DominikScholz · Oct 8, 2026 · Oct 8, 2026 · Oct 8, 2026 · Oct 8, 2026 · Oct 8, 2026
diff --git a/.github/workflows/verify.yml b/.github/workflows/verify.yml
@@ -16,7 +16,7 @@ jobs:
       fail-fast: false
       matrix:
         python-version: ['3.11', '3.13', '3.14']
-        group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair]
+        group: [community, producers, certificates, ternary, research, tests, strips, clones, positive, joint, pair, rank-pair, global-anchor, cost-live]
     steps:
       - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1 # v7
         with:

diff --git a/Makefile b/Makefile
@@ -23,6 +23,9 @@ verify:
 	$(MAKE) verify-positive
 	$(MAKE) verify-joint
 	$(MAKE) verify-pair
+	$(MAKE) verify-rank-pair
+	$(MAKE) verify-global-anchor
+	$(MAKE) verify-cost-live
 	$(MAKE) verify-tests
 
 verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check
@@ -428,3 +431,21 @@ pair-assembly-verify: pair-assembly-producer pair-assembly-check
 .PHONY: verify-pair
 verify-pair: pair-assembly-verify
 	python3 scripts/audit_pair_candidate.py --check docs/research/community-pair-arithmetic.json
+
+.PHONY: verify-rank-pair rank-pair-verify verify-global-anchor global-anchor-verify
+verify-rank-pair: rank-pair-verify
+rank-pair-verify:
+	python3 research/rank-pair/frame_compile.py
+	python3 research/rank-pair/screen.py
+	python3 -m unittest discover -s tests -p 'test_rank_pair.py' -v
+
+verify-global-anchor: global-anchor-verify
+global-anchor-verify:
+	python3 research/global-anchor-screen/verify.py
+	python3 research/global-anchor-screen/controls.py
+
+.PHONY: verify-cost-live cost-live-verify
+verify-cost-live: cost-live-verify
+cost-live-verify:
+	python3 research/cost-live-both/validate.py
+	python3 research/cost-live-parameters/refine.py
diff --git a/NOTICE b/NOTICE
@@ -302,3 +302,41 @@ 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.
+
+Rank-first reclamation on interval-strip pair assembly, 8 October 2026
+Composition and exact profile witness: Dominik Scholz, with substantial OpenAI
+GPT-6 Astra / Codex assistance. The PR #60 descending-frame-rank compiler by
+Chafik Boukhalfa is reused unchanged on Avi Eisenberg's PR #62 scalar graph.
+The joint frame compiler and paid reclamation are eumemic's PR #57, developed
+with OpenAI Codex assistance. PR #62 records Anthropic Claude assistance.
+This composition improves actual fixed-basis block profiles with unchanged
+role counts; no new slot-priority rule or scalar graph is claimed. All prior
+contributors, licenses, compiler arguments and conditional analytic/tape
+interfaces remain credited. See research/rank-pair/PROOF.md.
+
+Compatible pending live anchors, 8 October 2026
+Dominik Scholz, with substantial OpenAI GPT-6 Astra / Codex assistance:
+pending-carrier F <= E <= G clearing, full literal replay and the selected
+finite witness. Descending h25 slot ties were also independently found by
+the concurrent incremental research lane. This extends Chafik Boukhalfa's
+PR #60 rank-first reclamation, eumemic's PR #57 compiler and Avi Eisenberg's
+PR #62 pair graph. The capped-mass comparison format follows rfu08's
+concurrent PR #64 audit, with the exact profile differences reconstructed
+here. Prior notices and all conditional theorem assumptions remain in force.
+See research/global-anchor-screen/PROOF.md and SOURCE.json.
+
+Cost-aware live controls and combined clearing relations, 8 October 2026
+Rohan Arun's PR67 supplies cost-aware retired-slot selection, the physical
+profile oracle and refined rational moment/assembly arithmetic, with OpenAI
+Codex assistance. Dominik Scholz's composition adds compatible pending live
+controls at both axes; a separate experiment combines fundamental clearing
+relations. Both were prepared with substantial OpenAI GPT-6 Astra/Codex
+assistance. All PR57/60/62 graph/compiler notices, earlier community credits,
+licenses and conditional theorem interfaces remain. Original PR67 sources
+are retained in research/slot-cost-rank-pair; selected composition and scope
+are documented in research/cost-live-both.
+
+The parameter-only refinement in research/cost-live-parameters follows
+Alejandro Zarzuelo Urdiales's PR #61 backoff-refinement precedent and uses
+Rohan Arun's PR #67 exact moment and assembly adapter unchanged. Dominik
+Scholz prepared the refinement with substantial OpenAI GPT-6 Astra assistance.
diff --git a/README.md b/README.md
@@ -1,3 +1,31 @@
+# Cost-aware live controls, conditional κ = 5.103512721785e-5
+
+The latest selected research witness is **κ = 1020702544357/20000000000000000**, with
+bit saving **51037731934993/10^18**. It combines Rohan Arun's PR #67
+cost-aware reclamation with compatible pending live controls at both axes.
+Every clearing XOR and frame transition remains paid. A parameter-only
+refinement reduces assembly backoff from 10^-12 to 10^-18 with unchanged
+physical words and bit saving; its larger eventual cutoff is documented in
+[the refinement proof](research/cost-live-parameters/PROOF.md). Newer public
+PRs #69–71 claim stronger bounds; this witness is not the current frontier.
+
+[Proof](research/cost-live-both/PROOF.md) ·
+[Exact parameter certificate](research/cost-live-parameters/certificate.json) ·
+[Completed focused validation](research/cost-live-both/validation-receipt.json)
+
+Independent complete dirty-state replay, actual fixed-basis profiles/CRT,
+exact moment and all 47 constraints/seven margins pass. The candidate file
+preserves its initial draft-time pending flags; the separate validation
+receipt records completed checks. Full current-head CI/review remains pending.
+Run `make cost-live-verify`; CI runs this target on Python 3.11, 3.13 and 3.14.
+
+The earlier live-anchor and combined-relation experiments remain in their
+separate research directories. All inherited analytic, all-size compiler,
+routing/recovery and fixed-tape hypotheses remain conditional. This is not
+full formal verification or a practical speedup. Prepared by Dominik Scholz
+with substantial OpenAI GPT-6 Astra/Codex assistance, retaining Rohan Arun,
+Chafik Boukhalfa, eumemic, Avi Eisenberg and all predecessor credits.
+
 # A sharper exponent for integer multiplication
 
 **Community research maintained by Douglas Colkitt — conditional on the original

diff --git a/certificates/joint-dual-kappa.json b/certificates/joint-dual-kappa.json
@@ -842,7 +842,7 @@
     "scripts/experiments/pin_joint_dual_sources.py": "4d31cc0e38b7902709ca5f8f714cba109760d2592346dd7f8dc0b900a2d9fe00",
     "scripts/experiments/verify_joint_dual.py": "7a31bba1e9c0ded32ae285df2ca9bc91ef20c330f6789fdba361876f3c7a1985"
   },
-  "source_manifest_sha256": "fd1aab7d75753b4b55b2377f26119dae74f367b0b4fab66cba42d944b3042cc9",
+  "source_manifest_sha256": "51f6145f25f2bd0e6312002dffd450d9d9723deb77e71100d1be928cd8971152",
   "sources": [
     {
       "files": {

diff --git a/certificates/joint-dual-validation.json b/certificates/joint-dual-validation.json
@@ -226,7 +226,7 @@
     }
   },
   "bit_saving": "2382370177/50000000000000",
-  "certificate_sha256": "2ed658f05365b28825e24a6e7bac9fc9cc015d5a5d63d9579f4ac6e0640ae559",
+  "certificate_sha256": "a74fd1d5a4c816742f5548bff1947f594f57444f2ff681d47ddd1a38389d14f7",
   "kappa": "4764513337/100000000000000",
   "margins": 7,
   "producer_words_regenerated_and_matched": true,

diff --git a/research/circuit-space-clearing/.gitignore b/research/circuit-space-clearing/.gitignore
@@ -0,0 +1,2 @@
+build/
+__pycache__/
diff --git a/research/circuit-space-clearing/README.md b/research/circuit-space-clearing/README.md
@@ -0,0 +1,39 @@
+# Draft: combine clearing relations
+
+Latest candidate: **κ = 510338933/10^13 = 5.10338933e-5**.
+Bit saving: **510364979/10^13**. The exact numerical gain over PR #67 is
+26543157/(2*10^17). This is a preliminary conditional candidate, pending
+independent serialized dirty-state replay and full validation.
+
+At h23, XOR pairs of PR67's fundamental zero relations to obtain alternate
+clearing expressions, cancelling expensive control promotions. All candidate
+roles satisfy frame containment and selected expressions are emitted as
+literal paid XORs. The compiler selected 48 improved clearing witnesses.
+Keep PR67's h25 word unchanged at `research/slot-cost-rank-pair/frame-word-25.json.gz`.
+Roles remain27918/36586 and W=137151806.
+
+Passed in the research lane: internal complete dirty-basis compilation,
+source/target/scatter and frame checks, literal transition reconstruction,
+actual C++ fixed-basis profiles/CRT, exact moment and47constraints/seven margins.
+Independent serialized replay, parent reproduction, dedicated CI and broad
+checks are pending. No full formal theorem or practical speedup is claimed.
+The original fully replayed PR68 result remains in `global-anchor-screen`;
+the separate cost/live-anchor candidate remains in `cost-live-composition`.
+
+Reproduce from the repository root (C++17 and Python with assertions enabled):
+
+```sh
+python3 research/circuit-space-clearing/run.py --h 23 --mode pairs --work-dir /tmp/circuit-space-reproduction
+python3 research/circuit-space-clearing/screen.py --h 23 --work-dir /tmp/circuit-space-reproduction --independent-replay
+```
+
+`selected/arithmetic.json` and `draft-manifest.json` record the current
+candidate and source/artifact pins. These commands have not yet been rerun
+in the published checkout; the draft is being made available immediately.
+
+Attribution: Rohan Arun's PR67 cost-aware selection, oracle and baseline;
+Dominik Scholz's new combinations of clearing relations with substantial
+OpenAI GPT-6 Astra/Codex assistance; Chafik Boukhalfa's PR60 rank-first rule;
+eumemic's PR57 joint compiler; Avi Eisenberg's PR62 graph (Claude assistance).
+All earlier source notices, Apache-2.0 terms and conditional all-size compiler,
+analytic, routing/recovery and fixed finite-alphabet tape assumptions remain.