Research: compose R420 circuits with 16,704 fewer hosted instructions (no new kappa)

research/r420-two-block-composition/CLAIM.json

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+{
+  "track": "Bit supplier",
+  "assignment_seed": 15,
+  "random_source": "secrets.randbelow(100), backed by operating-system randomness",
+  "started_utc": "2026-10-13T03:24:37Z",
+  "base_commit": "66849e1475c930fd7732b1a0067ffee7e1e95f60",
+  "selected_kappa": "51110230636731/31250000000000000",
+  "candidates": [
+    {
+      "task": "Retiming R420 phase-B frames",
+      "decision": "Excluded: PR661 covers all fixed-order simultaneous frame reassignments."
+    },
+    {
+      "task": "Change the nine retained decoder totals",
+      "decision": "Deferred: decoder-rank work and prior fitting experiments make this a larger interface change."
+    },
+    {
+      "task": "Resynthesize R420 block 5 at frame 547",
+      "decision": "Selected: replace the fixed 46-gate, 12-wire scalar map using two-sided elimination, outside the random LU and fixed-order frame classes."
+    }
+  ],
+  "scope": "Only B[371:417] of the pinned R420 word and its literal inverse in C. Keep the exact ordered output map, arbitrary-input restoration, every other gate, stock and decoder interface. Check full frame paths and cancellation-free coefficient bills. No new kappa claim.",
+  "method": "Bounded two-sided binary row/column elimination with deterministic seed 15; exact matrix and full-word checks; reject any unpaid work or invalid frame path.",
+  "stopping_rule": "At most 10000 synthesis trials or 10 CPU minutes for the initial search. One evidence-driven pivot is permitted. Reserve final quarter for verification and handoff.",
+  "expected_deliverable": "One exact smaller local circuit and reproducible verifier, or a precisely scoped negative result if the experiment warrants publication.",
+  "expected_finish_utc": "2026-10-13T04:35:00Z",
+  "coordination": "No pinned issues in GitHub GraphQL; only open issue #650 concerns Discussions. Claim recorded locally.",
+  "overlap_checked": [
+    543,
+    589,
+    612,
+    661
+  ],
+  "contributor": "Ali Romman",
+  "assistance": "Substantial OpenAI Codex assistance.",
+  "pivot": {
+    "reason": "Concurrent PR674 supplies a stronger 34-gate circuit on the same block. PR670 supplies a separate block-3 circuit. Neither reports native multistage or whole-owner replay.",
+    "scope": "Compose only the pinned PR670 and PR674 local replacements in PR543 R420; rebuild cleanup; add native 5/9/11-stage and nine-stage whole-owner/invoice verification. Credit both circuit authors. No new kappa.",
+    "original_search": "10000 greedy two-sided trials with seed 15 found a 37-gate circuit. It is archived locally and is not submitted as a competing construction.",
+    "expected_deliverable": "Combined finite bit circuit with 58 fewer local ADDs and fresh integration evidence."
+  },
+  "result": {
+    "status": "PASS focused local, native, whole-owner and invoice replay",
+    "local_additions_before": 26916,
+    "local_additions_after": 26858,
+    "canonical_word_sha256": "362325782cc1b2b3c427312d56b0450d7255f2afcaf17e07a29827e722159026",
+    "predecessors": [
+      670,
+      674
+    ],
+    "publication": "The submitted PR link will be recorded in the workspace sprint handoff.",
+    "physical_emitted_instructions_before": 8603712,
+    "physical_emitted_instructions_after": 8587008,
+    "full_suite": "Interrupted for disk resource limit; not a pass"
+  }
+}

research/r420-two-block-composition/LOCAL-CERTIFICATE.json

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+{
+  "status": "PASS_R420_TWO_BLOCK_COMPOSITION",
+  "components": [
+    {
+      "pr": 670,
+      "inputs": 4096,
+      "before": 50,
+      "after": 33
+    },
+    {
+      "pr": 674,
+      "inputs": 4096,
+      "before": 46,
+      "after": 34
+    }
+  ],
+  "labels": {
+    "labels": 120,
+    "lattice_rank": 8,
+    "gram_det": 1,
+    "frames": 672
+  },
+  "full_word": {
+    "columns": 660,
+    "gates": {
+      "D": 120,
+      "A": 2064,
+      "B": 808,
+      "C": 2632
+    },
+    "scatter_terms": 568
+  },
+  "hypotheses": {
+    "H1_no_target_feeds_z": true,
+    "H2_D_frame0_targets_from_helpers": true,
+    "H3_A_z_only_scatter_targets_B_split": true,
+    "H4_C_literal_reverse_at_full": true,
+    "H5_V_identity": true
+  },
+  "conclusion": {
+    "U_block_form": true,
+    "J_identity": true,
+    "K_equals_D": true,
+    "C_is_U_inverse": true
+  },
+  "controls": {
+    "wrong_block_670_with_correct_inverse": "targets not y + x: [19, 24, 35, 40, 54]",
+    "wrong_block_674_with_correct_inverse": "targets not y + x: [21, 29, 37, 53, 62]",
+    "missing_cleanup_gate": "sources not restored: [45]",
+    "unpaid_low_frame": "climb not nested: register 45 from frame 182 (dim 2) to frame 47 (dim 1)",
+    "ascending_stale_slice_offsets": "targets not y + x: [8, 13, 21, 29, 33]",
+    "stale_cleanup": "scalar map accepted; H4 literal-reversal contract rejected"
+  },
+  "unchanged_register_paths": 660,
+  "original_additions": 26916,
+  "replacement_additions": 26858,
+  "replacement_canonical_sha256": "362325782cc1b2b3c427312d56b0450d7255f2afcaf17e07a29827e722159026"
+}

research/r420-two-block-composition/README.md

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+# Compose and replay the PR670 and PR674 R420 circuits
+
+This package combines **yongjae321's PR670 block-3 circuit** and
+**x0hu's PR674 block-5 circuit** in eumemic's PR543 R420 supplier. The new
+contribution is their checked composition and fresh native and whole-owner
+replay. The two input circuit improvements belong to those authors.
+
+The combined word uses **26,858 scalar ADDs instead of 26,916**, a saving of
+58 per local invocation, including literal cleanup. Its 660 register frame
+paths, 420 helpers, nine retained totals and paid rank mass 5,112 stay the
+same. **There is no new bit exponent or integer κ.** No selected-frontier
+file or predecessor source is changed.
+
+## Reproduce
+
+From the repository root, use Python 3.10 or later for the standard-library
+check of the composition, complete local word and controls:
+
+```sh
+python3 -B research/r420-two-block-composition/verify.py
+```
+
+For the full contribution, provide NumPy, SciPy, SymPy, a C++17 compiler and
+Boost headers, then run:
+
+```sh
+python3 -B research/r420-two-block-composition/verify.py --hosted
+```
+
+`--hosted` includes fresh five-, nine- and eleven-stage C++ checks on both
+words, then the nine-stage physical hosting and invoice checks on both.
+`--native` runs only the C++ part. Run with Python assertions enabled.
+Set `CXX` and `BOOST_INCLUDE` for installations outside the default search
+paths. The author used `CXX=/opt/homebrew/bin/g++-16` and
+`BOOST_INCLUDE=/opt/homebrew/include` on macOS.
+
+The command creates a temporary output directory and prints its path.
+Use `--output /absolute/new/directory` to keep outputs at another location.
+Expected final line:
+
+```text
+PASS_R420_TWO_BLOCK_COMPOSITION local_additions=26916->26858 saved=58 kappa=unchanged
+```
+
+The outputs include both words, exact receipts and each subprocess log.
+Use the canonical decoded JSON hash in `RESULT.json` to identify a generated
+word. Gzip container bytes can differ across environments.
+
+## Pins and provenance
+
+Base: `66849e1475c930fd7732b1a0067ffee7e1e95f60`.
+The selected conditional κ at this base is
+`51110230636731/31250000000000000 = 0.001635527380375392`, from #626 with
+#543. This composition does not depend on claims in newer frontier PRs.
+
+| Source | Pinned head | Role |
+|---|---|---|
+| PR543, eumemic | `2065fe4f72a914d907f1046603f5a36f17018535` | Original R420 word and replay chain |
+| PR670, yongjae321 | `2e31fcad7f9ecc8b97039ecb2333e581fd725fa1` | Block 3: 50 to 33 XORs |
+| PR674, x0hu | `1b01fd8b135fb2c458554fbbbab4338336bf366d` | Block 5: 46 to 34 XORs |
+
+[SOURCES.json](SOURCES.json) pins every consumed research source and input
+by SHA-256 and Git blob ID. The original circuit certificates and READMEs
+are retained byte for byte under `vendor/`. Neither predecessor's verifier
+is imported. Each single-block reconstruction must match its author's
+canonical complete-word hash before the circuits are combined.
+
+Assignment seed 15 came from operating-system randomness. It initially
+selected block 5. A 10,000-trial two-sided synthesis search found a 37-gate
+word, but PR674 then supplied a stronger circuit for the same block. That
+local experiment is archived and is not submitted as a competing result.
+The one scope pivot was to compose and verify the two concurrent circuits.
+[CLAIM.json](CLAIM.json) records the selection and pivot. No pinned sprint
+issue existed at the claim or overlap checks. This composition performs no
+new search and makes no optimality claim.
+
+## Exact composition argument
+
+The original slices are `B[263:313]` at frame 545 and `B[371:417]` at frame
+547. These are zero-based, half-open intervals. The circuits use disjoint
+sets of twelve source registers. No target reads occur inside either slice.
+The builder applies the higher slice first, so the first replacement does
+not invalidate the second slice's offsets. It then regenerates C once as
+the literal reverse of all non-target gates in A and the new B.
+
+The checker independently enumerates all 4,096 scalar inputs for each
+block. Each replacement has exactly the same ordered F2 output map as its
+original, with no free output permutation. Thus each block produces the
+same values for all later gates, including partially formed sums. Their
+composition has the same raw source and target maps. Literal reverse
+cleanup restores arbitrary source and helper values. The inherited PR543
+checker verifies this conclusion on all 660 symbolic columns, and checks
+H1–H5 and all 672 closed rational frames.
+
+The checker also constructs the forward and reverse nonnegative transfer
+matrices for both blocks. Each replacement matrix is entrywise no larger
+than the original. This establishes non-increase for arbitrary nonnegative
+input bounds at each substituted slice. These matrices bound the signed
+lift; F2 equality is not presented as an integer-ring endpoint identity.
+Fresh C++ replay checks the actual complete lifted word at all three stage
+counts and computes its prefix bounds.
+
+Every register has exactly the same ordered frame path. D, A, scatter,
+retained totals, labels, endpoints and helper stock are unchanged. Thus
+source access, dirty compensation, copies, restoration and all recursive
+children are included. The paid local profile remains
+
+```text
+1320 H_1 + 1440 H_2 + 60 H_4 + 120 H_5 + 9 H_8.
+```
+
+| Local quantity | Original | Composition |
+|---|---:|---:|
+| B gates | 837 | 808 |
+| C gates | 2,661 | 2,632 |
+| Scalar ADDs, including D and scatter | 26,916 | 26,858 |
+| Serialized native records | 29,874 | 29,816 |
+| Forward cancellation-free signed row bound | 144,651 | 144,651 |
+| Reverse cancellation-free signed row bound | 2,270,064 | 2,145,492 |
+| Payload prefix charge, in bits | 100 | 100 |
+
+The nine-stage replay uses the original frozen owner selection. It does
+not rerun the discovery optimizer. The unchanged emitter and independent
+auditor check the actual new scalar stream, every whole helper owner,
+idle window, residual coordinate and paid remainder. Both the baseline
+and composition must pass the 17 parent-template and 16 hosted-template
+mutation controls. The 120,960 helper invocations remain fully hosted,
+with zero banks. The physical program has 288 local invocations, so the
+replay must show exactly `288 * 58 = 16,704` fewer emitted instructions.
+
+Both exact moment engines and the finite invoice are rerun. The bit
+exponent must remain `0.001653826988146798944268`. The rounded invoice and
+paid global profile must match the fresh baseline. The unrounded global
+prefix and coefficient bounds each decrease from 189 to 188 bits; their
+charged prefix stays at 192 bits. The two-level charge stays at 512 bits.
+The emitted instruction count decreases from 8,603,712 to 8,587,008.
+The inherited price
+script also runs its historical cited-PR484 arithmetic control. That is
+not a replay of PR484's complex construction or a new selected assembly.
+
+## Controls and verification boundary
+
+The local controls deliberately break each component's map while rebuilding
+its correct inverse, omit a cleanup gate, use an unpaid low frame, and
+apply both edits with stale ascending offsets. Each must fail for its
+stated target, restoration or frame reason. Keeping the old cleanup still
+passes scalar replay because its map is the same, but fails the required
+literal-reversal hypothesis H4. It is classified as an interface failure.
+The C++ replay also rejects 6, 18 and 24 omitted bridges at five, nine and
+eleven stages for each word, covering 900, 1,380 and 1,620 formal columns.
+
+See [VALIDATION.json](VALIDATION.json) for the actual runs and limits.
+The repository-wide `make verify` was started once. It passed the earlier
+community, producer, partial-gauge, three-stage-cover and paired-cube
+groups, then was stopped during recycled-bit verification after free disk
+space fell below the workspace's prior resource threshold. It is not a
+full-suite pass. Extra checkout copies from that broad run were removed;
+existing research and `upstream/` were preserved.
+
+No new complex supplier, selected outer assembly, Lean theorem or practical
+runtime speedup is claimed. The all-size compiler, common-label and mutable
+basis realization, whole-owner hosting, precision/tape and analytic-transfer
+assumptions remain. Finite replay does not prove the full multiplication
+theorem. The original PR612 Lean literals do not certify these new gates.
+PR661 fixes the gate stream and excludes resynthesis, so its frame result
+is not contradicted.
+
+## Credit and license
+
+The block-3 circuit is yongjae321's PR670 contribution. The block-5 circuit
+is x0hu's PR674 contribution. Both disclose substantial OpenAI Codex
+assistance. Their original notices remain in the vendored READMEs.
+Ali Romman prepared this composition and integration replay with
+substantial OpenAI Codex assistance. No separate human review is claimed.
+New files are under the repository's Apache-2.0 license.
+
+The R420 word, scalar interface and independent local checker are eumemic's
+PR543/493 work. Credit is retained for Zhihao Chen's interface and geometry;
+Dylan Crow's bit format, exporter and cohort checkers; DaysSky's bridged
+checker and hosting; DreamingOfClouds' nine-stage accounting and moment
+engines; chafreaky's owner emitter, audit and invoice; and the cumulative
+supplier lineage in the original R420 README. Their sources stay unchanged.