_bounds, log_ratio_bounds
+
+ROOT = Path(__file__).resolve().parents[1]
+BIT_SAVING = Q(296, 10**11)
+
+
+def guard(beta, zeta=Q(1, 100), h=50):
+ """Explicit guard for any fixed rational beta in (0,1); see the proof note."""
+ require(0 < beta < 1 and zeta > 0, 'Need 00')
+ n = network(h)
+ m, s, B = n['m'], n['sc'], n['B']
+ E = B-s
+ require(m >= 3 and 2 <= s < m**5, 'Unverified coefficient-depth hypothesis')
+ require(s*(8+E) <= 9*B*B, 'One-piece constant failed')
+ C1 = 5-4*beta+zeta
+ raw_C0 = max(Q(128*m*B*B), 18*m*B*B*(1+1/zeta))
+ C0 = -(-raw_C0.numerator//raw_C0.denominator)
+ require(9*m*B*B*(1+1/zeta)+18 <= C0, 'Whole-layer constant failed')
+ return dict(h=h, m=m, s=s, E=E, B=B, beta=beta, zeta=zeta,
+ C0=C0, C1=C1, one_piece_exponent=5-4*beta)
+
+
+def packed_exponents(tau, sigma, beta, c, *, theta=None):
+ """Sum the recurrence for either exponent ordering.
+
+ theta=tau is the EXISTING packed bound. Any other theta is only a
+ hypothetical O(V e^tau K^theta) primitive with the same remaining contract.
+ """
+ require(0 < tau < 1 and 0 <= sigma < 1 and 0 < beta < 1 and c > 0,
+ 'Invalid recurrence parameters')
+ theta = tau if theta is None else theta
+ require(theta >= 0, 'Negative spacing exponent is not supported')
+ internal = tau+(1-beta)*max(sigma-tau, Q(0))+theta*c
+ leaf = sigma+beta*(1-sigma)
+ return dict(internal=internal, leaf=leaf, layer=max(internal, leaf),
+ theta=theta, hypothetical=theta != tau)
+
+
+def check_parameters(p, g, *, hypothetical_theta=None):
+ """Check the stated extensions, without relaxing the published checker."""
+ require(g == guard(g['beta'],g['zeta'],g['h']), 'Guard certificate was altered')
+ require(p.beta == g['beta'] and p.C1 == g['C1'], 'Guard/parameter mismatch')
+ require(1-p.tau <= BIT_SAVING, 'Preparation retains the published bit saving')
+ require(1-p.sigma < complex_saving_bounds(g['h'])[0],
+ 'Complex exponent is not supported by the chosen motif')
+ exp = packed_exponents(p.tau, p.sigma, p.beta, p.c, theta=hypothetical_theta)
+ slacks = constraints(p, layout_model='nonadjacent', assembly_model='tight-gaussian')
+ slacks['packed_overhead'] = p.lam-exp['internal']
+ for name, slack in slacks.items():
+ require(slack > 0, 'Failed preparation constraint: '+name)
+ gs = margins(p, layout_model='nonadjacent', assembly_model='tight-gaussian')
+ require(min(gs.values()) > p.kappa, 'No strict final margin')
+ return dict(status=('HYPOTHETICAL SPARSE PRIMITIVE; NOT A MULTIPLICATION RESULT'
+ if exp['hypothetical'] else
+ 'Existing packed routine; conditional preparation estimates'),
+ parameters=vars(p), guard=g, recurrence=exp,
+ constraint_slacks=slacks, margins=gs, minimum_margin=min(gs.values()))
+
+
+def complex_saving_bounds(h):
+ n = network(h)
+ eta = n['eta_c']
+ require(0 < eta < Q(1, 2), 'Complex deficit must be positive')
+ lo, hi = log_ratio_bounds(1/(1-eta), terms=3)
+ dlo, dhi = log_integer_bounds(n['m'])
+ return lo/dhi, hi/dlo
+
+
+def complex_search():
+ # L_c3h(h+1) iff h^2-21h-16>0, hence integer h>=22.
+ bounds = {h: complex_saving_bounds(h) for h in range(22, 200)}
+ winner = max(bounds, key=lambda h: bounds[h][0])
+ lo, hi = bounds[winner]
+ require(all(lo > b[1] for h, b in bounds.items() if h != winner),
+ 'Finite winner not separated')
+ n200 = network(200)
+ # eta_c<2/(3*z_c*m), log(m)>1; every factor increases for h>=200.
+ tail = Q(2, 3*n200['zc']*n200['m']-2)
+ require(log_integer_bounds(n200['m'])[0] > 1, 'Tail log denominator failed')
+ require(lo > tail, 'Tail could improve the result')
+ n = network(winner)
+ certified = Q(418, 10**12)
+ _, log_hi = log_integer_bounds(n['m'])
+ require(n['eta_c'] > certified*log_hi, 'Chosen simple complex saving failed')
+ require(n['Lc'] < n['N'] and 2*n['Lc'] >= n['N'],
+ 'Expected the complex-only admissibility range')
+ require(n['sc'] < n['m']**5, 'Guard requires a different depth bound')
+ fixed50 = Q(169, 10**13)
+ require(network(50)['eta_c'] > fixed50*log_integer_bounds(50**3)[1],
+ 'Fixed-h=50 saving failed')
+ return dict(status='Conditional complex interface; separate-arity integration not patched',
+ winner_h=winner, admissible_integer_h_minimum=22,
+ saving_lower=lo, saving_upper=hi, certified_saving=certified,
+ counts={k:n[k] for k in ('h','m','v','N','Wc','sc','Lc','eta_c')},
+ fixed_h50_saving=fixed50, tail_start=200, tail_upper=tail,
+ finite_enclosures={str(h):dict(lower=b[0],upper=b[1]) for h,b in bounds.items()},
+ scope='Original complex motif only, all integer h>=22; no shared bit positivity requirement. Written interface audit required, not a formal proof.')
+
+
+def scenarios():
+ a = BIT_SAVING
+ epsilon = Q(199,1000)
+ # The published numerical choice remains valid under the generalized proof.
+ beta = Q(999,1000)
+ g = guard(beta)
+ existing = Parameters(1-a, 1-Q(1,10**11), epsilon, beta*a,
+ 1-(1+beta)*a*a/2, 1-beta*a*a, Q(1,2**59),
+ beta=beta, delta=Q(1,10000), C1=g['C1'])
+ result = {'existing_59_control':check_parameters(existing,g)}
+ # These two rows assume theta=a instead of theta=tau. No such primitive
+ # is supplied here. They expose exact research targets and guard budgets.
+ for name,h,ac,beta,c,q,k in (
+ ('hypothetical_39',50,Q(1,10**11),Q(1,100),Q(1,200),Q(95,10**13),39),
+ ('hypothetical_34',25,Q(418,10**12),Q(1,5),Q(1,10),Q(3,10**10),34)):
+ g = guard(beta,h=h)
+ exp = packed_exponents(1-a,1-ac,beta,c,theta=a)
+ lamp = 1-q
+ lam = (max(1-a,1-ac,exp['internal'])+lamp)/2
+ p = Parameters(1-a,1-ac,epsilon,c,lam,lamp,Q(1,2**k),
+ beta=beta,delta=Q(1,10000),C1=g['C1'])
+ result[name] = check_parameters(p,g,hypothetical_theta=a)
+ actual = packed_exponents(p.tau,p.sigma,p.beta,p.c)
+ require(actual['internal'] > 1, 'Hypothetical target accidentally uses an existing bound')
+ result[name]['existing_primitive_internal_exponent'] = actual['internal']
+ result[name]['missing_hypothesis'] = 'Uniform fixed-tape O(V f^(1-a) K^a) selected-bit primitive, up to fixed powers of log(p) only, including descriptors, exceptional repair, and dirty-scratch restoration.'
+ return result
+
+
+def certificate():
+ return dict(status='PREPARATION PASS; published headline remains conditional 2^-59',
+ upstream_commit=verify_sources(), complex_family=complex_search(),
+ scenarios=scenarios(),
+ verification_boundary='Exact arithmetic and finite recurrence checks accompany written proofs. Sparse scenarios are unproved design targets, not certificates of new algorithms.')
+
+
+def serializable(value):
+ if isinstance(value,Q):
+ return str(value)
+ if isinstance(value,dict):
+ return {k:serializable(v) for k,v in value.items()}
+ if isinstance(value,(list,tuple)):
+ return [serializable(v) for v in value]
+ return value
+
+
+if __name__ == '__main__':
+ result = certificate()
+ (ROOT/'certificates/layer-preparation.json').write_text(
+ json.dumps(serializable(result),indent=2,sort_keys=True)+'\n')
+ print('PASS preparation estimates; complex-family optimum h='+str(result['complex_family']['winner_h']))
+ print('Published result remains 2^-59. Sparse targets 2^-39 and 2^-34 remain hypothetical.')
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/search_network.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/search_network.py
new file mode 100644
index 0000000000..f03d5c1b2c
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/search_network.py
@@ -0,0 +1,105 @@
+#!/usr/bin/env python3
+"""Certify the best shared recurrence exponent within the generalized h family.
+
+Uses rational enclosures of logarithms, plus a tail bound for all h>=200.
+The result concerns the counting formulas, conditional on the network proof.
+"""
+from fractions import Fraction as Q
+import json
+from pathlib import Path
+from certify import network, require
+
+ROOT = Path(__file__).resolve().parents[1]
+
+
+def log_ratio_bounds(x, terms=24):
+ """Bounds for log(x), 1 <= x <= 2, by the atanh series."""
+ require(1 <= x <= 2, "Log series expects 1<=x<=2")
+ z = (x-1)/(x+1)
+ lower = 2*sum((z**(2*j+1)/Q(2*j+1) for j in range(terms)), Q(0))
+ tail = 2*z**(2*terms+1)/((2*terms+1)*(1-z*z))
+ return lower, lower+tail
+
+
+def log_integer_bounds(m):
+ k = m.bit_length()-1
+ lo2, hi2 = log_ratio_bounds(Q(2))
+ lo, hi = log_ratio_bounds(Q(m, 2**k))
+ return k*lo2+lo, k*hi2+hi
+
+
+def saving_bounds(n, bit_only=False):
+ eta = n["eta_b"] if bit_only else min(n["eta_b"], n["eta_c"])
+ require(0 < eta < Q(1, 2), "Need a positive small rank deficit")
+ # Shared exponent saving is min(-log(1-eta_b),-log(1-eta_c))/log(m).
+ lo_num, hi_num = log_ratio_bounds(1/(1-eta), terms=3)
+ lo_den, hi_den = log_integer_bounds(n["m"])
+ return lo_num/hi_den, hi_num/lo_den
+
+
+def search(bit_only=False):
+ bounds = {}
+ rejected = []
+ for h in range(7, 200):
+ if h == 9:
+ rejected.append(h)
+ continue
+ n = network(h)
+ if 2*n["Lb"] >= n["N"] or 2*n["Lc"] >= n["N"]:
+ rejected.append(h)
+ continue
+ bounds[h] = saving_bounds(n, bit_only=bit_only)
+ winner = max(bounds, key=lambda h: bounds[h][0])
+ lo, hi = bounds[winner]
+ require(all(lo > b[1] for h, b in bounds.items() if h != winner),
+ "Enclosures do not separate a unique winner")
+ # eta_b < 1/(3*z_b*m), and -log(1-eta_b) < eta_b/(1-eta_b).
+ # For h>=200, z_b and m increase and log(m)>1. This bounds ALL the tail.
+ n200 = network(200)
+ tail_upper = Q(1, 3*n200["zb"]*n200["m"]-1)
+ require(lo > tail_upper, "Tail could contain a better network")
+ dyadic_power = 1
+ while Q(1, 2**dyadic_power) >= lo:
+ dyadic_power += 1
+ require(hi < Q(1, 2**(dyadic_power-1)), "Cannot certify optimal dyadic saving")
+ return {
+ "scope": ("Bit-network saving alone" if bit_only else "Common tau=sigma saving")
+ + "; generalized counting formulas, construction conditional",
+ "winner_h": winner,
+ "saving_lower": str(lo), "saving_upper": str(hi),
+ "largest_certified_dyadic_saving": f"2^-{dyadic_power}",
+ "tail_start": 200, "tail_saving_upper": str(tail_upper),
+ "excluded_h": rejected,
+ "finite_enclosures": {str(h): {"lower": str(b[0]), "upper": str(b[1])}
+ for h, b in bounds.items()},
+ }
+
+
+def parameter_ceiling():
+ """Upper bound for kappa even with variable beta and separate sigma.
+
+ Put a=1-tau. The final g4>0 gives epsilon Q(99, 100)*upper, "Witness below 99% of ceiling")
+ return {"bit_network_search": result, "kappa_upper": str(upper),
+ "simple_kappa_upper": str(Q(5838, 10**36)),
+ "witness": str(witness), "witness_fraction_of_upper": str(witness/upper),
+ "next_dyadic_excluded": "2^-107",
+ "scope": "Seven-margin accounting and stated network rank bounds; not all algorithms"}
+
+
+if __name__ == "__main__":
+ result = search()
+ result["parameter_ceiling"] = parameter_ceiling()
+ path = ROOT / "certificates/network-search.json"
+ path.parent.mkdir(exist_ok=True)
+ path.write_text(json.dumps(result, indent=2, sort_keys=True)+"\n")
+ print(f"Certified h={result['winner_h']} best within the stated counting family,")
+ print(f"including all h>=200 by a tail bound; dyadic saving {result['largest_certified_dyadic_saving']}")
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/shared_point_circuit.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/shared_point_circuit.py
new file mode 100644
index 0000000000..8347a0bda6
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/shared_point_circuit.py
@@ -0,0 +1,149 @@
+#!/usr/bin/env python3
+"""Merge equal sums across the common-point circuits, with exact certificates.
+
+Supports are represented by their provenance in the small pair circuit, not
+by half a million dense global bit vectors. A sum that occurs in two distinct
+common-point groups must be a pair-star; its fixed pair and union of vertices
+identify its support exactly.
+"""
+from functools import lru_cache
+from hashlib import sha256
+from itertools import combinations
+import json
+
+from exclusion_circuit import ExclusionCircuit
+
+
+class SharedPointCircuit:
+ def __init__(self,h,circuit=None):
+ assert h>=6 and h!=9, 'The ambient form I-J/9 must be nondegenerate'
+ self.h=h
+ self.local=circuit or ExclusionCircuit(h-1)
+ assert self.local.n==h-1, 'Pair circuit has the wrong ground size'
+ self.inputs=list(combinations(range(h),3))
+ self.variables={t:i+1 for i,t in enumerate(self.inputs)}
+ self.args=[None]*(len(self.inputs)+1)
+ self.core=[0]+[sum(1<=2 and key in lookup:
+ mapping[node]=lookup[key];self.merged+=1
+ continue
+ new=len(self.args);mapping[node]=new
+ self.args.append((a,b));self.core.append(core);self.union.append(union)
+ self.provenance.append((common,node))
+ if core.bit_count()>=2:lookup[key]=new
+ for pair,node in sorted(self.local.outputs.items()):
+ t=tuple(sorted((common,*(self.points[common][x] for x in pair))))
+ self.outputs[common,t]=mapping[node]
+ self.active=set();stack=list(self.outputs.values())
+ while stack:
+ n=stack.pop()
+ if n in self.active:continue
+ self.active.add(n)
+ if self.args[n]:stack.extend(self.args[n])
+ self.additions=sum(self.args[n] is not None for n in self.active)
+
+ @lru_cache(maxsize=16384)
+ def support_in(self,node,common):
+ """Exact pair-input support in coordinates with this common point."""
+ assert self.core[node]&(1<=6 and h%2==0,'Even ground size required')
+ c=circuit or SharedPointCircuit(h)
+ require(c.h==h,'Mismatched circuit')
+ v=comb(h,3);N=v**3;m=h**3;R=c.additions+len(c.outputs)
+ W=2*N+2*v*v*(R+h);L=3*v*v*h*h;D=N-2*L
+ return dict(h=h,v=v,N=N,m=m,side_roles_per_invocation=R,
+ W=W,L=L,D=D,s=W*m-D,eta=Q(D,W*m))
+
+
+def parameters():
+ a=BIT_SAVING
+ return Parameters(1-a,1-A,Q(1,21),9*a/10,1-19*a*a/20,
+ 1-9*a*a/10,KAPPA,beta=Q(9,10))
+
+
+def certificate():
+ c=SharedPointCircuit(46);n=counts(circuit=c)
+ symbolic=c.verify();frames=c.verify_frames()
+ _,log_hi=log_integer_bounds(n['m'])
+ require(log_hiBIT_SAVING*LOG_BOUND,'Insufficient saving')
+ witness=certify_parameters(parameters(),generalized_beta=True,strict_margin=True,
+ layout_model='nonadjacent')
+ require(Q(witness['minimum_margin'])==3*BIT_SAVING**2/70,'Wrong minimum')
+ # Necessary bound for this particular circuit and downstream constraints.
+ log_lo,_=log_integer_bounds(n['m'])
+ a_upper=n['eta']/((1-n['eta'])*log_lo)
+ ceiling=a_upper*a_upper/(20*(1-a_upper))
+ require(ceilingQ(1,2**59),'Invalid target saving')
+ budget=n['D']/(2*n['v']**2*n['m']*target_a*LOG_BOUND)-n['v']-n['h']
+ return dict(status='CONDITIONAL 13*2^-66 WITNESS; frame-transfer proof supplied separately',
+ upstream_commit=verify_sources(),bit_counts={k:str(v) for k,v in n.items()},
+ circuit=symbolic,frames=frames,bit_saving=str(BIT_SAVING),
+ complex_saving_unchanged=str(A),log_m_upper=str(LOG_BOUND),
+ deficit_slack=str(n['eta']-BIT_SAVING*LOG_BOUND),witness=witness,
+ exact_circuit_kappa_upper=str(ceiling),
+ target_59=dict(bit_saving=str(target_a),
+ sufficient_maximum_integer_side_roles=(budget.numerator-1)//budget.denominator),
+ scope='Conditional on the written source-span/complement-frame transfer and unchanged upstream interfaces; no general optimality claim.')
+
+
+if __name__=='__main__':
+ result=certificate()
+ (ROOT/'certificates/shared-point-network.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+ print('PASS conditional shared-point witness 13*2^-66; minimum',result['witness']['minimum_margin'])
+ print(result['bit_counts'])
+ print('Target 59:',result['target_59'])
diff --git a/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/structured_bulk_assembly.py b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/structured_bulk_assembly.py
new file mode 100644
index 0000000000..b76f9cb5a4
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/repo/scripts/structured_bulk_assembly.py
@@ -0,0 +1,103 @@
+#!/usr/bin/env python3
+"""Copyright 2026 icekylinx. Apache-2.0.
+Substantial OpenAI GPT-6 Astra and Codex assistance.
+
+Exact finite bridge and assembly for the round-three networks.
+
+Adapted parameter calculation and semantic/product-row proof from PR23,
+Zhihao Chen (jacklightChen), which attributes routing, phase-cell inverse
+and bulk resampling to the RaD project (hipotures), commit
+45d9b60355872041f9275f77c057514def0d45bc. This file does not regenerate,
+audit, or substitute for the finite-network or analytic source proofs.
+"""
+from fractions import Fraction as Q
+
+def js(x):
+ if isinstance(x,Q):return str(x)
+ if isinstance(x,dict):return {str(k):js(v) for k,v in x.items()}
+ if isinstance(x,(tuple,list)):return [js(v) for v in x]
+ return x
+
+def halving(m,r):
+ assert 0=s+E and 2*B+18Q(coeff*51,25)
+ return dict(bit=dict(m=bit_m,W=bit_W,maxchild=bit_maxchild,
+ halving_degree=db,wire_bits=wb),
+ complex=dict(m=m,W=W,s=s,maxchild=r,halving_degree=dc,
+ wire_bits=wc,scalar_terms=scalar_terms,scalar_group_upper=G),
+ semantic=dict(E=E,literal_charge=charge,strict_literal_gap=E-charge,
+ B=B,C0=C0,C1=1,induction_gap=2*B*(m-r)-s-E),
+ rows=dict(coefficient=coeff,degree=degree,suffix_slope=4*degree,
+ degree_gap=Q(degree)-Q(coeff*51,25),
+ contract='W_complex^D_complex * W_bit^D_bit; preceding row prefix, single complete-row padding, nested bit stock restored'))
+
+def assembly(bit_saving,complex_saving,bridge,kappa,eta=Q(1,10**8),beta=Q(1,4)):
+ a,b=bit_saving,complex_saving
+ tau,sigma=1-a,1-b
+ q=a*(1-2*eta); lp=1-q; lam=(tau+lp)/2
+ c=q*(1+eta); eps=(1-eta)/(1+c+q)
+ minimum=eps*q; r=(minimum+1-eps)/2; delta=eta/8
+ internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+ margins=dict(original_prefix=1-eps*(1+c),coordinate_movement=a,
+ compact_phase_layer=minimum,bulk_exposure=a,
+ Gaussian_arithmetic=min(1-eps-delta,r-delta),
+ scalar_work=1-eps-delta,dimension=eps)
+ slacks=dict(bit_positive=a,complex_above_bit=b-a,
+ complex_below_one_over32=Q(1,32)-b,beta_positive=beta,
+ beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,
+ q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,
+ c_positive=c,c_below_one=1-c,q_below_reservations=c-q,
+ lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,
+ lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,
+ compact_leaf=lp-leaf,compact_reservations=lp-(1-c),
+ lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,
+ guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,
+ record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=r-delta,
+ gamma_sublinear=1-eps-r,cell_above_band=eps-(1-r)/2,
+ prime_interval_packing=1-eps,alpha_positive=r,alpha_below_one=1-r,
+ alpha_below_one_fourth=Q(1,4)-r,delta_positive=delta,
+ delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,
+ small_field_exposure=1-eps-minimum,
+ artificial_boundary=8-eps+r-delta-minimum,
+ literal_scalar_guard=Q(bridge['semantic']['strict_literal_gap']),
+ row_product_gap=bridge['rows']['degree_gap'])
+ slacks.update({name+'_above_kappa':val-kappa for name,val in margins.items()})
+ assert all(v>0 for v in slacks.values()),{k:str(v) for k,v in slacks.items() if v<=0}
+ assert min(margins.values())==minimum
+ assert margins['original_prefix']-minimum==eta
+ return dict(parameters=dict(a_bit=a,a_complex=b,tau=tau,sigma=sigma,
+ eta=eta,beta=beta,q=q,c=c,epsilon=eps,lambda_=lam,
+ lambda_prime=lp,alpha_squared_power=r,delta=delta,
+ C0=bridge['semantic']['C0'],C1=1,kappa=kappa),
+ strict_constraints=slacks,margins=margins,minimum_margin=minimum,
+ absorption_gap=minimum-kappa,
+ recurrence=dict(internal=internal,leaf=leaf,reservations=1-c))
diff --git a/research/shrunk-birth-terminal/search/original-runtime/verify_candidate.py b/research/shrunk-birth-terminal/search/original-runtime/verify_candidate.py
new file mode 100644
index 0000000000..fb23464023
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/original-runtime/verify_candidate.py
@@ -0,0 +1,17 @@
+from pathlib import Path
+from hashlib import sha256
+import datetime,importlib.util,json,os,sys,time,pickle
+W=Path(__file__).resolve().parent;P=W/'repo/research/r12-logical-frames'
+name=sys.argv[1];O=W/name;O.mkdir(exist_ok=True)
+def load(name,path):
+ spec=importlib.util.spec_from_file_location(name,path);module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module);return module
+config={k:os.environ[k] for k in ('R12_FRAME_MODE','R12_FRAME_ROUNDS','R12_DEFER_MODE')};sources={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')};start=time.monotonic()
+(O/'process.json').write_text(json.dumps(dict(started_utc=datetime.datetime.now(datetime.timezone.utc).isoformat(),config=config,sources=sources),indent=2)+'\n')
+sys.path.insert(0,str(P));ref=load('r12_reflection',P/'reflection_audit.py');d=ref.capture(P/'complex_deferred.py')
+(O/'complex-profile.json').write_text(json.dumps(d['out'],indent=2,sort_keys=True)+'\n')
+adapter=load('r12_birth_checkpoint',W/'references/birth_checkpoint.py');adapter.export_checkpoint(d,O)
+result=ref.audit(d);result['source_sha256']=sha256((P/'complex_deferred.py').read_bytes()).hexdigest();result['audit_sha256']=sha256((P/'reflection_audit.py').read_bytes()).hexdigest()
+(O/'reflection-audit.json').write_text(json.dumps(result,indent=2,sort_keys=True)+'\n')
+assert sources=={str(p.relative_to(P)):sha256(p.read_bytes()).hexdigest() for p in P.glob('*.py')}
+receipt=dict(status='PASS complete own-candidate compiler, dirty replay, exact binary frames, exact all-input supports and independent literal reflection',elapsed_seconds=round(time.monotonic()-start,3),config=config,sources=sources,profile_sha256=sha256((O/'complex-profile.json').read_bytes()).hexdigest(),checkpoint_sha256=sha256((O/'FRAMES.pkl').read_bytes()).hexdigest(),reflection_sha256=sha256((O/'reflection-audit.json').read_bytes()).hexdigest())
+(O/'verification.json').write_text(json.dumps(receipt,indent=2,sort_keys=True)+'\n');print(json.dumps(receipt,indent=2))
diff --git a/research/shrunk-birth-terminal/search/recipe/coordinates.json b/research/shrunk-birth-terminal/search/recipe/coordinates.json
new file mode 100644
index 0000000000..3673f8c4cc
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/recipe/coordinates.json
@@ -0,0 +1,401 @@
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+}
diff --git a/research/shrunk-birth-terminal/search/recipe/expansion.json b/research/shrunk-birth-terminal/search/recipe/expansion.json
new file mode 100644
index 0000000000..4969200999
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/recipe/expansion.json
@@ -0,0 +1,866 @@
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diff --git a/research/shrunk-birth-terminal/search/references/pr124/FETCH.json b/research/shrunk-birth-terminal/search/references/pr124/FETCH.json
new file mode 100644
index 0000000000..df2e50ce72
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/FETCH.json
@@ -0,0 +1,22 @@
+{
+ "author": "jamesyc",
+ "commit": "f36782865dfe81abaa40254e8f41b8ccb3c54556",
+ "files": {
+ "LICENSE": "c71d239df91726fc519c6eb72d318ec65820627232b2f796219e87dcf35d0ab4",
+ "NOTICE": "46b84a2254d554c8adbe67ddaf33640e1b99e31168a1d90305d470e4fdab8e23",
+ "research/birth-read-reuse/BASE_INPUTS.json": "a51527d8bd67453dc7b5b747973047211f9c92d47619f7fb015c13edc23c1916",
+ "research/birth-read-reuse/PROOF.md": "b9182866812a046563da3ab3c7f0a0f29ccf9abe7a20816343a07c7a3d997126",
+ "research/birth-read-reuse/README.md": "9ceec4380d5b26b71170781f42d4f0e40f48554411b453a3588fdcdd26ce69f6",
+ "research/birth-read-reuse/audit_birth_frames.py": "ea785e80e97ba7c3fd4dbc3082a0d131b40ecf07c764b81f1935717140fa1eb7",
+ "research/birth-read-reuse/build_frames.py": "a44aa0c83f586bff2aa52186077ae998e3ea3a2644fe7cda14fc1114fb6b6c85",
+ "research/birth-read-reuse/build_roles.py": "f51c6d9082f18d2967487f8a6eb2e7ca89f8e2e32471f091b6b953669a0ee9dd",
+ "research/birth-read-reuse/check_assembly.py": "5eea415da447730942ee3ec10e3a8431d7b7425ef4d5d1e7b2c90d0d17572ef0",
+ "research/birth-read-reuse/check_birth_lemma.py": "a9de1a07717afd7a9377cf53e6922d0d3fc22b09fb0348722bb07ae022e8288c",
+ "research/birth-read-reuse/load_graph.py": "cc1eb5c087b3cf6bbbc8e2461c345d2a0f1bcdf422b8a36d3bde0886e6eaa29e",
+ "research/birth-read-reuse/match_births.py": "f9f00396bccad1bbda2db94ab0c3f4d0fc4608485d265f9c2d78162f4dfcab78",
+ "research/birth-read-reuse/readout_cost.py": "ebc5ca6aeea6bdadfe067b32b4d2dd4e06f295dbe7e26216082caacde81a32bf"
+ },
+ "pr": 124,
+ "repository": "https://github.com/CrocSwap/integer-mult-bounds",
+ "status": "Exact original Git bytes retained; no foreign producer replay"
+}
diff --git a/research/shrunk-birth-terminal/search/references/pr124/LICENSE b/research/shrunk-birth-terminal/search/references/pr124/LICENSE
new file mode 100644
index 0000000000..261eeb9e9f
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/LICENSE
@@ -0,0 +1,201 @@
+ Apache License
+ Version 2.0, January 2004
+ http://www.apache.org/licenses/
+
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+ any Contribution intentionally submitted for inclusion in the Work
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+ Notwithstanding the above, nothing herein shall supersede or modify
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+ 6. Trademarks. This License does not grant permission to use the trade
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+ 7. Disclaimer of Warranty. Unless required by applicable law or
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+ Contributor provides its Contributions) on an "AS IS" BASIS,
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diff --git a/research/shrunk-birth-terminal/search/references/pr124/NOTICE b/research/shrunk-birth-terminal/search/references/pr124/NOTICE
new file mode 100644
index 0000000000..50c6d1236d
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/NOTICE
@@ -0,0 +1,321 @@
+A sharper exponent for integer multiplication
+Copyright 2026 Douglas Colkitt
+
+This project includes unmodified source files from OpenAI's manuscript
+"Integer multiplication below n log n" and its accompanying repository:
+https://github.com/openai/math
+Commit: adc7f1241b42e322a6451854ab7e4b4c146bf78a
+
+The original manuscript identifies OpenAI as its author. Its Apache-2.0
+license is retained at upstream/LICENSE. The exact source URLs and hashes
+are recorded in upstream/manifest.json. Proposed modifications are supplied
+as separate files under patches/; upstream source files remain unchanged.
+
+The original local research note, scripts, certificates, patches, and
+documentation were prepared by Douglas Colkitt with assistance from OpenAI
+Codex. The community release incorporates work by the contributors identified
+in the notices below; it is not solely Douglas Colkitt's work.
+This project is not an official OpenAI release or an OpenAI endorsement.
+
+Related contributions (not imported in this checkpoint):
+Zhihao Chen (jacklightChen), PR #7, supplied an earlier ternary five-subset
+motif, finite-alphabet transfer and a different compressed producer:
+https://github.com/CrocSwap/integer-mult-bounds/pull/7
+The present checkpoint claims no priority for that motif. Related compressed
+complex-network work was submitted by eumemic in PR #3:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+The pending contributions and their stronger bounds require their own review;
+this notice does not represent adoption or verification of their claims.
+
+Additional community work, including parallel and superseded submissions, is
+acknowledged in CONTRIBUTORS.md, with pinned submission metadata in
+docs/research/contribution-snapshot.json. These acknowledgements do not imply
+joint authorship of the checkpoint, incorporation of pending code, or verification
+of submitted mathematical claims. Original source-specific notices remain in force.
+
+Community release (accepted by conditional maintainer audit):
+The following original contributor notices apply to the imported PR #39 chain.
+The preceding non-import statements describe the preserved 2^-30 checkpoint.
+
+Ternary five-subset construction and common-four-point resynthesis
+Copyright 2026 Zhihao Chen (jacklightChen)
+
+This is Zhihao Chen's first submission of this specific construction to this
+repository. Research, proof development, code and verification were prepared
+with substantial assistance from GPT-6 Astra (OpenAI Codex), as identified by
+the contributor. This is not independent review or an OpenAI endorsement.
+Future research building on this contribution should explicitly acknowledge
+Zhihao Chen (jacklightChen), cite the accompanying note and pull request, and
+retain the preceding contributors' attribution. This notice records research
+provenance; the repository's Apache-2.0 license remains unchanged.
+
+Dependencies retained from eumemic's Claude-assisted PRs #3 and #5:
+https://github.com/CrocSwap/integer-mult-bounds/pull/3
+https://github.com/CrocSwap/integer-mult-bounds/pull/5
+PR #5 commit: d3d370c34937503bd3fa63c83d505a05e8e50893
+These include complex_circuit.py, complex_network.py, fast_gaussian.py,
+their generators, construction notes and certificates. The Gaussian input
+scaling proof is corrected in this derivative; see the modification notice below.
+Aligned pairing also appears in Bortlesboat's PR #2. Retained totals and bank
+sharing appear in dleen's PR #4 and cheaper retained centers in eumemic's PR #6.
+Their results and ideas are credited separately from this new construction.
+
+Bulk recursion and controlled tensor basis, 8 October 2026
+Copyright 2026 icekylinx
+
+The new projector batching, controlled simultaneous basis, mixed-width tape
+recursions, whole-residual complex recursion, and dependency-path precision
+guard in the batched-23 proof package are contributed by icekylinx, developed
+with substantial OpenAI GPT-6 Astra assistance. Review corrections and
+repository integration were prepared with OpenAI Codex assistance. They build on the retained
+PR #7 finite producers and the preceding contributions credited above.
+The new package retains the repository's Apache-2.0 license and the original
+authors' attribution. It is not an official OpenAI release or endorsement.
+
+Modification notice, 8 October 2026 (icekylinx): the retained fast Gaussian
+proof now bounds shifted approximation error by F=2^ceil(1.14 alpha^2).
+The P=34p precision budget and asymptotic exponent are unchanged. New batching
+checks are integrated into make verify. Existing attribution and licenses
+are retained.
+
+Partial-swap extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The partial-swap framing, binary retained-total triple construction,
+dependency-preserving positive labels and carrier reuse, unequal (25,23,57)
+common basis, improved complex batching, and exact assembly are contributed
+by icekylinx with substantial OpenAI GPT-6 Astra and Codex assistance.
+This extension directly inherits PR #10, commit
+62691e395a0458ce089a1c7b5d89e74291e95e29. The portable producer adapters
+modify the retained paired-exclusion and shared-point implementations credited
+above. The original licenses, attribution, and Gaussian correction are retained.
+
+Endpoint-gauge extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The complementary auxiliary endpoint gauges, (32,30,40) controlled basis,
+general nondegenerate binary phase residuals, retained-center complex producer,
+updated path guard and exact assembly are contributed by icekylinx with
+substantial OpenAI GPT-6 Astra and Codex assistance. This extension inherits
+f2ab41aebad47861caf6316282c1793e5513845e and its PR #10 ancestry. New portable
+adapters retain the paired-exclusion and shared-point contributions credited
+above. Original licenses, notices and the Gaussian correction are retained.
+
+Structured-basis and semantic-bulk extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The selected (32,30,36) bit construction, A1/A5 block refinements, fixed
+middle-axis I+J profiles with bounded-minor CRT certificates, mixed dyadic
+complex centers, complete data-front batching and circuit-specific assembly
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. The immediate parent is ed90fd940279c336ebc45968631bdebfb087b505.
+
+The semantic/bulk compatibility argument, literal scalar charge, product row
+stock and parameterization adapt Zhihao Chen (jacklightChen)'s PR #23,
+commit 661ebabc1076c9f525d7ce4967c876b203fa9827. Translated complex endpoints
+are adopted from the same contributor's PR #21,
+commit 5ba6cf0bfb68f2be8d15610e7972207c50254d6a, following eumemic's source-frame
+work and the earlier nested-basis contributions.
+
+Completed-child semantic precision, arbitrary-coordinate routing, phase-cell
+Gaussian inversion and bulk tape transfer are credited to the RaD project
+(hipotures), commit 45d9b60355872041f9275f77c057514def0d45bc, exposed through
+PR #20 at 4f8d6c8272b5ff307a0da51df545ec3cd96a8b6e. Their selected proof
+sources retain their separate CC0 license and original NOTICE under
+references/semantic-bulk/rad20. The PR #23 source retains its recorded OpenAI
+Codex assistance; RaD retains its recorded Codex and GPT-6.1-Sol Ultra
+assistance. These are source attributions, not claims about this session's
+runtime model. Related contributions by Rohan Arun and Aurel Prosz remain
+acknowledged in the imported notices. No exclusive priority or additional
+license condition is asserted.
+
+Copied retained-center extension, 8 October 2026
+Copyright 2026 icekylinx
+
+The copied retained-center schedule in both orientations, its complex-phase
+transfer, the Wm-N+L rank budget, and the selected (25,23)/(28,28) composition
+are contributed by icekylinx with substantial OpenAI GPT-6 Astra and Codex
+assistance. This extension inherits PR #32 at
+0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52 and the preceding PR #10/#18/#24 work.
+
+The two-stage topology and paid copied-stream endpoint correction are due
+to Aurel Prosz (Paureel), c82d09eb4781b68435e3fa3eb6beea72fa900fab,
+through Zhihao Chen (jacklightChen)'s PR #29 unequal-axis composition,
+9d963275075fa98f1da821e27757b238dafd6b3c. That source also credits Swapnil
+Jain's two-stage development at ae405eb474d1486b2d8aef90139869f927f4836a.
+
+The contiguous corner method, incidence factorization and exact partition
+certificates are due to Rohan Arun (PR #31), method commit
+02f68f95369c39955c5ffcfddbd75cd83e26b305. The selected (25,23) certificate
+specializes Dominik Scholz's parameterization (PR #33),
+a499a345c040aa15b68e984a0904eadc485c7a7e. Their source notices and proof
+snapshots are preserved in references/copied-centers. Historical OpenAI
+Codex, GPT-6 Astra and Anthropic Claude Opus 5.5 assistance is credited to
+the respective imported sources. Existing PR #21/#23 and RaD attribution,
+licenses and the Gaussian correction remain in force.
+
+Copied centers with reversed (23,25) data corners, 2026-10-08
+Rohan Arun with substantial OpenAI Codex assistance supplies the composition,
+exact dimension23 controls and cost/assembly integration. James Chang's PR34
+supplies the reversed boundary family; icekylinx's PR36 supplies copied retained
+centers and the selected complex graph. The balanced assembly remains attributed
+to RaD/hipotures and its PR34 specialization. Retain Dominik Scholz PR33, Rohan
+Arun PR31, Zhihao Chen PR29/21/23, Paureel/Aurel Prosz, Swapnil Jain, icekylinx,
+eumemic, Douglas Colkitt, OpenAI and all earlier notices and hypotheses.
+This is not a claim of formal verification, new foundational rank identities,
+global optimality or measured runtime speedup.
+
+Fixed middle basis with copied reversed corners (2026-10-08):
+Rohan Arun, with substantial OpenAI Codex assistance. Composition and
+simultaneous-basis proof retain icekylinx PR32/36, James Chang PR34,
+Dominik Scholz PR35/38, Zhihao Chen, Paureel, Swapnil Jain, RaD/hipotures,
+eumemic and all preceding attribution and licenses. See research/copied-fixed-reversed.
+
+Changed-graph composition with copied centers and fixed bases, 8 October 2026
+Prepared with OpenAI Codex assistance.
+The new composition uses icekylinx PR36 copied centers and PR32 fixed-I+J
+projectors/profiler, Dominik Scholz PR35 two fixed factors and CRT argument,
+Zhihao Chen (jacklightChen) PR29/23 interfaces, Aurel Prosz (Paureel) and
+Swapnil Jain's two-stage development, Rohan Arun PR25/31 corner methods,
+Dominik Scholz PR33/38 dimension/composition work; James Chang (jamesyc)
+PR34 reversed geometry and balanced transfer; Rohan Arun PR37/39/40
+reversed integration, modular data tests and both-fixed baseline;
+RaD (hipotures) PR41 changed scalar DAGs, alternating point order and
+independent role compiler; RaD balanced routing/bulk interfaces, and all
+retained predecessors.
+Complete attribution and the conditional proof boundary are recorded in
+research/copied-fixed/PROOF.md; imported originals and source pins are retained.
+Original Apache-2.0 and CC0 notices remain applicable.
+
+Community follow-up integration (PRs #49, #45 and #26), 8 October 2026:
+Rohan Arun contributes weighted carrier matching and climbed summand/leave-one-out
+orders (PRs #44/#47/#49), with Anthropic Claude assistance. The final construction
+composes Chafik Boukhalfa's changed-graph checks, exact rational data recovery and
+reordered exclusion sums (PRs #43/#46/#48, OpenAI Codex assistance) with RaD /
+hipotures's alternating pair order and independent physical role compiler (#41).
+All predecessor attribution and conditional proof interfaces remain in force.
+
+Alejandro Zarzuelo Urdiales contributes Gaussian parity and canonical arithmetic
+proofs, finite tensor execution, profile precision accounting and mixed-center
+reference checks (#45), with substantial OpenAI Codex assistance. See
+research/gaussian-parity-synthesis/PROVENANCE.md for his full attribution.
+Ryan S / princezuda contributes historical Lean certificate arithmetic, algebraic
+frame/movement/guard lemmas and independent paired-circuit checks (#26). Original
+source notices and historical snapshots are preserved. Neither formal package
+claims a full formal proof of the multiplication algorithm or a new kappa.
+
+Joint frame compilation of skip-prefix strips
+
+The local compiler and exact finite witnesses were prepared by eumemic with
+substantial OpenAI Codex assistance. Avi Eisenberg / ikeboy with Anthropic
+Claude assistance supplied the unmodified PR #53 skip-prefix producer.
+The pinned PR #48 pipeline is Chafik Boukhalfa's contribution, incorporating
+Rohan Arun, RaD / hipotures, icekylinx, Dominik Scholz, James Chang,
+Zhihao Chen, Aurel Prosz / Paureel, Swapnil Jain, eumemic, Douglas Colkitt,
+OpenAI, David Harvey, Joris van der Hoeven and the earlier contributors
+credited in the retained sources. See references/frame-compiler/pr48/NOTICE
+and references/frame-compiler/pr53/NOTICE for their original attribution.
+No authorship or review by those predecessors is claimed for this compiler.
+
+Joint dual-skip/frame-compiler composition (2026-10-08)
+---------------------------------------------------
+Rohan Gupta / gupt1156 with Anthropic Claude assistance: PR55 dual-skip
+scalar graph; original LICENSE and NOTICE are retained under
+references/frame-compiler/pr55. eumemic with substantial OpenAI Codex
+assistance: PR57 joint reversible frame compiler, serialized physical-word
+replay and profile reconstruction. Chafik Boukhalfa with OpenAI Codex
+assistance: this composition, independent integration and exact certificate.
+Avi Eisenberg / ikeboy, Rohan Arun, RaD / hipotures, icekylinx, and all
+predecessor authors retain the notices above and in pinned source files.
+No original copyright or Apache-2.0 notice is removed.
+
+Ranked reclamation after the PR58 joint-dual composition (2026-10-08)
+----------------------------------------------------------------
+Chafik Boukhalfa with OpenAI Codex assistance: prioritize retired physical
+slots by descending current frame rank, retaining slot ID as the tie-breaker;
+complete replay, exact profiles, comparison and adversarial controls.
+The dedicated joint_dual_reclaim_compiler.py is derived from eumemic's PR57
+compiler. Its original shared compiler remains byte-identical. The PR55
+producer and all preceding attribution remain unchanged. The complete PR58
+comparison certificate and its original source/proof provenance are retained
+under references/frame-compiler/pr58.
+
+Skip-prefix strip producer, 8 October 2026
+By Avi Eisenberg (ikeboy), with Anthropic Claude (Claude Opus 5.5)
+assistance. The skip-prefix leave-one-out strip layout in
+research/skip-strips/skip_graph.py is new. Everything else reuses Chafik
+Boukhalfa's PR #43/#46/#48 research/copied-fixed pipeline, its verification
+code, exact data recovery and support-order sorting, together with:
+- Rohan Arun's PR #44 weighted carrier matching optimizer;
+- RaD (hipotures) PR #41 alternating point order;
+- every predecessor credited above.
+Complete attribution and the conditional proof boundary are recorded in
+research/skip-strips/PROOF.md. Original Apache-2.0 and CC0 notices remain
+applicable.
+
+Local split-pair skip-prefix research continuation (2026-10-08)
+Prepared with substantial OpenAI Codex assistance at the user's request.
+New contribution: singleton/pair recursive partition refinement, finite summand
+order and moment search, and verified composition with inherited paid clones.
+Avi Eisenberg/ikeboy with Anthropic Claude assistance: PR53 skip-prefix strips.
+Chafik Boukhalfa with OpenAI Codex assistance: PR54 original-envelope clone
+specialization and PR43/46/48 checking interfaces. RaD/hipotures: PR51
+whole-chain/source-partition cloning and earlier producer/interfaces.
+Rohan Arun: PR44 weighted matching and earlier fixed/reversed work, with all
+stated historical AI assistance. All predecessor notices remain applicable.
+
+Original-envelope whole-chain clones on skip-prefix strips (research/skip-clones):
+Chafik Boukhalfa, prepared with OpenAI Codex assistance. The complete-chain
+source-partition clone operation is adapted from RaD / hipotures, PR #51,
+with original envelopes retained here. The scalar base is Avi Eisenberg's
+PR #53 skip-prefix layout, prepared with Anthropic Claude assistance.
+All credited PR #43/#46/#48, PR #44 and earlier code/proof notices remain
+in force. This extension is provided under the repository's Apache-2.0 terms.
+
+Community review checkpoint #50–#61, 8 October 2026
+Maintainer integration and independent arithmetic: Douglas Colkitt, with OpenAI Codex.
+Avi Eisenberg / ikeboy: skip-prefix strip framework (#53), with Anthropic Claude.
+Rohan Gupta / gupt1156: parallel order search (#50, stated Antigravity assistance)
+and dual-suffix strips (#55, Anthropic Claude assistance).
+Eumemic: equal-frame joint compilation and paid signal reclamation (#57), with Codex.
+Chafik Boukhalfa: original-envelope paid clones (#54), composition (#58) and ranked
+reclamation (#60), with Codex. Rohan Arun: order search (#52) and positive-frame
+composition (#56), with Anthropic Claude and stated Codex validation assistance.
+RaD / hipotures: enlarged frames, source partitions and paid whole-chain clones
+(#51), with Codex. Rohan Garg / rohangar1: singleton/pair recursion and paid-clone
+composition (#59), with Codex. Alejandro Zarzuelo Urdiales: exact parameter
+refinement, scoped Lean arithmetic, matrix/parity and search tools (#61), with
+his disclosed multi-tool and Codex assistance.
+Parallel #50/#52 records are reviewed and credited without replacing the earlier
+climbed-48 implementation; their exact commit history is retained. The separate
+#51 witness is retained as research; its source-graph/negative-basis data proof
+has not received the same full replay as #56's consumed compiler machinery.
+See docs/research/community-round2-review.md for precise validation boundaries.
+All earlier licenses, contributions and notices remain applicable.
+
+Interval strips and core-aware pair assembly
+
+The interval leave-one-out strips and the core-aware group-pair assembly in
+research/pair-assembly were prepared by Avi Eisenberg / ikeboy with Anthropic
+Claude assistance. They build on PR #53's skip-prefix pipeline and its
+inherited PR #48 sources. The stacked witness in research/pair-assembly/frame
+uses eumemic's PR #57 joint frame compiler unchanged; its driver and verifier
+are adaptations of PR #57's skip_frame_compiler.py, skip_frame_compose.py and
+verify_skip_frame.py. Original notices are retained.
+
+Stopped product-ring extension, 9 October 2026
+Copyright 2026 icekylinx
+
+The opposite-bank generic projector factorization, componentwise atom-ring
+adapters, stopped recurrence and outer ordinary-interchange conversion,
+aligned pair-star producer with rational centers, exact denominator-21
+grid and selected (23,23)/(24,24) composition are contributed by icekylinx
+with substantial OpenAI GPT-6 Astra and Codex assistance. This extension
+builds on merged PR #36, 11817ccacb564bb7f98789c20dc11d3fece207e3, and is
+integrated on upstream main 56b66d58297deca1d7dd130247d720e960f77a37.
+
+The retained ordinary leaf uses the preceding projector, corner and
+copied-center proofs. The selected two-stage topology retains Aurel Prosz
+(Paureel), Swapnil Jain and Zhihao Chen's credits; the semantic assembly
+retains PR #21/#23 and RaD's attribution. Paired producers, carrier matching,
+original source notices and each imported license remain unchanged.
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/BASE_INPUTS.json b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/BASE_INPUTS.json
new file mode 100644
index 0000000000..36c46849a3
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/BASE_INPUTS.json
@@ -0,0 +1,9 @@
+{
+ "head": "6ec868e8568ca9a74b7245494de1b187c7be78fe",
+ "files": {
+ "research/deferred-replayed-117/complex-dag.json.gz": "3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b",
+ "research/deferred-replayed-117/complex-profile.json": "ff5e9bbc1a3794d8dd3f75e194ea002cef8439c40a5d434c4a84e46967edc98e",
+ "research/deferred-replayed-117/certificate.json": "f1d77d26036cf2b01bc630a572b2cdea0027e0faa2e4899b5b907b9d455ff916",
+ "certificates/copied-centers-network.json": "7dbd675e42e22ac076280360f8750031851564bb7a56079e66236fee5d0a6cdf"
+ }
+}
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/PROOF.md b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/PROOF.md
new file mode 100644
index 0000000000..2f65bed9a8
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/PROOF.md
@@ -0,0 +1,45 @@
+# Dirty readouts permit physical slot reuse
+
+Base: rohanarun/integer-mult-bounds at6ec868e8568ca9a74b7245494de1b187c7be78fe (corrected PR118). The operand/root DAG and virtual role/frame profile are unchanged fromec862a5af51537495c745d9f2323e8a5736ee265. Under its retained analytic, exact-recovery, prime, whole-residual, complete-row and fixed-tape hypotheses, this construction gives
+
+ T(n)=O(n(log n)^(1−kappa)),
+ kappa=5519166047173/50000000000000000=0.00011038332094346.
+
+This is an author-checked conditional draft; independent review remains pending. No upstream program is executed by the supplied checks.
+
+## The new operation
+
+In a linear virtual program, regard the initial value of each newly born register as an independent symbol g_a. Let D_a be its exact future contribution to output accumulators, cutting propagation at each subsequent birth on that storage. Then the output is Fx+sum(D_a g_a). A physical birth may leave any old value in its slot: read that value and add −D_a g_a to the output. The corrections cancel identically even if birth values contain source signals or are correlated with earlier dirt. Reverse every actual workspace/source gate chronologically to restore all original workspace.
+
+Sources, workspace and output banks must be disjoint. Outputs are never later controls, sources, guards or addresses. Every correction is paid and must occur at a legal common frame. There is no physical dirty reset and no assumption that a fresh-signal relation is equality of dirty contents.
+
+PR118 already reads each untouched deferred register B negatively at sigma_B after center phase one. Choose an old role A whose last forward gate and every terminal read are already finished, with final frame E contained in sigma_B. Raise A to sigma_B; use its actual value in B's existing negative readout; route B's future virtual life through A. The virtual program and D_B are unchanged. The new offset is canceled by the same readout. Selected pairs are disjoint, and all selected recipients have no source injection. The implementation nevertheless uses true reverse chronology for every inverse source gate.
+
+Per matched local role, put e=dim E and s=dim sigma_B. Remove children24−e and552+s; add child s−e (record zero rank explicitly); remove one original physical role. Weighted rank drops by576. All target read frames, copied centers and response coefficients remain unchanged. Added positive residuals are checked nonalternating. For0v for s in removed),'Selected deferred source injection requires explicit inverse insertion review'
+for b,a in merge.items():assert a not in g['placed']and b in g['placed']and b not in g['touched']and g['last'][a]in g['phase']and a not in g['terminal']
+frames=[()];ids={():0}
+def fid(F):
+ if F not in ids:ids[F]=len(frames);frames.append(F)
+ return ids[F]
+FULL=fid(fulltuple);tm=[fid((m,))for m in g['tm']];U=[fid(F)for F in g['U']]
+def basis(rows):
+ piv={}
+ for x in rows:
+ for p in sorted(piv,reverse=True):
+ if x>>p&1:x^=piv[p]
+ if x:
+ p=x.bit_length()-1
+ for q in piv:
+ if piv[q]>>p&1:piv[q]^=x
+ piv[p]=x
+ return tuple(piv[p]for p in sorted(piv,reverse=True))
+@lru_cache(None)
+def dual(i):
+ A=frames[i];piv={r.bit_length()-1 for r in A};out=[]
+ for j in range(24):
+ if j not in piv:
+ x=1<>j&1:x|=1<<(r.bit_length()-1)
+ out.append(x)
+ return fid(basis(out))
+@lru_cache(131072)
+def nested(i,j):
+ for x in frames[i]:
+ for r in frames[j]:
+ if x>>(r.bit_length()-1)&1:x^=r
+ if x:return False
+ return True
+word=[];forward_workspace=[]
+def gate(d,s,c,F,remember=False):
+ assert d!=s;word.append(('g',d,s,c,F))
+ if remember:forward_workspace.append((d,s,c,F))
+def oldread(s,F):
+ mask=ALL if g['reach_all'][s]else g['reach'][s]
+ word.append(('r',physical(s),v,mask,-1,F,('old',s)))
+def source(s):
+ x=g['first'][s];assert 1<=x<=v;gate(physical(s),x-1,1,U[x],True)
+def mix(i):
+ op,s,t,x=g['ops'][i]
+ if op==1:gate(physical(s),physical(t),1,U[x],True)
+ elif op==2:gate(physical(t),physical(s),1,U[x],True)
+for s in range(R):
+ if s not in g['placed']:oldread(s,0)
+for s,x in enumerate(g['first']):
+ if x<=v and s not in g['placed']:source(s)
+for i in sorted(g['phase']):mix(i)
+for s in g['center_roles']:
+ j=g['terminal'][s];F=fid(g['U'][g['roots'][j]]);assert len(frames[F])==23
+ word.append(('c',physical(s),v,ALL,1,F,0,('center',j-(len(g['roots'])-24))))
+for s,F in sorted(g['placed'].items(),key=lambda item:(len(item[1]),item[0])):oldread(s,fid(F))
+for s,x in enumerate(g['first']):
+ if x<=v and s in g['placed']:source(s)
+for i in range(len(g['ops'])):
+ if i not in g['phase']:mix(i)
+for s,j in sorted(g['terminal'].items(),key=lambda item:item[1]):
+ if j0
+ hist[r]+=1;current[s]=F;incidences+=1
+ if s<2*v:
+ bank=s//v;counts[bank][old]-=1
+ if not counts[bank][old]:del counts[bank][old]
+ counts[bank][F]+=1
+ def targets(bank,mask,F):
+ if len(counts[bank//v])==1 and counts[bank//v].get(F)==v:return
+ while mask:
+ b=mask&-mask;mask-=b;promote(bank+b.bit_length()-1,F)
+ for e in events:
+ digest.update(repr(e).encode())
+ if e[0]=='g':_,d,s,c,F=e;assert c in(-1,1);promote(d,F);promote(s,F)
+ elif e[0]=='r':_,s,bank,mask,sign,F,key=e;assert mask>=0 and not(mask&~ALL);promote(s,F);targets(bank,mask,F)
+ else:
+ _,s,bank,mask,sign,F,T,key=e;promote(s,F);targets(bank,mask,T)
+ assert (F==FULL and T==0)or nested(F,T)or nested(T,F)
+ r=abs(len(frames[F])-len(frames[T]));assert r==23;hist[r]+=1;copies+=1
+ for s in active:promote(s,end[s])
+ assert current==end
+ return hist,copies,incidences,digest.hexdigest()
+active_set=set(active);forward=scan(word,initial,finish)
+def swap(s):return s+v if s>p&1:x^=piv[p]
+ if x:
+ p=x.bit_length()-1
+ for q in piv:
+ if piv[q]>>p&1:piv[q]^=x
+ piv[p]=x
+ return tuple(piv[p]for p in sorted(piv,reverse=True))
+@lru_cache(65536)
+def contained(A,B):
+ for x in A:
+ for r in B:
+ if x>>(r.bit_length()-1)&1:x^=r
+ if x:return False
+ return True
+@lru_cache(65536)
+def perpendicular(A):
+ piv={r.bit_length()-1 for r in A};out=[]
+ for j in range(H):
+ if j not in piv:
+ x=1<>j&1:x|=1<<(r.bit_length()-1)
+ out.append(x)
+ return basis(out)
+@lru_cache(65536)
+def intersection(A,B):return perpendicular(basis(perpendicular(A)+perpendicular(B)))
+@lru_cache(65536)
+def nondeg(A):return len(basis(sum(((x&y).bit_count()%2)<=0 else 1<<(j-(len(roots)-H))for j,t in enumerate(g['targets'])]
+ succ=[set()for _ in range(n)];rootf=[[]for _ in range(n)]
+ def connect(x,uid):
+ _,typ,dest,_=use[uid]
+ if typ:rootf[x].append(fun[dest])
+ else:succ[x].add(dest)
+ for x in active:
+ for uid in uses[x]:
+ if matched[uid]<0:connect(x,uid)
+ for x,uid in links.items():connect(x,uid)
+ order=sorted(active,key=lambda x:(rank[x],x),reverse=True);demand=[()]*n
+ for x in order:demand[x]=basis(rootf[x]+[r for y in sorted(succ[x])for r in demand[y]])
+ def envelope(x):
+ if not args[x]:return (tm[x-1],)
+ if kind[x]==2:return basis(1<=len(roots)-H:dense[s]=True
+ else:reach[s]=1<rank[x]for x in active))
+ assert g['lifted']==39989,g['lifted'];save('LIFTED.pkl',g)
+ print('Lifted checkpoint',len(cand),'candidates',round(time.monotonic()-start,2),flush=True)
+# Only this saturating placement is repeated if a previous cap ended after LIFTED.
+U=g['U'];reach=g['reach'];cand=g['candidates'];bytarget=defaultdict(list);placed={};order=sorted(cand,key=lambda s:(-len(cand[s]),s))
+for step,s in enumerate(order):
+ X=cand[s];changed=True
+ while changed and X:
+ changed=False
+ for t in bits(reach[s]):
+ for prior in bytarget[t]:
+ B=placed[prior]
+ if (len(B)>=len(X)and not contained(X,B))or(len(B)=len(g['roots'])-H else perpendicular((g['tm'][g['targets'][j]],))
+ actual.append(terminal_frame)
+ assert all(contained(a,b)for a,b in zip(actual,actual[1:]))and all(nondeg(A)for A in actual)
+ ds=[len(A)for A in actual];chains[s]=ds
+ for a,b in zip(ds,ds[1:]):
+ if b>a:hist[b-a]+=2*v
+ if s in g['terminal']and g['terminal'][s]>=len(g['roots'])-H:hist[H-1]+=2*v
+ if H>ds[-1]:hist[H-ds[-1]]+=2*v
+ hist[576-H+ds[0]]+=2*v
+for t in range(v):
+ levels=sorted({0,H-1}|{len(placed[s])for s in bytarget[t]})
+ for a,b in zip(levels,levels[1:]):hist[b-a]+=2*v
+hist[H-1]+=2*N;hist[(H-1)**2]+=2*N;hist[1]+=N
+expected=json.loads((REPO/'research/deferred-replayed-117/complex-profile.json').read_text())
+assert dict(hist)=={int(k):v for k,v in expected['child_multiplicities'].items()},('Histogram mismatch',hist)
+assert Counter(len(A)for A in placed.values())==Counter({int(k):v for k,v in expected['deferred_dims'].items()})
+g.update(placed=placed,bytarget=dict(bytarget),histogram=dict(hist),chain_dims=chains);digest=save('FRAMES.pkl',g)
+result=dict(status='PASS original118 full frame/profile reconstruction',roles=roles,deferred=len(placed),maxchild=max(hist),weighted_rank=sum(t*n for t,n in hist.items()),all_bins_match=True,frame_sha256=digest,seconds=time.monotonic()-start,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)
+(ROOT/'FRAMES_CHECK.json').write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result,indent=2))
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/build_roles.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/build_roles.py
new file mode 100644
index 0000000000..427d518e8f
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/build_roles.py
@@ -0,0 +1,109 @@
+"""Original exact carrier matching/role reconstruction, no upstream imports."""
+import sys,os
+if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required')
+from pathlib import Path
+from collections import deque
+import pickle,json,time,resource,hashlib
+ROOT=Path(__file__).resolve().parent;REPO=Path(os.environ.get('BIRTH_REPO',ROOT.parents[1]));start=time.monotonic()
+resource.setrlimit(resource.RLIMIT_AS,(512*1024**2,512*1024**2));resource.setrlimit(resource.RLIMIT_CPU,(30,30));sys.setrecursionlimit(5000)
+g=pickle.loads((ROOT/'GRAPH.pkl').read_bytes());h,v=g['h'],g['v'];args,core,cover,rank,kind=[g[k]for k in ('args','core','cover','rank','kind')];active=g['active'];roots=g['roots'];n=len(args);full=(1<=shortest:continue
+ for uid in adj[x]:
+ y=R[uid]
+ if y<0:shortest=dist[x]+1
+ elif dist[y]==INF:dist[y]=dist[x]+1;queue.append(y)
+ if shortest==INF:break
+ def augment(x):
+ for uid in adj[x]:
+ y=R[uid]
+ if (y<0 and dist[x]+1==shortest)or(y>=0 and dist[y]==dist[x]+1 and augment(y)):
+ L[x]=uid;R[uid]=x;return True
+ dist[x]=INF;return False
+ gained=sum(augment(x)for x in left if L[x]<0);assert gained;rounds.append((shortest,gained))
+links={x:L[x]for x in left if L[x]>=0};assert len(links)==71185,len(links)
+# Every matched edge is an actual unchanged input continuation into a later use.
+assert len(set(links.values()))==len(links)
+for x,uid in links.items():assert use[uid][0]in args[x]and uid in adj[x]
+held=[];first=[];ops=[];role_of={};terminal={}
+def alloc(x):
+ s=len(first);first.append(x);held.append([x]);return s
+for x in sorted(active,key=lambda x:(rank[x],x)):
+ free=[uid for uid in uses[x]if R[uid]<0]
+ if not args[x]:
+ for uid in free:
+ s=alloc(x);ops.append((0,s,x,-1));role_of[uid]=s
+ continue
+ a,b=args[x];sa,sb=role_of.pop(edge[x,0]),role_of.pop(edge[x,1]);assert sa!=sb
+ if x in links and use[links[x]][0]==a:sa,sb=sb,sa
+ ops.append((1,sa,sb,x));held[sa].append(x);held[sb].append(x)
+ if x in links:role_of[links[x]]=sb
+ assert free;role_of[free[0]]=sa
+ for uid in free[1:]:
+ s=alloc(x);ops.append((2,sa,s,x));role_of[uid]=s
+for uid,row in enumerate(use):
+ if row[1]:terminal[role_of.pop(uid)]=row[2]
+assert not role_of and len(first)==28705 and len(terminal)==len(roots)
+# All original-role fresh signals, not sampled values.
+values=[0]*len(first)
+for op,s,t,x in ops:
+ if op==0:values[s]=1<<(t-1)
+ elif op==1:
+ assert not(values[s]&values[t]);values[s]|=values[t];assert values[s]==g['support'][x]
+ else:assert values[t]==0;values[t]=values[s];assert values[t]==g['support'][x]
+for s,j in terminal.items():assert values[s]==g['support'][roots[j]]
+for chain in held:
+ for a,b in zip(chain,chain[1:]):assert contains(a,b)
+# Dependencies in the exact selected chronological program.
+previous=[-1]*len(first);pred=[[]for _ in ops];last=[-1]*len(first)
+for i,(op,s,t,x)in enumerate(ops):
+ if op:
+ for r in(s,t):
+ if previous[r]>=0:pred[i].append(previous[r])
+ previous[r]=i;last[r]=i
+centers=[s for s,j in terminal.items()if j>=len(roots)-h]
+phase=set();todo=[last[s]for s in centers]
+while todo:
+ i=todo.pop()
+ if i not in phase:phase.add(i);todo.extend(pred[i])
+touched=set(centers)
+for i in phase:
+ _,s,t,_=ops[i];touched.update((s,t))
+expected=json.loads((REPO/'research/deferred-replayed-117/complex-profile.json').read_text());assert (len(phase),len(touched))==(expected['phase_one_ops'],expected['phase_one_roles']),(len(phase),len(touched))
+g.update(uses=uses,use=use,links=links,matched_use=R,holds=held,first=first,ops=ops,terminal=terminal,last=last,phase=phase,touched=touched,center_roles=centers)
+raw=pickle.dumps(g,protocol=4);(ROOT/'ROLES.pkl').write_bytes(raw)
+receipt=dict(status='PASS original exact118 matching/role/source reconstruction',links=len(links),roles=len(first),ops=len(ops),phase_one_ops=len(phase),phase_one_roles=len(touched),augmenting_rounds=rounds,checkpoint_sha256=hashlib.sha256(raw).hexdigest(),seconds=time.monotonic()-start,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)
+(ROOT/'ROLES_CHECK.json').write_text(json.dumps(receipt,indent=2)+'\n');print(json.dumps(receipt,indent=2))
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_assembly.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_assembly.py
new file mode 100644
index 0000000000..088f44ee93
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_assembly.py
@@ -0,0 +1,71 @@
+"""Original exact assembly for paid birth-read slot reuse. No upstream imports."""
+import sys,os,gzip
+if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required')
+from pathlib import Path
+from fractions import Fraction as Q
+from math import factorial
+import json,hashlib,time,resource
+root=Path(__file__).resolve().parent;repo=Path(os.environ.get('BIRTH_REPO',root.parents[1]));start=time.monotonic()
+profile=json.loads(gzip.decompress((root/'BIRTH_MATCHES.json.gz').read_bytes()));bill=json.loads((root/'READOUT_COST.json').read_text())
+source=repo/'research/deferred-replayed-117/certificate.json'
+oldpath=repo/'certificates/copied-centers-network.json'
+cert=json.loads(source.read_text());old_leaf=json.loads(oldpath.read_text())
+logcache={}
+def smalllog(x):
+ z=(x-1)/(x+1);N=40;lo=2*sum((z**(2*j+1)/Q(2*j+1)for j in range(N)),Q(0));tail=2*z**(2*N+1)/(Q(2*N+1)*(1-z*z));return lo,lo+tail
+ln2=smalllog(Q(2))
+def logbound(x):
+ if x in logcache:return logcache[x]
+ k=0;y=x
+ while y>=2:y/=2;k+=1
+ lo,hi=smalllog(y);out=(k*ln2[0]+lo,k*ln2[1]+hi);logcache[x]=out;return out
+
+def expbound(lo,hi):
+ n=8;assert 0<=lo<=hi<1
+ a=sum((lo**j/Q(factorial(j))for j in range(n+1)),Q(0));b=sum((hi**j/Q(factorial(j))for j in range(n+1)),Q(0));b+=hi**(n+1)/Q(factorial(n+1))/(1-hi/Q(n+2));return a,b
+
+def moment(label,m,W,children,saving):
+ rows={int(t):int(n)for t,n in children.items()};assert rows and all(00 for t,n in rows.items());lo=Q(0);hi=Q(0)
+ for t,n in sorted(rows.items()):
+ ll,lh=logbound(Q(m,t));a,b=expbound(saving*ll,saving*lh);weight=Q(n*t,m*W);lo+=weight*a;hi+=weight*b
+ scale=1<<192
+ lo=Q((lo*scale).numerator//(lo*scale).denominator,scale)
+ u=hi*scale;hi=Q((u.numerator+u.denominator-1)//u.denominator,scale)
+ assert hi<1,label
+ return dict(label=label,m=m,W=W,saving=saving,rank=sum(t*n for t,n in rows.items()),lower=lo,upper=hi,strict_gap=1-hi,enclosure_grid_bits=192,log_terms=40,exponential_degree=8)
+
+
+coarse=cert['bit_profile'];old=old_leaf['bit']['counts'];alpha=Q(1,1000);a0=Q(620523,5000000000);old_a=Q(384599,10**10)
+aactual=(1-alpha)*a0+alpha*old_a;b=Q(11040781,10**11);beta=Q(1,10**6);buffer=Q(1,10**12);a=min(aactual,(1-beta)*b-buffer)
+assert aactual==Q(1240189553,10**13)==Q(cert['actual_bit_saving'])and aactual>a>0
+moments=[moment('coarse_bit',529,coarse['W'],coarse['child_multiplicities'],a0),moment('old_ordinary',old['m'],old['W'],old['child_multiplicities'],old_a),moment('birth_reused_complex',576,profile['W'],profile['child_histogram'],b)]
+m,W,s,rmax,R=576,profile['W'],profile['rank'],max(map(int,profile['child_histogram'])),profile['R'];G=bill['global_scalar_group_upper']
+assert (W,s,R,rmax)==(115865904,66736898624,26599,574)
+E=64*(W+m+G+1)**3;charge=2*G*W*W+8*s+4*W+4+32*m;B=s+E;C0=32*m*B*B
+assert charge=s+E and 2*B+182*r**t)
+stock=[dict(m=mm,W=ww,maxchild=rr,depth=halving(mm,rr),wire_bits=ww.bit_length())for mm,ww,rr in [(529,coarse['W'],528),(575,old['W'],529),(576,W,rmax)]]
+rows=sum(x['depth']*x['wire_bits']for x in stock);rowgap=Q(32000)-Q(51,25)*rows
+assert rows==15561 and rowgap==Q(6389,25)
+bridge=dict(m=m,W=W,rank=s,R=R,maxchild=rmax,G=G,E=E,literal_charge=charge,B=B,C0=C0,C1=1,stock=stock,rows=rows,row_degree=32000,row_gap=rowgap,suffix_slope=128000,odd_grid='2^-P21^-K; K=G*(D_complex+1), with completed child preserving incoming odd exponent')
+# Exact retained assembly formulas, written independently and never imported.
+eta=Q(1,10**8);beta=Q(1,10**6);tau=1-a;sigma=1-b;q=a*(1-2*eta);c=q*(1+eta);eps=(1-eta)/(1+c+q);lp=1-q;lam=(tau+lp)/2;g=eps*q;rr=(g+1-eps)/2;delta=eta/8
+internal=tau+(1-beta)*max(sigma-tau,Q(0));leaf=sigma+beta*(1-sigma)
+grid=10**17;kappa=Q((g*grid).numerator//(g*grid).denominator,grid)
+if kappa==g:kappa-=Q(1,grid)
+margins=dict(original_prefix=1-eps*(1+c),coordinate_movement=a,compact_phase_layer=g,bulk_exposure=a,Gaussian_arithmetic=min(1-eps-delta,rr-delta),scalar_work=1-eps-delta,dimension=eps)
+slacks=dict(bit_positive=a,complex_above_bit=b-a,complex_below_one_over32=Q(1,32)-b,beta_positive=beta,beta_below_one=1-beta,leaf_saving_above_bit=(1-beta)*b-a,q_positive=q,q_below_internal=1-internal-q,q_below_leaf=1-leaf-q,c_positive=c,c_below_one=1-c,q_below_reservations=c-q,lambda_above_tau=lam-tau,lambda_above_sigma=lam-sigma,lambda_above_internal=lam-internal,lambda_prime_above_lambda=lp-lam,compact_leaf=lp-leaf,compact_reservations=lp-(1-c),lambda_prime_below_one=q,epsilon_positive=eps,epsilon_below_one=1-eps,guard_width=1-eps,K_geometry=1-eps*(1+c),K_dominates_log=eps*c,record_suffix=1-eps,phase_local=1-eps-delta,phase_boundary=rr-delta,gamma_sublinear=1-eps-rr,cell_above_band=eps-(1-rr)/2,prime_interval_packing=1-eps,alpha_positive=rr,alpha_below_one=1-rr,alpha_below_one_fourth=Q(1,4)-rr,delta_positive=delta,delta_below_one_eighth=Q(1,8)-delta,short_record_fallback=eps-a,small_field_exposure=1-eps-g,artificial_boundary=8-eps+rr-delta-g,literal_scalar_guard=Q(E-charge),row_product_gap=rowgap)
+slacks.update({name+'_above_kappa':v-kappa for name,v in margins.items()})
+assert len(slacks)==47 and len(margins)==7 and all(v>0 for v in slacks.values());assert min(margins.values())==g and margins['original_prefix']-g==eta
+next_kappa=kappa+Q(1,grid);assert g-next_kappa<=0
+
+
+inputfiles=[root/'BIRTH_MATCHES.json.gz',root/'READOUT_COST.json',source,oldpath]
+pins={('new/'+p.name)if p.parent==root else('base/'+str(p.relative_to(repo))):hashlib.sha256(p.read_bytes()).hexdigest()for p in inputfiles}
+out=dict(status='AUTHOR_CHECKED_CONDITIONAL_ASSEMBLY; independent review pending',source_head='6ec868e8568ca9a74b7245494de1b187c7be78fe',profile_source_head='ec862a5af51537495c745d9f2323e8a5736ee265',pins=pins,kappa=kappa,complex_saving=b,actual_bit_saving=aactual,supported_bit_parameter=a,moments=moments,finite_bridge=bridge,assembly=dict(parameters=dict(a=a,b=b,beta=beta,eta=eta,q=q,c=c,epsilon=eps,lambda_=lam,lambda_prime=lp,r=rr,delta=delta,C0=C0,C1=1),constraints=slacks,margins=margins,minimum_margin=g,absorption_gap=g-kappa),next_grid=next_kappa,next_grid_gap=g-next_kappa)
+def js(x):
+ if isinstance(x,Q):return str(x)
+ if isinstance(x,dict):return {str(k):js(v)for k,v in x.items()}
+ if isinstance(x,(list,tuple)):return [js(v)for v in x]
+ return x
+(root/'CANDIDATE.json').write_text(json.dumps(js(out),indent=2)+'\n');print(json.dumps(dict(kappa=str(kappa),decimal=float(kappa),complex_saving=str(b),G=G,W=W,R=R,constraints=len(slacks),margins=len(margins),seconds=time.monotonic()-start),indent=2))
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_birth_lemma.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_birth_lemma.py
new file mode 100644
index 0000000000..67f9e2c1e9
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/check_birth_lemma.py
@@ -0,0 +1,87 @@
+"""Original exact adversarial check of reset compensation; no upstream imports."""
+import sys,os
+if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required')
+from fractions import Fraction as F
+from random import Random
+from pathlib import Path
+import json,time,resource
+T0=time.monotonic()
+def add(a,b,c=F(1)):
+ for i,x in enumerate(b):a[i]+=c*x
+
+def response(events,R,X,Y,cut=True):
+ B=[[F(0)for _ in range(Y)]for _ in range(R)];M=[[F(0)for _ in range(Y)]for _ in range(X)];D={}
+ for k in range(len(events)-1,-1,-1):
+ e=events[k];kind,r=e[:2]
+ if kind=='read':_,r,t,c=e;B[r][t]+=c
+ elif kind=='gate':_,r,s,c=e;add(B[s],B[r],c)
+ elif kind=='source':_,r,j,c=e;add(M[j],B[r],c)
+ elif kind=='birth':
+ D[k]=B[r][:]
+ if cut:B[r]=[F(0)for _ in range(Y)]
+ else:raise AssertionError(e)
+ return B,M,D
+
+def run(events,R,X,Y,x,z,D=None,uncompute=True,omit=None,fresh_only=False):
+ a=z[:];out=[F(0)for _ in range(Y)];gates=[];births=[]
+ for k,e in enumerate(events):
+ kind,r=e[:2]
+ if kind=='birth':
+ if D is None:a[r]=F(0)
+ else:
+ g=a[r];births.append((k,g))
+ if k!=omit:
+ for t,d in enumerate(D[k]):out[t]-=d*g
+ elif kind=='gate':_,r,s,c=e;a[r]+=c*a[s];gates.append(e)
+ elif kind=='source':_,r,j,c=e;a[r]+=c*x[j];gates.append(e)
+ elif kind=='read':_,r,t,c=e;out[t]+=c*a[r]
+ if D is not None and uncompute:
+ for e in reversed(gates):
+ kind,r,j,c=e;a[r]-=c*(a[j]if kind=='gate'else x[j])
+ return out,a,births
+rng=Random(114113);basis_checks=0;dependent_nonzero_births=0;coefficient_max=F(0)
+for case in range(96):
+ R=1+case%5;X=1+(case//5)%4;Y=1+(case//20)%4
+ events=[('birth',r)for r in range(R)]
+ for step in range(24):
+ kind=rng.choice(['birth','source','read','gate']if R>1 else['birth','source','read'])
+ r=rng.randrange(R);c=rng.choice([F(1),F(-1),F(2),F(-2),F(1,2),F(-1,3)])
+ if kind=='birth':events.append((kind,r))
+ elif kind=='source':events.append((kind,r,rng.randrange(X),c))
+ elif kind=='read':events.append((kind,r,rng.randrange(Y),c))
+ else:
+ s=rng.choice([i for i in range(R)if i!=r]);events.append((kind,r,s,c))
+ # Force a genuinely used reuse with a nonzero old-source offset.
+ events += [('source',0,0,F(1)),('read',0,0,F(1)),('birth',0),('source',0,0,F(2)),('read',0,Y-1,F(1))]
+ B,M,D=response(events,R,X,Y);assert all(not any(row)for row in B)
+ coefficient_max=max(coefficient_max,max((abs(c)for row in D.values()for c in row),default=F(0)))
+ for b in range(X+R):
+ x=[F(i==b)for i in range(X)];z=[F(X+i==b)for i in range(R)]
+ expected=run(events,R,X,Y,x,[F(0)]*R)[0]
+ actual,restored,births=run(events,R,X,Y,x,z,D)
+ assert actual==expected and restored==z
+ assert expected==[sum(M[i][t]*x[i]for i in range(X))for t in range(Y)]
+ basis_checks+=1;dependent_nonzero_births+=sum(bool(g)for _,g in births)
+ # Dense signed rational source/dirty inputs exercise dependent birth values.
+ x=[F(rng.randrange(-7,8),rng.randrange(1,5))for _ in range(X)];z=[F(rng.randrange(-7,8),rng.randrange(1,5))for _ in range(R)]
+ assert run(events,R,X,Y,x,z,D)[:2]==(run(events,R,X,Y,x,[F(0)]*R)[0],z)
+# A one-slot two-life example: x0 is still in the slot at its second birth.
+e=[('birth',0),('source',0,0,F(1)),('read',0,0,F(1)),('birth',0),('source',0,1,F(1)),('read',0,1,F(1))]
+B,M,D=response(e,1,2,2);x=[F(3),F(5)];z=[F(7)]
+out,restored,births=run(e,1,2,2,x,z,D);assert out==x and restored==z and births==[(0,F(7)),(3,F(10))]
+controls={}
+controls['omit_reuse_readout']=run(e,1,2,2,x,z,D,omit=3)[0]!=x
+controls['do_not_cut_next_birth']=run(e,1,2,2,x,z,response(e,1,2,2,cut=False)[2])[0]!=x
+controls['omit_inverse_workspace']=run(e,1,2,2,x,z,D,uncompute=False)[1]!=z
+# Grouping negative source injections at the end fails after role aliasing.
+e2=[('birth',0),('birth',1),('source',0,0,F(1)),('gate',1,0,F(1)),('read',1,0,F(1)),('birth',0),('source',0,1,F(1)),('read',0,1,F(1))]
+_,_,D2=response(e2,2,2,2);z2=[F(7),F(11)]
+assert run(e2,2,2,2,x,z2,D2)[:2]==(x,z2)
+a=run(e2,2,2,2,x,z2,D2,uncompute=False)[1]
+for kind,r,s,c in reversed([v for v in e2 if v[0]=='gate']):a[r]-=c*a[s]
+for kind,r,j,c in reversed([v for v in e2 if v[0]=='source']):a[r]-=c*x[j]
+controls['group_negative_sources_at_end']=a!=z2
+# The gate/readout model forbids source-target-workspace aliasing by construction.
+assert all(controls.values())
+result=dict(status='PASS exact scalar lemma controls; no actual114 word or bound yet',cases=96,complete_source_dirty_basis_vectors=basis_checks,dense_rational_cases=96,nonzero_dependent_birth_values=dependent_nonzero_births,largest_test_response_coefficient=str(coefficient_max),rejected_controls=controls,one_slot_example=dict(source=['3','5'],dirty='7',birth_values=['7','10'],output=['3','5'],restored='7'),seconds=time.monotonic()-T0,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)
+Path(__file__).with_name('CHECKS.json').write_text(json.dumps(result,indent=2)+'\n');print(json.dumps(result,indent=2))
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/load_graph.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/load_graph.py
new file mode 100644
index 0000000000..72118a4c86
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/load_graph.py
@@ -0,0 +1,31 @@
+"""Original exact reconstruction from PR117's passive operand/root witness."""
+import sys,os
+if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required')
+from pathlib import Path
+from itertools import combinations
+import json,gzip,pickle,time,resource,hashlib
+ROOT=Path(__file__).resolve().parent;REPO=Path(os.environ.get('BIRTH_REPO',ROOT.parents[1]));start=time.monotonic();resource.setrlimit(resource.RLIMIT_AS,(512*1024**2,512*1024**2));resource.setrlimit(resource.RLIMIT_CPU,(30,30))
+p=REPO/'research/deferred-replayed-117/complex-dag.json.gz';raw=p.read_bytes();assert hashlib.sha256(raw).hexdigest()=='3c034d0aae388ef567a454826f4f48b26fd8a94c71e8ffed4835271b349a783b';w=json.loads(gzip.decompress(raw));h=24;tr=list(combinations(range(h),3));v=len(tr);assert (w['h'],w['v'],w['central_disjoint'],w['center_denominator'])==(24,v,24,21)
+args=[None]*(v+1);support=[0]+[1<=2 else 2;kind.append(ty);rank.append(support[x].bit_count()if ty==1 else cover[x].bit_count())
+point=[sum(1<>p&1:x^=piv[p]
+ if x:
+ p=x.bit_length()-1
+ for q in piv:
+ if piv[q]>>p&1:piv[q]^=x
+ piv[p]=x
+ return tuple(piv[p]for p in sorted(piv,reverse=True))
+def perp(A):
+ piv={x.bit_length()-1 for x in A};out=[]
+ for j in range(24):
+ if j not in piv:
+ x=1<>j&1:x|=1<<(r.bit_length()-1)
+ out.append(x)
+ return basis(out)
+def contained(A,B):return all(not any((a&b).bit_count()%2 for a in A)for b in perp(B))
+@lru_cache(None)
+def characteristic(A):
+ k=len(A);rows=[sum(((a&b).bit_count()%2)<>j&1);rows[j],rows[p]=rows[p],rows[j]
+ for i in range(k):
+ if i!=j and rows[i]>>j&1:rows[i]^=rows[j]
+ result=0
+ for j in range(k):
+ if rows[j]>>k&1:result^=A[j]
+ return result
+DG=defaultdict(list)
+for s,last in enumerate(g['last']):
+ if last in g['phase']and(s not in g['terminal']or s in g['center_roles']):DG[g['U'][g['holds'][s][-1]]].append(s)
+frames=sorted(DG,key=lambda F:(-len(F),F));pool=[DG[F][:]for F in frames];byB=defaultdict(list)
+for b,F in g['placed'].items():byB[F].append(b)
+allgroups=(1<25:raise RuntimeError('Bounded eligibility screen capped before matching; no partial claim')
+# Deterministic most-constrained frame classes, highest-rank legal donor first.
+available=allgroups;pairs=[]
+for F in sorted(byB,key=lambda F:(capacity[F],len(F),F)):
+ for b in sorted(byB[F]):
+ mask=eligible[F]&available
+ if not mask:break
+ i=(mask&-mask).bit_length()-1;a=pool[i].pop();A=frames[i]
+ if not pool[i]:available^=1<e:H[s-e]+=2*v
+assert min(H.values())>=0
+roles=len(g['first'])-len(pairs);W=2*v*v+2*v*roles;mass=sum(r*n for r,n in H.items());assert mass==576*W-1862080
+assert len({p['donor']for p in pairs})==len(pairs)==len({p['recipient']for p in pairs})
+def moment(a):return math.fsum(n*r*math.exp(a*math.log(576/r))for r,n in H.items()if n)/(576*W)
+lo,hi=0.,.001
+for _ in range(65):
+ mid=(lo+hi)/2
+ if moment(mid)<1:lo=mid
+ else:hi=mid
+res=dict(status='Author exact liveness/containment/paid-profile birth-reuse screen; scalar expansion and full reflected word still to check',source_head='ec862a5af51537495c745d9f2323e8a5736ee265',base_roles=len(g['first']),donors=sum(len(v)for v in DG.values()),donor_frame_classes=len(frames),births=len(g['placed']),matched=len(pairs),R=roles,W=W,rank=mass,deficit=1862080,child_histogram=dict(sorted((r,n)for r,n in H.items()if n)),match_ranks=dict(Counter(f"{r['e']}->{r['s']}"for r in pairs)),new_positive_residuals_nonalternating=True,root_float_screen=(lo+hi)/2,zero_rank_merge_records=sum(r['e']==r['s']for r in pairs),pairs=pairs,source_frame_checkpoint_sha256=hashlib.sha256((ROOT/'FRAMES.pkl').read_bytes()).hexdigest(),seconds=time.monotonic()-start,rss_KiB=resource.getrusage(resource.RUSAGE_SELF).ru_maxrss)
+(ROOT/'BIRTH_MATCHES.json.gz').write_bytes(gzip.compress((json.dumps(res,indent=2)+'\n').encode(),mtime=0));print(json.dumps({k:v for k,v in res.items()if k not in('pairs','child_histogram','match_ranks')},indent=2))
diff --git a/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/readout_cost.py b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/readout_cost.py
new file mode 100644
index 0000000000..a5b3bc5075
--- /dev/null
+++ b/research/shrunk-birth-terminal/search/references/pr124/research/birth-read-reuse/readout_cost.py
@@ -0,0 +1,70 @@
+"""Original exact signed integer dirty-readout responses and literal unit bill.
+All coefficients are represented over42 by unsigned bitplanes; no modular test.
+"""
+import sys,os
+if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):raise RuntimeError('Assertions required')
+from pathlib import Path
+from functools import reduce
+from operator import or_
+from itertools import combinations
+import pickle,json,time,resource,hashlib
+ROOT=Path(__file__).resolve().parent;start=time.monotonic();resource.setrlimit(resource.RLIMIT_AS,(512*1024**2,512*1024**2));resource.setrlimit(resource.RLIMIT_CPU,(30,30))
+g=pickle.loads((ROOT/'FRAMES.pkl').read_bytes());R=len(g['first']);v=g['v'];N=v*v;allbits=(1<>i&1 else 0 for i in range(n.bit_length()))
+def plus(a,b):
+ out=[];carry=0
+ for i in range(max(len(a),len(b))):
+ x=a[i]if i=len(g['roots'])-24:
+ i=j-(len(g['roots'])-24);P[s]=scaled(allbits^point[i],2);M[s]=scaled(point[i],19)
+ elif jmaximum:maximum=maxhere;max_role=s
+ # Pin full exact responses, including zero coefficients and signs.
+ digest.update(s.to_bytes(4,'little'));digest.update(len(z).to_bytes(4,'little'));digest.update(neg.to_bytes((v+7)//8,'little'))
+ for w in z:digest.update(w.to_bytes((v+7)//8,'little'))
+ if s in g['placed']:
+ # Deferred origin has no center contribution; every actual target is in the conservative reach set.
+ assert not(nonzero&~g['reach'][s]);dense_reached+=nonzero.bit_count()
+terminal_weight=0;terminal_count=0
+for a,b in zip(*seeds):
+ z,_=absdiff(a,b);terminal_weight+=sum(w.bit_count()*(1<a:H[b-a]+=2*v
+ if s in g['terminal']and g['terminal'][s]>=len(g['roots'])-h:H[h-1]+=2*v
+ H[h-ds[-1]]+=2*v;H[ext+ds[0]]+=2*v
+ for t in range(v):
+ ds=sorted(levels[t]|{0,h-1})
+ for a,b in zip(ds,ds[1:]):H[b-a]+=2*v
+ N=v*v;H[h-1]+=2*N;H[(h-1)**2]+=2*N;H[1]+=N;H.pop(0,None)
+ g['histogram']=dict(sorted((r,n)for r,n in H.items()if n));p=g['base_profile']
+ assert sum(r*n for r,n in H.items())==p['total_rank']==m*p['W']-p['deficit']
+ p.update(child_multiplicities=g['histogram'],deferred_roles=len(g['placed']),
+ deferred_dims=dict(Counter(map(len,g['placed'].values()))))
+
+phase_inputs=[('prune','recipe/prune.json','recipe/protected-birth-matches.json.gz'),
+ ('coordinates','recipe/coordinates.json','evidence/protected-prune/BIRTH_MATCHES.json.gz'),
+ ('expansion','recipe/expansion.json','evidence/protected-coordinates/BIRTH_MATCHES.json.gz')]
+for phase,recipe_path,match_path in phase_inputs:
+ recipe=read(HERE/recipe_path)
+ matches=json.loads(gzip.decompress((HERE/match_path).read_bytes()))
+ protected={r['recipient']:tuple(r['birth_frame'])for r in matches['pairs']}
+ assert all(g['placed'][s]==F for s,F in protected.items())
+ if phase=='prune':
+ for row in recipe['removed']:
+ s=row['role'];assert s not in protected and len(g['placed'][s])==row['dimension']
+ del g['placed'][s]
+ else:
+ for row in recipe['moves']:
+ s=row['role'];assert s not in protected
+ assert tuple(row['before'])==g['placed'].get(s,())
+ if row['after']:g['placed'][s]=tuple(row['after'])
+ else:g['placed'].pop(s,None)
+ rebuild();assert all(g['placed'][s]==F for s,F in protected.items());mark(phase+'_recorded_moves_and_complete_frame_checks')
+expected=read(HERE/'recipe/expected-geometry.json')
+digest=sha256(canonical_geometry(g)).hexdigest();assert digest==expected['canonical_geometry_sha256'],'Entire selected geometry mismatch'
+assert sha256(source.read_bytes()).hexdigest()==source_unchanged
+(OUT/'FRAMES.pkl').write_bytes(pickle.dumps(g,protocol=4))
+record=dict(status='PASS from-source graph and exact selected geometry regeneration',
+ canonical_geometry_sha256=digest,selected_fixture_sha256=expected['selected_pickle_sha256'],
+ reproduced_pickle_sha256=sha256((OUT/'FRAMES.pkl').read_bytes()).hexdigest(),
+ original_runtime_imports_sha256=sha256((HERE/'IMPORTS.json').read_bytes()).hexdigest(),
+ wrapper_sha256=sha256(Path(__file__).read_bytes()).hexdigest(),
+ stage_seconds=timings,total_seconds=time.monotonic()-start,
+ scalar_dirty_word_replay='Not repeated here; enclosing selected physical word has separate full exact rational source/dirty and reflection audits.',
+ scope='All geometric keys regenerated and compared, excluding descriptive base_profile metadata. Pickle bytes may differ. Explicit recorded legal moves reproduce a selected witness; no heuristic-search or global-optimality claim.')
+(OUT/'REPRODUCTION.json').write_text(json.dumps(record,indent=2,sort_keys=True)+'\n');print(json.dumps(record,indent=2))
diff --git a/research/shrunk-birth-terminal/selected/INPUTS.json b/research/shrunk-birth-terminal/selected/INPUTS.json
new file mode 100644
index 0000000000..99d03c09b4
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/INPUTS.json
@@ -0,0 +1,42 @@
+{
+ "BIRTH_MATCHES.json.gz": {
+ "bytes": 38343,
+ "encoding": "identity",
+ "sha256": "1cc40ab44413de0953dfa039fa7446008f3f480062560e9e7833dd48dced5de5",
+ "stored_bytes": 38343,
+ "stored_name": "BIRTH_MATCHES.json.gz",
+ "stored_sha256": "1cc40ab44413de0953dfa039fa7446008f3f480062560e9e7833dd48dced5de5"
+ },
+ "FRAMES.pkl": {
+ "bytes": 30960758,
+ "encoding": "gzip",
+ "sha256": "3e3b2158ebad61910433735562de52d51c2bf803474662e90b7c478f90112a83",
+ "stored_bytes": 4159341,
+ "stored_name": "FRAMES.pkl.gz",
+ "stored_sha256": "c213d6ea7302ea4dd2a63eea54d9459289c1ab363f750fcdc37f109fd5c5c16a"
+ },
+ "READOUTS.pkl": {
+ "bytes": 30742405,
+ "encoding": "gzip",
+ "sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb",
+ "stored_bytes": 2337744,
+ "stored_name": "READOUTS.pkl.gz",
+ "stored_sha256": "7db47c7dcb0cc508f414ff3c43e799e0de4924e1fda81dfe33cc2b04456c3fcd"
+ },
+ "READOUT_COST.json": {
+ "bytes": 1252,
+ "encoding": "identity",
+ "sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10",
+ "stored_bytes": 1252,
+ "stored_name": "READOUT_COST.json",
+ "stored_sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10"
+ },
+ "TERMINAL_ROLES.json": {
+ "bytes": 3432,
+ "encoding": "identity",
+ "sha256": "17c0132f5b7e1aea34313173fc8059f5199cc281ee582c843ea7650af5e6bd19",
+ "stored_bytes": 3432,
+ "stored_name": "TERMINAL_ROLES.json",
+ "stored_sha256": "17c0132f5b7e1aea34313173fc8059f5199cc281ee582c843ea7650af5e6bd19"
+ }
+}
diff --git a/research/shrunk-birth-terminal/selected/READOUT_COST.json b/research/shrunk-birth-terminal/selected/READOUT_COST.json
new file mode 100644
index 0000000000..87a498b5bc
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/READOUT_COST.json
@@ -0,0 +1,29 @@
+{
+ "checkpoint_sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb",
+ "deferred_readout_count_scope": "The inherited count describes the input billing snapshot. Virtual count uses every deferred role in the selected geometry; retained count excludes precisely the eliminated terminal roles. All are exact nonzero signed old-response terms. The scalar upper bound retains the entire inherited virtual bill without taking credit for removed work.",
+ "deferred_retained_readout_terms": 11503,
+ "deferred_virtual_readout_terms": 11884,
+ "denominator": 42,
+ "exact_response_sha256": "61631cf8189e99212bbb9b38faf11e32f10147e085054e7c84b5474b116c8ea8",
+ "expansion": "Each numerator n/42 is |n| same-frame shears of coefficient sign(n)/42, with no new roles, source copies or frame transitions. Reverse all workspace/source gates chronologically. The retained eight-scan allowance, factor16 and explicit endpoint groups conservatively bound scalar bookkeeping/wrappers. Direct terminal updates use the same expansion, with eight additional bookkeeping groups per update.",
+ "global_scalar_group_upper": 3116113870848,
+ "inherited_deferred_readout_terms": 9732,
+ "inherited_local_scalar_upper": 48069997,
+ "local_scalar_upper": 48103840,
+ "max_abs_coefficient": "55/42",
+ "max_abs_numerator": 55,
+ "max_role": 22053,
+ "odd_grid": "Denominator42=2*21; retain common odd21 grid with per-local-word G and completed-child preservation.",
+ "original_bill_sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10",
+ "readout_copy_scan_bill": 47369383,
+ "readout_nonzero_terms": 11862912,
+ "readout_numerator_L1": 46704391,
+ "source_injection_count": 13481,
+ "status": "PASS conservative scalar upper bound for new terminal composition",
+ "terminal_charge_rule": "Keep the entire inherited scalar bill and add 29 groups per direct output update: 21 same-frame shears of coefficient +/-1/42, plus eight conservative bookkeeping groups. No new role, source copy or frame incidence is introduced; denominator42 and odd21 grid are unchanged.",
+ "terminal_direct_updates": 1167,
+ "terminal_extra_scalar_charge": 33843,
+ "terminal_numerator_L1": 370392,
+ "terminal_terms": 56672,
+ "workspace_gate_count": 106994
+}
diff --git a/research/shrunk-birth-terminal/selected/SOURCE.json b/research/shrunk-birth-terminal/selected/SOURCE.json
new file mode 100644
index 0000000000..f679b07026
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/SOURCE.json
@@ -0,0 +1,34 @@
+{
+ "construction_sources": {
+ "construction-sources/compose_terminal.py": "2ad76ef2c8b403b0f86d7abfdcedcd86359d3a239e493dcba4928b21119ffe53",
+ "construction-sources/terminal_inventory.py": "04c6fe763a2e5def477f3b1c3b4a886834a1e7617cfdd5c8de1daa827766b6e9"
+ },
+ "inputs": {
+ "BIRTH_MATCHES.json.gz": {
+ "bytes": 38343,
+ "sha256": "1cc40ab44413de0953dfa039fa7446008f3f480062560e9e7833dd48dced5de5",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/BIRTH_MATCHES.json.gz"
+ },
+ "FRAMES.pkl": {
+ "bytes": 30960758,
+ "sha256": "3e3b2158ebad61910433735562de52d51c2bf803474662e90b7c478f90112a83",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/FRAMES.pkl"
+ },
+ "READOUTS.pkl": {
+ "bytes": 30742405,
+ "sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/READOUTS.pkl"
+ },
+ "READOUT_COST.json": {
+ "bytes": 1252,
+ "sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/READOUT_COST.json"
+ },
+ "TERMINAL_ROLES.json": {
+ "bytes": 3432,
+ "sha256": "17c0132f5b7e1aea34313173fc8059f5199cc281ee582c843ea7650af5e6bd19",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/TERMINAL_ROLES.json"
+ }
+ },
+ "source_attribution": "PR122 terminal-elision identity; PR125 shrunk frames; PR124 birth reuse; PR117 scalar DAG; this new explicit composition and audits with OpenAI Codex assistance."
+}
diff --git a/research/shrunk-birth-terminal/selected/complex-profile.json b/research/shrunk-birth-terminal/selected/complex-profile.json
new file mode 100644
index 0000000000..85900527f6
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/complex-profile.json
@@ -0,0 +1,1293 @@
+{
+ "L": 2234496,
+ "N": 4096576,
+ "R": 26216,
+ "W": 114315520,
+ "additions": 91770,
+ "birth_aware_coordinates": {
+ "moves": [
+ {
+ "after": [
+ 9437184,
+ 5242880
+ ],
+ "before": [],
+ "integer_gain": 5065097324,
+ "role": 19526,
+ "sweep": 0
+ },
+ {
+ "after": [
+ 9437184,
+ 5242880
+ ],
+ "before": [],
+ "integer_gain": 5065097324,
+ "role": 19548,
+ "sweep": 0
+ },
+ {
+ "after": [
+ 9437184,
+ 5242880
+ ],
+ "before": [],
+ "integer_gain": 624424240,
+ "role": 19600,
+ "sweep": 0
+ },
+ {
+ "after": [
+ 9437184,
+ 5242880
+ ],
+ "before": [],
+ "integer_gain": 4443509250,
+ "role": 19601,
+ "sweep": 0
+ },
+ {
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+ 5242880
+ ],
+ "before": [],
+ "integer_gain": 2833661810,
+ "role": 19602,
+ "sweep": 0
+ },
+ {
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+ "role": 19603,
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+ "method": "Exact signed bit-plane all-column responses over Q, both orientations",
+ "reflected_signed_identity": -1,
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+ },
+ "role_count_scope": "Explicit physical birth-reused and terminal-elided word; DAG role formula is the pre-composition virtual count.",
+ "roots": 8120,
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+}
diff --git a/research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py b/research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py
new file mode 100644
index 0000000000..a3b0826651
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/construction-sources/compose_terminal.py
@@ -0,0 +1,328 @@
+#!/usr/bin/env python3
+"""Compose disjoint terminal elimination with an exact shrunk/birth word.
+
+Original terminal-elision identity: SovereignSteak, PR122.
+Shrunk frames: Joel Pulikkan, PR125. Birth reuse: James Chang, PR124.
+PR117 DAG: eumemic; deferred compiler: Avi Eisenberg and Rohan Arun.
+This explicit composition, complete word/profile checks and all-column
+response audit were prepared with OpenAI Codex assistance. Apache-2.0.
+"""
+from pathlib import Path
+from collections import Counter
+from functools import lru_cache
+from hashlib import sha256
+import argparse, gzip, json, pickle, resource, subprocess, sys, time
+
+assert not sys.flags.optimize, 'Assertions must remain enabled'
+W=Path(__file__).resolve().parent
+p=argparse.ArgumentParser(description=__doc__)
+p.add_argument('--frames',type=Path,required=True)
+p.add_argument('--matches',type=Path,required=True)
+p.add_argument('--readouts',type=Path,required=True)
+p.add_argument('--scalar-bill',type=Path,required=True)
+p.add_argument('--out',type=Path,required=True)
+p.add_argument('--terminal-roles',type=Path,help='JSON list of exact terminal IDs; validated after supplied real birth matches.')
+a=p.parse_args();start=time.monotonic();O=a.out.resolve();O.mkdir(parents=True,exist_ok=False)
+source_directory=O/'construction-sources';source_directory.mkdir()
+source_bytes={q.name:q.read_bytes() for q in [Path(__file__),W/'terminal_inventory.py']}
+for name,data in source_bytes.items():(source_directory/name).write_bytes(data)
+inputs=O/'inputs';inputs.mkdir();pins={}
+for source,name in [(a.frames,'FRAMES.pkl'),(a.matches,'BIRTH_MATCHES.json.gz'),(a.readouts,'READOUTS.pkl'),(a.scalar_bill,'READOUT_COST.json')]:
+ data=source.read_bytes();(inputs/name).write_bytes(data);assert source.read_bytes()==data
+ pins[name]={'source_path':str(source.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)}
+selection_args=[]
+if a.terminal_roles:
+ data=a.terminal_roles.read_bytes();(inputs/'TERMINAL_ROLES.json').write_bytes(data);assert a.terminal_roles.read_bytes()==data
+ pins['TERMINAL_ROLES.json']={'source_path':str(a.terminal_roles.resolve()),'sha256':sha256(data).hexdigest(),'bytes':len(data)}
+ selection_args=['--terminal-roles',str(inputs/'TERMINAL_ROLES.json')]
+subprocess.run([sys.executable,str(source_directory/'terminal_inventory.py'),'--frames',str(inputs/'FRAMES.pkl'),'--matches',str(inputs/'BIRTH_MATCHES.json.gz'),'--readouts',str(inputs/'READOUTS.pkl'),'--out',str(O/'inventory.json'),*selection_args],check=True,stdout=subprocess.DEVNULL)
+inventory=json.loads((O/'inventory.json').read_text())
+g=pickle.loads((inputs/'FRAMES.pkl').read_bytes());readouts=pickle.loads((inputs/'READOUTS.pkl').read_bytes())
+choice=json.loads(gzip.decompress((inputs/'BIRTH_MATCHES.json.gz').read_bytes()))
+bill=json.loads((inputs/'READOUT_COST.json').read_text())
+R=len(g['first']);v=g['v'];h=g['h'];m=h*h;N=v*v
+merge={r['recipient']:r['donor'] for r in choice['pairs']}
+removed={r['role'] for r in inventory['selected']};selected={r['role']:r for r in inventory['selected']}
+assert removed and not removed & (set(merge)|set(merge.values()))
+live=set(range(R))-set(merge)-removed
+assert len(live)==choice['R']-len(removed)
+physical=lambda s:2*v+merge.get(s,s)
+
+frames=[()];ids={():0}
+def fid(F):
+ F=tuple(F)
+ if F not in ids:ids[F]=len(frames);frames.append(F)
+ return ids[F]
+def basis(rows):
+ piv={}
+ for x in rows:
+ for q in sorted(piv,reverse=True):
+ if x>>q&1:x^=piv[q]
+ if x:
+ q=x.bit_length()-1
+ for r in piv:
+ if piv[r]>>q&1:piv[r]^=x
+ piv[q]=x
+ return tuple(piv[q] for q in sorted(piv,reverse=True))
+FULL=fid(tuple(1<>j&1:x|=1<<(r.bit_length()-1)
+ out.append(x)
+ return fid(basis(out))
+@lru_cache(None)
+def nested(i,j):
+ for x in frames[i]:
+ for r in frames[j]:
+ if x>>(r.bit_length()-1)&1:x^=r
+ if x:return False
+ return True
+@lru_cache(None)
+def nondeg(i):
+ A=frames[i]
+ return len(basis(sum(((x&y).bit_count()&1)<=2*v and d-2*v in live
+ e=('g',d,s,sign,F);word.append(e)
+ if remember:forward_workspace.append(e)
+def oldread(s,F):
+ mask=ALL if g['reach_all'][s] else g['reach'][s]
+ if s in removed:
+ assert mask==1<0
+ hist[r]+=1;current[s]=F;incidences+=1
+ if s<2*v:
+ bank=s//v;counts[bank][old]-=1
+ if not counts[bank][old]:del counts[bank][old]
+ counts[bank][F]+=1
+ def targets(bank,mask,F):
+ assert bank in (0,v) and mask>=0 and not(mask&~ALL)
+ if len(counts[bank//v])==1 and counts[bank//v].get(F)==v:return
+ while mask:
+ b=mask&-mask;mask-=b;promote(bank+b.bit_length()-1,F)
+ for e in events:
+ digest.update(repr(e).encode())
+ if e[0]=='g':
+ _,d,s,c,F=e;assert c in (-1,1);promote(d,F);promote(s,F)
+ elif e[0]=='d':
+ _,d,s,c,F,idx,role=e;assert c in (-21,21);promote(d,F);promote(s,F)
+ elif e[0]=='r':
+ _,s,bank,mask,sign,F,key=e;promote(s,F);targets(bank,mask,F)
+ elif e[0]=='f':
+ _,bank,mask,F,key=e;targets(bank,mask,F)
+ else:
+ _,s,bank,mask,sign,F,T,key=e;promote(s,F);targets(bank,mask,T)
+ assert (F==FULL and T==0) or nested(F,T) or nested(T,F)
+ rank=abs(len(frames[F])-len(frames[T]));assert rank==h-1;hist[rank]+=1;copies+=1
+ for s in active:promote(s,end[s])
+ assert current==end
+ return {'histogram':dict(hist),'copies':copies,'transitions':incidences,'word_sha256':digest.hexdigest()}
+
+forward=scan(word,initial,finish)
+def swap(s):return s+v if s=sum(before_sorted[:k]) for k in range(1,5))
+ assert before_sorted!=after_sorted
+ for width in before:
+ if width:delta[width]-=2*v
+ # The width-m term is only the padding used to compare changing W.
+ if F0>M:delta[F0-M]+=2*v
+ packets.append({'role':row['role'],'target':row['target'],'old':before,'new_with_dummy_m':after})
+expected=Counter(oldH)
+expected.update(delta);expected=Counter({r:n for r,n in expected.items() if n})
+assert all(n>=0 for n in expected.values()) and H==expected,('Full profile != exact complete packet sum',H-expected,expected-H)
+newR=len(live);newW=2*v*v+2*v*newR;rank=sum(r*n for r,n in H.items())
+assert m*newW-rank==choice['deficit']==g['base_profile']['deficit']
+hinges={k:sum(min(r,k)*n for r,n in H.items())+2*v*len(removed)*min(m,k)-sum(min(r,k)*n for r,n in oldH.items()) for k in range(1,m+1)}
+assert all(x<=0 for x in hinges.values()) and min(hinges.values())<0
+
+def plus(a,b):
+ out=[];carry=0
+ for i in range(max(len(a),len(b))):
+ x=a[i] if i>i&1 else 0 for i in range(n.bit_length()))
+
+def responses(events,inputbank,outputbank,expected_sign):
+ P,M=[()]*R,[()]*R;XP,XM=[()]*v,[()]*v
+ def accumulate(aux,positive,negative):
+ assert aux>=2*v and aux-2*v in live
+ r=aux-2*v;P[r],M[r]=plus(P[r],positive),plus(M[r],negative)
+ for e in reversed(events):
+ kind=e[0]
+ if kind=='f':continue
+ if kind in ('r','c'):
+ aux,bank,sign=e[1],e[2],e[4];assert bank==outputbank
+ key=e[-1]
+ if key[0]=='old':s=key[1];seed=False
+ elif key[0]=='side':s=key[2];seed=True
+ else:s=next(s for s in g['center_roles'] if g['terminal'][s]==len(g['roots'])-h+key[1]);seed=True
+ aa=readouts['terminal_positive' if seed else 'positive'][s]
+ bb=readouts['terminal_negative' if seed else 'negative'][s]
+ if sign<0:aa,bb=bb,aa
+ accumulate(aux,aa,bb)
+ elif kind=='d':
+ _,dst,src,num,F,idx,role=e
+ assert outputbank<=dst=2*v
+ aa,bb=P[dst-2*v],M[dst-2*v]
+ if sign<0:aa,bb=bb,aa
+ if src>=2*v:accumulate(src,aa,bb)
+ else:
+ assert inputbank<=src0:source_ok=all(aa==plus(bb,scaled(1<=bill['global_scalar_group_upper']
+profile=dict(g['base_profile']);profile.update(R=newR,W=newW,total_rank=rank,maxchild=max(H),child_multiplicities=dict(sorted(H.items())),pre_terminal_physical_roles=choice['R'],virtual_roles=R,birth_reuses=len(merge),terminal_eliminations=len(removed),terminal_direct_updates=len(direct_origins),deferred_roles=len(g['placed'])-len(removed),role_count_scope='Explicit physical birth-reused and terminal-elided word; DAG role formula is the pre-composition virtual count.',replay={'method':'Exact signed bit-plane all-column responses over Q, both orientations','source_columns':v,'dirty_columns':newR,'target_columns':v,'forward_signed_identity':1,'reflected_signed_identity':-1,'scratch_restored':True})
+dd=Counter({int(k):n for k,n in profile['deferred_dims'].items()})
+for row in inventory['selected']:dd[row['sigma']]-=1
+profile['deferred_dims']=dict(sorted((k,n) for k,n in dd.items() if n))
+scalar_bill={**{k:value for k,value in bill.items() if k not in {'rss_KiB','rss_bytes','seconds'}},'status':'PASS conservative scalar upper bound for new terminal composition','inherited_local_scalar_upper':bill['local_scalar_upper'],'terminal_direct_updates':len(direct_origins),'terminal_extra_scalar_charge':extra_scalar,'local_scalar_upper':newlocal,'global_scalar_group_upper':newG,'terminal_charge_rule':'Keep the entire inherited scalar bill and add 29 groups per direct output update: 21 same-frame shears of coefficient +/-1/42, plus eight conservative bookkeeping groups. No new role, source copy or frame incidence is introduced; denominator42 and odd21 grid are unchanged.','expansion':'Each numerator n/42 is |n| same-frame shears of coefficient sign(n)/42, with no new roles, source copies or frame transitions. Reverse all workspace/source gates chronologically. The retained eight-scan allowance, factor16 and explicit endpoint groups conservatively bound scalar bookkeeping/wrappers. Direct terminal updates use the same expansion, with eight additional bookkeeping groups per update.','original_bill_sha256':pins['READOUT_COST.json']['sha256']}
+# The inherited bill is a conservative charge for the full virtual graph.
+# Its descriptive deferred support count may belong to another placement.
+def old_readout_support(role):
+ positive=readouts['positive'][role];negative=readouts['negative'][role];mask=0
+ for i in range(max(len(positive),len(negative))):
+ mask|=(positive[i] if i>(r.bit_length()-1)&1:x^=r
+ if x:return False
+ return True
+
+incoming=defaultdict(list);outgoing=Counter()
+for i,(op,s,t,x) in enumerate(g['ops']):
+ if op==1:dst,src=s,t
+ elif op==2:dst,src=t,s
+ else:continue
+ incoming[dst].append((i,src,x));outgoing[src]+=1
+
+target_front=[() for _ in range(v)]
+for s,F in sorted(g['placed'].items(),key=lambda z:(len(z[1]),z[0])):
+ targets=g['reach'][s]
+ while targets:
+ b=targets&-targets;targets-=b;t=b.bit_length()-1
+ assert contains(target_front[t],F)
+ target_front[t]=F
+
+def scaled(mask,n):return tuple(mask if n>>i&1 else 0 for i in range(n.bit_length()))
+
+blocked=Counter();eligible=[]
+for s,j in sorted(g['terminal'].items()):
+ if j>=len(g['roots'])-h:blocked['center_root']+=1;continue
+ if outgoing[s]:blocked['controls_auxiliary']+=1;continue
+ if s in merge and not a.include_birth_recipients:blocked['physical_slot_shared_as_birth_recipient']+=1;continue
+ assert s not in set(merge.values())
+ if s not in g['placed']:blocked['not_deferred']+=1;continue
+ if g['first'][s]<=v:blocked['source_injection_excluded_from_this_bounded_pass']+=1;continue
+ if not incoming[s]:blocked['no_incoming_update']+=1;continue
+ if any(i in g['phase'] for i,_,_ in incoming[s]):blocked['early_update']+=1;continue
+ assert s not in g['touched']
+ t=g['targets'][j];sign=1 if j0 else ())
+ assert readouts['negative'][s]==(expected if sign<0 else ())
+ F0=g['U'][incoming[s][0][2]];M=target_front[t];sigma=g['placed'][s]
+ if not contains(M,F0):blocked['target_front_past_first_update']+=1;continue
+ fs=[M]+[g['U'][x] for _,_,x in incoming[s]]
+ assert all(contains(a,b) for a,b in zip(fs,fs[1:])),s
+ assert contains(sigma,M) and len(fs[-1])<=h-1
+ if a.include_birth_recipients and not len(sigma)==len(M)==len(F0):blocked['unequal_packet_dimensions_excluded_from_joint_options']+=1;continue
+ eligible.append({'role':s,'target':t,'root_index':j,'coefficient_numerator':21*sign,'sigma':len(sigma),'M':len(M),'F0':len(F0),'incoming_operations':[i for i,_,_ in incoming[s]],'incoming_count':len(incoming[s]),'frames':[list(F) for F in fs],'current_birth_donor':merge.get(s),'terminal_local_scalar_charge':29*len(incoming[s]),'packet_replication':2*v,'old_packet':[m-h+len(sigma),1,len(F0)-len(sigma),h-1-len(M)],'padded_new_packet':[m,len(F0)-len(M),0,0]})
+
+# One terminal per target gives disjoint target-front packets; this avoids
+# treating individually legal but interleaved output paths as simultaneous.
+bytarget=defaultdict(list)
+for row in eligible:bytarget[row['target']].append(row)
+selected=[min(group,key=lambda x:x['role']) for _,group in sorted(bytarget.items())]
+if a.terminal_roles:
+ requested=json.loads(a.terminal_roles.read_text())
+ assert isinstance(requested,list) and all(type(s) is int for s in requested), 'Selection must be a JSON list of integer role IDs'
+ assert len(requested)==len(set(requested)), 'Duplicate terminal role ID'
+ rows={row['role']:row for row in eligible}
+ assert set(requested)<=rows.keys(), f'Ineligible requested terminal roles: {sorted(set(requested)-rows.keys())}'
+ selected=[rows[s] for s in sorted(requested)]
+ assert len({row['target'] for row in selected})==len(selected), 'Selected terminals must have distinct targets'
+ assert not set(requested)&(set(merge)|set(merge.values())), 'Selected terminals must have no birth aliases'
+record={'status':'PASS exact local eligibility and disjoint-target selection on new composition inputs','base_virtual_roles':R,'base_physical_roles':choice['R'],'birth_merges_preserved':len(merge),'eligible_unshared_terminal_roles':len(eligible),'selected_terminal_roles':len(selected),'selected_targets':len(bytarget),'blocked':dict(blocked),'selection_rule':'Lowest eligible role id per target; no frame, deferral or birth matching changes.','selected':selected,'eligible':eligible,'expected_physical_roles':choice['R']-len(selected),'input_sha256':{str(p):sha256(p.read_bytes()).hexdigest() for p in [a.frames,a.readouts,a.matches]}}
+if a.terminal_roles:
+ record.update(selection_rule='Exact requested role-ID subset, validated against ordinary unshared eligibility and distinct targets',selected_targets=len(selected),selection_sha256=sha256(a.terminal_roles.read_bytes()).hexdigest())
+if a.include_birth_recipients:
+ record.update(status='PASS virtual eligibility options for joint birth/terminal optimization; not a legal simultaneous elimination selection',joint_optimization_options=True,eligible_virtual_terminal_roles=len(eligible),currently_birth_matched_options=sum(row['current_birth_donor'] is not None for row in eligible),selection_rule='All eligible options retained in eligible; selected is only the lowest role per target and may conflict with existing births. Choose at most one option per target and never choose both a terminal edge and a birth donor edge for the same role. After changing the birth matching, rerun the default inventory and full builder.')
+ record.pop('eligible_unshared_terminal_roles');record.pop('expected_physical_roles')
+a.out.parent.mkdir(parents=True,exist_ok=True)
+a.out.write_text(json.dumps(record,indent=2,sort_keys=True)+'\n')
+print(json.dumps({k:v for k,v in record.items() if k not in ['selected','eligible','input_sha256']},indent=2))
diff --git a/research/shrunk-birth-terminal/selected/inputs/BIRTH_MATCHES.json.gz b/research/shrunk-birth-terminal/selected/inputs/BIRTH_MATCHES.json.gz
new file mode 100644
index 0000000000..f6bf701f10
Binary files /dev/null and b/research/shrunk-birth-terminal/selected/inputs/BIRTH_MATCHES.json.gz differ
diff --git a/research/shrunk-birth-terminal/selected/inputs/FRAMES.pkl.gz b/research/shrunk-birth-terminal/selected/inputs/FRAMES.pkl.gz
new file mode 100644
index 0000000000..7176bb5a52
Binary files /dev/null and b/research/shrunk-birth-terminal/selected/inputs/FRAMES.pkl.gz differ
diff --git a/research/shrunk-birth-terminal/selected/inputs/READOUTS.pkl.gz b/research/shrunk-birth-terminal/selected/inputs/READOUTS.pkl.gz
new file mode 100644
index 0000000000..1560e7cf07
Binary files /dev/null and b/research/shrunk-birth-terminal/selected/inputs/READOUTS.pkl.gz differ
diff --git a/research/shrunk-birth-terminal/selected/inputs/READOUT_COST.json b/research/shrunk-birth-terminal/selected/inputs/READOUT_COST.json
new file mode 100644
index 0000000000..57eff56f89
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/inputs/READOUT_COST.json
@@ -0,0 +1,23 @@
+{
+ "status": "PASS exact integer old-readout response and explicit conservative scalar bill; no <=1 coefficient assumption",
+ "denominator": 42,
+ "readout_nonzero_terms": 11862912,
+ "readout_numerator_L1": 46704391,
+ "max_abs_numerator": 55,
+ "max_abs_coefficient": "55/42",
+ "max_role": 22053,
+ "deferred_readout_terms": 9732,
+ "terminal_terms": 56672,
+ "terminal_numerator_L1": 370392,
+ "source_injection_count": 13481,
+ "workspace_gate_count": 106994,
+ "readout_copy_scan_bill": 47369383,
+ "local_scalar_upper": 48069997,
+ "global_scalar_group_upper": 3113921927424,
+ "expansion": "Each numerator n/42 is |n| same-frame shears of coefficient sign(n)/42, with no new roles or frame transitions. Reverse all workspace/source gates chronologically. The retained eight-scan allowance, factor16 and explicit endpoint groups conservatively bound scalar bookkeeping/wrappers.",
+ "odd_grid": "Denominator42=2*21; retain common odd21 grid with per-local-word G and completed-child preservation.",
+ "exact_response_sha256": "61631cf8189e99212bbb9b38faf11e32f10147e085054e7c84b5474b116c8ea8",
+ "seconds": 0.3970359999802895,
+ "rss_KiB": 234766336,
+ "checkpoint_sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb"
+}
diff --git a/research/shrunk-birth-terminal/selected/inputs/TERMINAL_ROLES.json b/research/shrunk-birth-terminal/selected/inputs/TERMINAL_ROLES.json
new file mode 100644
index 0000000000..1a89950939
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/inputs/TERMINAL_ROLES.json
@@ -0,0 +1,383 @@
+[
+ 24058,
+ 24074,
+ 24588,
+ 26827,
+ 26887,
+ 26900,
+ 26909,
+ 26995,
+ 27092,
+ 27140,
+ 27149,
+ 27198,
+ 27220,
+ 27258,
+ 27344,
+ 27348,
+ 27375,
+ 27386,
+ 27389,
+ 27413,
+ 27460,
+ 27463,
+ 27470,
+ 27472,
+ 27477,
+ 27489,
+ 27532,
+ 27534,
+ 27537,
+ 27543,
+ 27547,
+ 27556,
+ 27560,
+ 27562,
+ 27574,
+ 27576,
+ 27581,
+ 27585,
+ 27601,
+ 27602,
+ 27603,
+ 27605,
+ 27608,
+ 27609,
+ 27617,
+ 27625,
+ 27631,
+ 27638,
+ 27643,
+ 27713,
+ 27717,
+ 27724,
+ 27731,
+ 27735,
+ 27736,
+ 27740,
+ 27744,
+ 27752,
+ 27765,
+ 27771,
+ 27799,
+ 27804,
+ 27806,
+ 27810,
+ 27813,
+ 27823,
+ 27839,
+ 27850,
+ 27855,
+ 27861,
+ 27865,
+ 27874,
+ 27876,
+ 27882,
+ 27884,
+ 27887,
+ 27889,
+ 27891,
+ 27894,
+ 27936,
+ 27940,
+ 27941,
+ 27942,
+ 27943,
+ 27946,
+ 27949,
+ 27952,
+ 27953,
+ 27954,
+ 27960,
+ 27961,
+ 27964,
+ 27965,
+ 27966,
+ 27968,
+ 27971,
+ 27980,
+ 27993,
+ 28010,
+ 28016,
+ 28018,
+ 28021,
+ 28028,
+ 28031,
+ 28034,
+ 28037,
+ 28038,
+ 28042,
+ 28044,
+ 28047,
+ 28051,
+ 28056,
+ 28063,
+ 28069,
+ 28074,
+ 28108,
+ 28109,
+ 28113,
+ 28115,
+ 28117,
+ 28123,
+ 28125,
+ 28127,
+ 28128,
+ 28132,
+ 28136,
+ 28143,
+ 28145,
+ 28146,
+ 28150,
+ 28151,
+ 28162,
+ 28163,
+ 28172,
+ 28181,
+ 28187,
+ 28194,
+ 28199,
+ 28202,
+ 28205,
+ 28210,
+ 28215,
+ 28226,
+ 28238,
+ 28239,
+ 28243,
+ 28245,
+ 28246,
+ 28251,
+ 28254,
+ 28255,
+ 28256,
+ 28257,
+ 28265,
+ 28266,
+ 28267,
+ 28269,
+ 28271,
+ 28273,
+ 28275,
+ 28303,
+ 28305,
+ 28307,
+ 28312,
+ 28315,
+ 28323,
+ 28326,
+ 28337,
+ 28343,
+ 28348,
+ 28352,
+ 28354,
+ 28359,
+ 28361,
+ 28384,
+ 28385,
+ 28386,
+ 28387,
+ 28388,
+ 28389,
+ 28390,
+ 28391,
+ 28392,
+ 28394,
+ 28395,
+ 28396,
+ 28397,
+ 28398,
+ 28399,
+ 28400,
+ 28401,
+ 28402,
+ 28403,
+ 28404,
+ 28405,
+ 28406,
+ 28407,
+ 28408,
+ 28409,
+ 28410,
+ 28411,
+ 28412,
+ 28413,
+ 28414,
+ 28415,
+ 28416,
+ 28417,
+ 28418,
+ 28419,
+ 28420,
+ 28421,
+ 28422,
+ 28424,
+ 28425,
+ 28426,
+ 28427,
+ 28428,
+ 28429,
+ 28430,
+ 28431,
+ 28432,
+ 28433,
+ 28434,
+ 28435,
+ 28436,
+ 28437,
+ 28438,
+ 28439,
+ 28440,
+ 28441,
+ 28442,
+ 28443,
+ 28444,
+ 28445,
+ 28446,
+ 28447,
+ 28448,
+ 28449,
+ 28450,
+ 28451,
+ 28452,
+ 28453,
+ 28454,
+ 28455,
+ 28456,
+ 28457,
+ 28458,
+ 28459,
+ 28460,
+ 28461,
+ 28462,
+ 28463,
+ 28464,
+ 28465,
+ 28466,
+ 28467,
+ 28469,
+ 28470,
+ 28471,
+ 28472,
+ 28473,
+ 28474,
+ 28475,
+ 28476,
+ 28477,
+ 28478,
+ 28479,
+ 28480,
+ 28481,
+ 28482,
+ 28483,
+ 28484,
+ 28485,
+ 28486,
+ 28487,
+ 28488,
+ 28489,
+ 28490,
+ 28491,
+ 28492,
+ 28493,
+ 28494,
+ 28495,
+ 28496,
+ 28497,
+ 28498,
+ 28499,
+ 28500,
+ 28501,
+ 28502,
+ 28503,
+ 28504,
+ 28505,
+ 28506,
+ 28507,
+ 28508,
+ 28509,
+ 28511,
+ 28512,
+ 28513,
+ 28514,
+ 28515,
+ 28516,
+ 28517,
+ 28518,
+ 28519,
+ 28520,
+ 28521,
+ 28522,
+ 28523,
+ 28524,
+ 28525,
+ 28526,
+ 28527,
+ 28528,
+ 28529,
+ 28530,
+ 28531,
+ 28532,
+ 28533,
+ 28534,
+ 28535,
+ 28536,
+ 28537,
+ 28538,
+ 28539,
+ 28540,
+ 28541,
+ 28542,
+ 28543,
+ 28544,
+ 28545,
+ 28546,
+ 28547,
+ 28549,
+ 28550,
+ 28551,
+ 28552,
+ 28553,
+ 28554,
+ 28555,
+ 28556,
+ 28557,
+ 28558,
+ 28559,
+ 28560,
+ 28561,
+ 28565,
+ 28570,
+ 28575,
+ 28576,
+ 28577,
+ 28597,
+ 28605,
+ 28608,
+ 28612,
+ 28615,
+ 28616,
+ 28618,
+ 28619,
+ 28620,
+ 28622,
+ 28623,
+ 28625,
+ 28626,
+ 28629,
+ 28631,
+ 28634,
+ 28635,
+ 28636,
+ 28637,
+ 28638,
+ 28640,
+ 28641,
+ 28642,
+ 28643,
+ 28645,
+ 28647,
+ 28649,
+ 28679,
+ 28690
+]
diff --git a/research/shrunk-birth-terminal/selected/inventory.json b/research/shrunk-birth-terminal/selected/inventory.json
new file mode 100644
index 0000000000..5be17cf639
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/inventory.json
@@ -0,0 +1,95804 @@
+{
+ "base_physical_roles": 26597,
+ "base_virtual_roles": 28705,
+ "birth_merges_preserved": 2108,
+ "blocked": {
+ "center_root": 24,
+ "controls_auxiliary": 7401,
+ "not_deferred": 22,
+ "physical_slot_shared_as_birth_recipient": 3,
+ "target_front_past_first_update": 289
+ },
+ "eligible": [
+ {
+ "F0": 8,
+ "M": 8,
+ "coefficient_numerator": 21,
+ "current_birth_donor": null,
+ "frames": [
+ [
+ 2049,
+ 1025,
+ 513,
+ 257,
+ 129,
+ 65,
+ 41,
+ 3
+ ],
+ [
+ 2049,
+ 1025,
+ 513,
+ 257,
+ 129,
+ 65,
+ 41,
+ 3
+ ],
+ [
+ 4097,
+ 2049,
+ 1025,
+ 513,
+ 257,
+ 129,
+ 65,
+ 41,
+ 3
+ ],
+ [
+ 8388609,
+ 4194305,
+ 2097153,
+ 1048577,
+ 524289,
+ 262145,
+ 131073,
+ 65537,
+ 32769,
+ 16385,
+ 4097,
+ 2049,
+ 1025,
+ 513,
+ 257,
+ 129,
+ 65,
+ 41,
+ 3
+ ],
+ [
+ 8388608,
+ 4194304,
+ 2097152,
+ 1048576,
+ 524288,
+ 262144,
+ 131072,
+ 65536,
+ 32768,
+ 16384,
+ 8196,
+ 4096,
+ 2048,
+ 1024,
+ 512,
+ 256,
+ 128,
+ 64,
+ 32,
+ 20,
+ 8,
+ 2,
+ 1
+ ],
+ [
+ 8388608,
+ 4194304,
+ 2097152,
+ 1048576,
+ 524288,
+ 262144,
+ 131072,
+ 65536,
+ 32768,
+ 16384,
+ 8196,
+ 4096,
+ 2048,
+ 1024,
+ 512,
+ 256,
+ 128,
+ 64,
+ 32,
+ 20,
+ 8,
+ 2,
+ 1
+ ]
+ ],
+ "incoming_count": 5,
+ "incoming_operations": [
+ 59302,
+ 68047,
+ 101166,
+ 110153,
+ 110154
+ ],
+ "old_packet": [
+ 560,
+ 1,
+ 0,
+ 15
+ ],
+ "packet_replication": 4048,
+ "padded_new_packet": [
+ 576,
+ 0,
+ 0,
+ 0
+ ],
+ "role": 24058,
+ "root_index": 512,
+ "sigma": 8,
+ "target": 512,
+ "terminal_local_scalar_charge": 145
+ },
+ {
+ "F0": 8,
+ "M": 8,
+ "coefficient_numerator": 21,
+ "current_birth_donor": null,
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diff --git a/research/shrunk-birth-terminal/selected/joint-profile-comparison.json b/research/shrunk-birth-terminal/selected/joint-profile-comparison.json
new file mode 100644
index 0000000000..cc29ea15f9
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/joint-profile-comparison.json
@@ -0,0 +1,6 @@
+{
+ "status": "PASS emitted complete physical histogram equals independently predicted joint optimization histogram",
+ "profile_sha256": "6a1ca866ddbb81c62f7fee08358849f2060e170bc48bae771da30d76eb9dc297",
+ "prediction_sha256": "c2bba82f548ac53ff3f5804ab30808bf39bb921194423e271a1b7b5384f7c688",
+ "construction_source_snapshots_valid": true
+}
diff --git a/research/shrunk-birth-terminal/selected/majorization.json b/research/shrunk-birth-terminal/selected/majorization.json
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index 0000000000..0fee689df0
--- /dev/null
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diff --git a/research/shrunk-birth-terminal/selected/physical-audit.json b/research/shrunk-birth-terminal/selected/physical-audit.json
new file mode 100644
index 0000000000..0b2b67f89b
--- /dev/null
+++ b/research/shrunk-birth-terminal/selected/physical-audit.json
@@ -0,0 +1,133 @@
+{
+ "all_integer_hinges_nonpositive": true,
+ "all_packets_sigma_equal_M_equal_F0": true,
+ "birth_reuses_preserved": 2108,
+ "coefficient_denominator": 42,
+ "complete_profile_equals_packet_sum": true,
+ "direct_output_coefficient_numerators": [
+ -21,
+ 21
+ ],
+ "dirty_columns": 26216,
+ "distinct_terminal_targets": 381,
+ "forward_frame": {
+ "copies": 24,
+ "histogram": {
+ "1": 106459,
+ "2": 65902,
+ "3": 7179,
+ "4": 14980,
+ "5": 6582,
+ "6": 3788,
+ "7": 2901,
+ "8": 5452,
+ "9": 973,
+ "10": 1911,
+ "11": 1645,
+ "12": 8295,
+ "13": 3257,
+ "14": 450,
+ "15": 800,
+ "16": 156,
+ "17": 100,
+ "18": 50,
+ "19": 77,
+ "20": 136,
+ "21": 302,
+ "22": 16,
+ "23": 2071
+ },
+ "transitions": 233458,
+ "word_sha256": "3a577291cf5b2342212118df353d10761f3d12b9e94efa4f523cc094b5d98b6c"
+ },
+ "forward_scalar": {
+ "all_dirty_zero": true,
+ "response_sha256": "0dd21eb9b6f975013c97b94355d3957e15455d5034e8debc6dcb69dbe652b1f6",
+ "source_is_expected_signed_identity": true
+ },
+ "forward_workspace_gates": 119308,
+ "input_pins": {
+ "BIRTH_MATCHES.json.gz": {
+ "bytes": 38343,
+ "sha256": "1cc40ab44413de0953dfa039fa7446008f3f480062560e9e7833dd48dced5de5",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/BIRTH_MATCHES.json.gz"
+ },
+ "FRAMES.pkl": {
+ "bytes": 30960758,
+ "sha256": "3e3b2158ebad61910433735562de52d51c2bf803474662e90b7c478f90112a83",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/FRAMES.pkl"
+ },
+ "READOUTS.pkl": {
+ "bytes": 30742405,
+ "sha256": "3fc2db8947189be57880cb55a5cb028592431f2c4175ea85827af53829c0dedb",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/READOUTS.pkl"
+ },
+ "READOUT_COST.json": {
+ "bytes": 1252,
+ "sha256": "12c38cecf8c154f3c365cadafc68a73a60abb2368bc0387c820a08a33c110c10",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/READOUT_COST.json"
+ },
+ "TERMINAL_ROLES.json": {
+ "bytes": 3432,
+ "sha256": "17c0132f5b7e1aea34313173fc8059f5199cc281ee582c843ea7650af5e6bd19",
+ "source_path": "/Users/chafreaky/Documents/Codex/2026-10-08/goal-improve-the-exponent-in-openai/work/r12-terminal/joint-expansion/inputs/TERMINAL_ROLES.json"
+ }
+ },
+ "inverse_exact_reverse_of_actual_retained_workspace_events": true,
+ "minimum_hinge": -6784448,
+ "mutations": {
+ "illegal_redirect_frame_rejected": true,
+ "omitted_redirect_rejected": true,
+ "wrong_redirect_sign_rejected": true
+ },
+ "no_birth_slot_removed": true,
+ "physical_roles": 26216,
+ "rank_deficit_preserved": true,
+ "reflected_frame": {
+ "copies": 24,
+ "histogram": {
+ "1": 106459,
+ "2": 65902,
+ "3": 7179,
+ "4": 14980,
+ "5": 6582,
+ "6": 3788,
+ "7": 2901,
+ "8": 5452,
+ "9": 973,
+ "10": 1911,
+ "11": 1645,
+ "12": 8295,
+ "13": 3257,
+ "14": 450,
+ "15": 800,
+ "16": 156,
+ "17": 100,
+ "18": 50,
+ "19": 77,
+ "20": 136,
+ "21": 302,
+ "22": 16,
+ "23": 2071
+ },
+ "transitions": 233458,
+ "word_sha256": "caf806fc99851819a20d30e7f88386e3563741f4fbda64bac4defc60837291a6"
+ },
+ "reflected_scalar": {
+ "all_dirty_zero": true,
+ "response_sha256": "fc9faf8e32a7fabf08c39d2c5749298aec2b01c8b36c5b3395ea6b6d66108407",
+ "source_is_expected_signed_identity": true
+ },
+ "rss_bytes": 727941120,
+ "scope": "Finite exact composed physical witness and conservative scalar accounting; inherited all-size, fixed-tape, stopped-product and analytic transfer remain hypotheses. New kappa must be assembled separately.",
+ "seconds": 9.532371499983128,
+ "source_columns": 2024,
+ "source_reads_at_original_operation_indices": true,
+ "status": "PASS new composed literal word, full exact source/dirty responses and complete paid frames in both orientations",
+ "target_columns": 2024,
+ "target_never_controls": true,
+ "terminal_roles_eliminated": 381,
+ "virtual_roles": 28705,
+ "word_blocks": 276608,
+ "word_file_sha256": "11dfe85123d23c17b4e1f4309b7c5fdfdac55faef7563881f2f3db5b2dfae82e"
+}
diff --git a/research/shrunk-birth-terminal/selected/word.json.gz b/research/shrunk-birth-terminal/selected/word.json.gz
new file mode 100644
index 0000000000..9fdde064c5
Binary files /dev/null and b/research/shrunk-birth-terminal/selected/word.json.gz differ
diff --git a/research/shrunk-birth-terminal/verify.py b/research/shrunk-birth-terminal/verify.py
new file mode 100644
index 0000000000..30c9120199
--- /dev/null
+++ b/research/shrunk-birth-terminal/verify.py
@@ -0,0 +1,88 @@
+#!/usr/bin/env python3
+"""Reconstruct the selected physical word and its exact portable certificate.
+
+This executes only the selected new composition. Archived external submissions
+are immutable reference material, not admission gates. Prepared by Chafik
+Boukhalfa with OpenAI Codex assistance; Apache-2.0.
+"""
+from pathlib import Path
+from hashlib import sha256
+import argparse, gzip, json, os, pickle, subprocess, sys, tempfile, time, resource
+
+if sys.flags.optimize or os.environ.get('PYTHONOPTIMIZE'):
+ raise RuntimeError('Assertions must remain enabled')
+HERE=Path(__file__).resolve().parent
+ROOT=HERE.parents[1]
+read=lambda p:json.loads(p.read_text())
+sha=lambda p:sha256(p.read_bytes()).hexdigest()
+def require(ok,reason):
+ if not ok:raise ValueError(reason)
+def verify_sources():
+ manifest=read(HERE/'SOURCE.json')
+ for name,digest in manifest['package_files'].items():
+ require(sha(HERE/name)==digest,'Package source mismatch: '+name)
+ for name,digest in manifest['repository_files'].items():
+ require(sha(ROOT/name)==digest,'Repository source mismatch: '+name)
+ return sha(HERE/'SOURCE.json')
+def unpack_inputs(destination):
+ destination.mkdir(parents=True,exist_ok=False)
+ pins=read(HERE/'selected/INPUTS.json')
+ for name,entry in pins.items():
+ stored=(HERE/'selected/inputs'/entry['stored_name']).read_bytes()
+ require(sha256(stored).hexdigest()==entry['stored_sha256'],'Stored input hash: '+name)
+ data=gzip.decompress(stored) if entry['encoding']=='gzip' else stored
+ require(len(data)==entry['bytes'] and sha256(data).hexdigest()==entry['sha256'],'Decoded input hash: '+name)
+ (destination/name).write_bytes(data)
+ return pins
+
+def canonical_geometry_bytes(graph):
+ def normalize(value):
+ if isinstance(value,dict):return {str(k):normalize(v) for k,v in value.items()}
+ if isinstance(value,(set,frozenset)):return [normalize(v) for v in sorted(value)]
+ if isinstance(value,(list,tuple)):return [normalize(v) for v in value]
+ return value
+ geometry={k:v for k,v in graph.items() if k!='base_profile'}
+ geometry['bytarget']={k:sorted(v) for k,v in geometry['bytarget'].items() if v}
+ return json.dumps(normalize(geometry),sort_keys=True,separators=(',',':')).encode()
+def bind_geometry(fixture,regenerated,receipt,expected_fixture_sha):
+ require(sha(fixture)==expected_fixture_sha==receipt['selected_fixture_sha256'],'Geometry replay selected-fixture hash mismatch')
+ original=canonical_geometry_bytes(pickle.loads(fixture.read_bytes()))
+ fresh=canonical_geometry_bytes(pickle.loads(regenerated.read_bytes()))
+ require(original==fresh,'Regenerated geometry differs from actual selected fixture')
+ digest=sha256(original).hexdigest()
+ require(digest==receipt['canonical_geometry_sha256'],'Selected canonical geometry digest mismatch')
+ return digest
+
+def main():
+ p=argparse.ArgumentParser(description=__doc__)
+ p.add_argument('--output',type=Path,help='Optional fresh-run receipt outside the frozen source closure')
+ args=p.parse_args();start=time.monotonic();source=verify_sources()
+ with tempfile.TemporaryDirectory(prefix='shrunk-birth-terminal-') as folder:
+ work=Path(folder);inputs=work/'inputs';pins=unpack_inputs(inputs);out=work/'physical'
+ subprocess.run([sys.executable,str(HERE/'search/reproduce_geometry.py'),'--out',str(work/'geometry')],check=True)
+ geometry_digest=bind_geometry(inputs/'FRAMES.pkl',work/'geometry/FRAMES.pkl',read(work/'geometry/REPRODUCTION.json'),pins['FRAMES.pkl']['sha256'])
+ command=[sys.executable,str(HERE/'construction/compose_terminal.py'),'--frames',str(inputs/'FRAMES.pkl'),'--matches',str(inputs/'BIRTH_MATCHES.json.gz'),'--readouts',str(inputs/'READOUTS.pkl'),'--scalar-bill',str(inputs/'READOUT_COST.json'),'--terminal-roles',str(inputs/'TERMINAL_ROLES.json'),'--out',str(out)]
+ subprocess.run(command,check=True)
+ actual=gzip.decompress((out/'word.json.gz').read_bytes());expected=gzip.decompress((HERE/'selected/word.json.gz').read_bytes())
+ require(actual==expected,'Complete regenerated physical word differs')
+ require(read(out/'complex-profile.json')==read(HERE/'selected/complex-profile.json'),'Complete regenerated profile differs')
+ require(read(out/'READOUT_COST.json')==read(HERE/'selected/READOUT_COST.json'),'Exact scalar bill differs')
+ require(read(out/'majorization.json')==read(HERE/'selected/majorization.json'),'Complete majorization proof differs')
+ audit=read(out/'physical-audit.json');saved=read(HERE/'selected/physical-audit.json')
+ volatile={'seconds','rss_bytes','input_pins','word_file_sha256'}
+ require({k:v for k,v in audit.items() if k not in volatile}=={k:v for k,v in saved.items() if k not in volatile},'Physical audit mathematical fields differ')
+ inventory=read(out/'inventory.json');oldinventory=read(HERE/'selected/inventory.json')
+ require({k:v for k,v in inventory.items() if k!='input_sha256'}=={k:v for k,v in oldinventory.items() if k!='input_sha256'},'Exact terminal selection differs')
+ for key,entry in pins.items():require(audit['input_pins'][key]['sha256']==entry['sha256'],'Reconstruction input binding: '+key)
+ # The arithmetic entrypoint reconstructs exact moments and every transfer
+ # parameter using two independent enclosure implementations.
+ subprocess.run([sys.executable,str(HERE/'arithmetic/certificate.py'),'--profile',str(out/'complex-profile.json'),'--scalar-bill',str(out/'READOUT_COST.json'),'--certificate',str(HERE/'certificate.json')],check=True)
+ subprocess.run([sys.executable,str(HERE/'arithmetic/validate.py'),'--certificate',str(HERE/'certificate.json'),'--reference-certificate',str(HERE/'audit/independent-prepackage-certificate.json'),'--receipt',str(work/'arithmetic-validation.json')],check=True)
+ subprocess.run([sys.executable,str(HERE/'search/audit_selected_semantics.py'),'--selected',str(out),'--certificate',str(HERE/'certificate.json'),'--out',str(work/'selected-semantics.json')],check=True)
+ subprocess.run([sys.executable,str(HERE/'audit_lean.py')],check=True)
+ require(source==verify_sources(),'Source manifest changed during verification')
+ record={'status':'PASS selected full physical word, both orientations, all source/dirty columns, frames, complete profile, scalar charge, two exact arithmetic enclosures and Lean input linkage','source_sha256':source,'canonical_geometry_sha256':geometry_digest,'geometry_matches_actual_selected_fixture':True,'certificate_sha256':sha(HERE/'certificate.json'),'word_sha256':sha256(actual).hexdigest(),'source_columns':audit['source_columns'],'dirty_columns':audit['dirty_columns'],'terminal_eliminations':audit['terminal_roles_eliminated'],'birth_reuses':audit['birth_reuses_preserved'],'mutations':audit['mutations'],'seconds':time.monotonic()-start,'rss_bytes':resource.getrusage(resource.RUSAGE_CHILDREN).ru_maxrss*(1024 if sys.platform=='linux' else 1),'scope':'Finite exact construction and rational arithmetic; retained all-size analytic, routing, fixed-tape and stopped-product contracts remain assumptions. Fresh Lean compilation is a separate formal CI gate.'}
+ if args.output:
+ args.output.parent.mkdir(parents=True,exist_ok=True);args.output.write_text(json.dumps(record,indent=2,sort_keys=True)+'\n')
+ print(json.dumps(record,indent=2,sort_keys=True))
+if __name__=='__main__':main()
diff --git a/scripts/check_lean_axioms.py b/scripts/check_lean_axioms.py
index 3709039da8..64449558aa 100644
--- a/scripts/check_lean_axioms.py
+++ b/scripts/check_lean_axioms.py
@@ -20,7 +20,7 @@
output = result.stdout + result.stderr
rows = re.findall(r"^'([^']+)' (?:depends on axioms: \[([^\]]*)\]|does not depend on any axioms)",
output, re.M)
-bad = [(name, ax) for name, ax in rows if set(ax.split(', '))-{''}-ALLOWED]
+bad = [(name, ax) for name, ax in rows if {name.strip() for name in ax.split(',')}-{''}-ALLOWED]
if result.returncode or len(rows) != len(expected) or {n for n, _ in rows} != set(expected) or bad:
print(output)
raise SystemExit(f'Axiom audit failed: reported {len(rows)}/{len(expected)}; unexpected {bad}')
diff --git a/tests/test_shrunk_birth_terminal.py b/tests/test_shrunk_birth_terminal.py
new file mode 100644
index 0000000000..bf69e0f49f
--- /dev/null
+++ b/tests/test_shrunk_birth_terminal.py
@@ -0,0 +1,63 @@
+"""Adverse controls for the selected physical witness and real Lean output parser."""
+from pathlib import Path
+import gzip, importlib.util, json, os, pickle, re, subprocess, sys, tempfile, unittest
+ROOT=Path(__file__).resolve().parents[1]
+PACKAGE=ROOT/'research/shrunk-birth-terminal'
+
+class TerminalSelectionControls(unittest.TestCase):
+ @classmethod
+ def setUpClass(cls):
+ cls.temp=tempfile.TemporaryDirectory(prefix='terminal-controls-');cls.work=Path(cls.temp.name)
+ cls.pins=json.loads((PACKAGE/'selected/INPUTS.json').read_text())
+ for name,record in cls.pins.items():
+ data=(PACKAGE/'selected/inputs'/record['stored_name']).read_bytes()
+ (cls.work/name).write_bytes(gzip.decompress(data) if record['encoding']=='gzip' else data)
+ cls.roles=json.loads((cls.work/'TERMINAL_ROLES.json').read_text())
+ @classmethod
+ def tearDownClass(cls):cls.temp.cleanup()
+ def rejection(self,ids,message):
+ selected=self.work/'adverse.json';selected.write_text(json.dumps(ids))
+ output=self.work/'invalid-output.json'
+ command=[sys.executable,str(PACKAGE/'construction/terminal_inventory.py'),'--frames',str(self.work/'FRAMES.pkl'),'--matches',str(self.work/'BIRTH_MATCHES.json.gz'),'--readouts',str(self.work/'READOUTS.pkl'),'--terminal-roles',str(selected),'--out',str(output)]
+ result=subprocess.run(command,capture_output=True,text=True)
+ self.assertNotEqual(result.returncode,0,result.stdout+result.stderr);self.assertIn(message,result.stderr);self.assertFalse(output.exists())
+ def test_geometry_replay_is_bound_to_actual_selected_fixture(self):
+ spec=importlib.util.spec_from_file_location('selected_portable_verify',PACKAGE/'verify.py');module=importlib.util.module_from_spec(spec);spec.loader.exec_module(module)
+ fixture=self.work/'FRAMES.pkl';expected=json.loads((PACKAGE/'search/recipe/expected-geometry.json').read_text())
+ receipt={'selected_fixture_sha256':self.pins['FRAMES.pkl']['sha256'],'canonical_geometry_sha256':expected['canonical_geometry_sha256']}
+ self.assertEqual(module.bind_geometry(fixture,fixture,receipt,receipt['selected_fixture_sha256']),expected['canonical_geometry_sha256'])
+ wrong=dict(receipt,selected_fixture_sha256='0'*64)
+ with self.assertRaisesRegex(ValueError,'selected-fixture hash'):module.bind_geometry(fixture,fixture,wrong,receipt['selected_fixture_sha256'])
+ graph=pickle.loads(fixture.read_bytes());graph['h']+=1;mutant=self.work/'wrong-geometry.pkl';mutant.write_bytes(pickle.dumps(graph,protocol=4))
+ with self.assertRaisesRegex(ValueError,'differs from actual selected fixture'):module.bind_geometry(fixture,mutant,receipt,receipt['selected_fixture_sha256'])
+ def test_duplicate_terminal_rejected(self):self.rejection([self.roles[0],self.roles[0]],'Duplicate terminal')
+ def test_non_integer_terminal_rejected(self):self.rejection([float(self.roles[0])],'integer role IDs')
+ def test_current_birth_recipient_rejected(self):
+ choice=json.loads(gzip.decompress((self.work/'BIRTH_MATCHES.json.gz').read_bytes()));self.rejection([choice['pairs'][0]['recipient']],'Ineligible requested terminal')
+ def test_assertion_disabled_verifier_rejected(self):
+ result=subprocess.run([sys.executable,'-O',str(PACKAGE/'verify.py')],capture_output=True,text=True)
+ self.assertNotEqual(result.returncode,0);self.assertIn('Assertions must remain enabled',result.stderr)
+
+class LeanAxiomOutputControls(unittest.TestCase):
+ @classmethod
+ def setUpClass(cls):
+ cls.output=(PACKAGE/'lean/receipts/compile/output.log').read_text()
+ source=(PACKAGE/'lean/ShrunkBirthTerminal.lean').read_text()
+ cls.audit='\n'.join(line for line in source.splitlines() if line.startswith('#print axioms '))+'\n'
+ def check_output(self,output):
+ with tempfile.TemporaryDirectory(prefix='lean-output-controls-') as folder:
+ work=Path(folder);(work/'Audit.lean').write_text(self.audit);(work/'output.txt').write_text(output)
+ # Transport stub only: preserve the actual saved kernel output.
+ (work/'lake').write_text('#!'+sys.executable+'\nfrom pathlib import Path\nprint(Path(__file__).with_name("output.txt").read_text(),end="")\n');(work/'lake').chmod(0o755)
+ env=os.environ.copy();env['PATH']=str(work)+os.pathsep+env.get('PATH','')
+ return subprocess.run([sys.executable,str(ROOT/'scripts/check_lean_axioms.py'),'--project',folder,'--audit',str(work/'Audit.lean')],capture_output=True,text=True,env=env)
+ def test_real_wrapped_240_theorem_output_passes(self):
+ self.assertIn('propext,\n Classical.choice,\n Quot.sound',self.output)
+ result=self.check_output(self.output);self.assertEqual(result.returncode,0,result.stdout+result.stderr);self.assertIn('PASS 240 declarations',result.stdout)
+ def test_forbidden_axiom_rejected(self):
+ result=self.check_output(self.output.replace('propext','forbidden_axiom',1));self.assertNotEqual(result.returncode,0);self.assertIn('forbidden_axiom',result.stdout+result.stderr)
+ def test_missing_theorem_rejected(self):
+ result=self.check_output(self.output.split('\n',1)[1]);self.assertNotEqual(result.returncode,0);self.assertIn('239/240',result.stdout+result.stderr)
+ def test_duplicate_theorem_rejected(self):
+ result=self.check_output(self.output+'\n'+self.output.split('\n',1)[0]+'\n');self.assertNotEqual(result.returncode,0);self.assertIn('241/240',result.stdout+result.stderr)
+if __name__=='__main__':unittest.main()