Conditional kappa 0.001018766833114736: checker-clean chronological gauges and R767 reuse

.gitattributes

@@ -18,3 +18,8 @@ research/coordinated-frames-and-entrance-banks/** -text -whitespace
 # Frozen PR210 package and round-nine evidence retain their audited bytes.
 research/five-stage-source527-banks/** -text -whitespace
 research/community-round9-audit/** -text -whitespace
+# The E8 candidate binds exact third-party bytes and regenerated records.
+research/e8-coupled-bit-retiming/** -text -whitespace
+# These finite candidates and proof receipts likewise bind literal source bytes.
+research/e8-clean-reuse-extension/** -text -whitespace
+research/e8-structural-frontiers/** -text -whitespace

.github/workflows/e8-clean-reuse-extension.yml

@@ -0,0 +1,53 @@
+name: E8 clean helper reuse extension
+on:
+  push:
+    paths:
+      - 'research/e8-clean-reuse-extension/**'
+      - 'research/e8-coupled-bit-retiming/**'
+      - 'research/e8-structural-frontiers/**'
+      - '.github/workflows/e8-clean-reuse-extension.yml'
+  pull_request:
+    paths:
+      - 'research/e8-clean-reuse-extension/**'
+      - 'research/e8-coupled-bit-retiming/**'
+      - 'research/e8-structural-frontiers/**'
+      - '.github/workflows/e8-clean-reuse-extension.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  replay:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 60
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.13', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python -m pip install -r research/e8-clean-reuse-extension/requirements.txt
+      - name: Install exact arithmetic headers
+        run: |
+          if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then
+            sudo apt-get update
+            sudo apt-get install -y libboost-dev
+          fi
+      - name: Full suppliers, changed words, invoices and outer controls
+        run: python -B research/e8-clean-reuse-extension/verify.py "${RUNNER_TEMP}/e8-clean-reuse"
+      - name: Check both pending records
+        run: |
+          python -B research/e8-coupled-bit-retiming/record.py
+          python -B research/e8-clean-reuse-extension/record.py
+      - name: Fresh exact structural obstruction proofs
+        run: python -B research/e8-structural-frontiers/verify.py "${RUNNER_TEMP}/e8-structural-frontiers"
+      - run: git diff --exit-code
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: e8-clean-reuse-${{ matrix.python-version }}
+          path: ${{ runner.temp }}/e8-clean-reuse

.github/workflows/e8-coupled-bit-retiming.yml

@@ -0,0 +1,45 @@
+name: E8 coupled bit retiming
+on:
+  push:
+    paths:
+      - 'research/e8-coupled-bit-retiming/**'
+      - '.github/workflows/e8-coupled-bit-retiming.yml'
+  pull_request:
+    paths:
+      - 'research/e8-coupled-bit-retiming/**'
+      - '.github/workflows/e8-coupled-bit-retiming.yml'
+  workflow_dispatch:
+permissions:
+  contents: read
+jobs:
+  replay:
+    runs-on: ubuntu-24.04
+    timeout-minutes: 25
+    strategy:
+      fail-fast: false
+      matrix:
+        python-version: ['3.13', '3.14']
+    steps:
+      - uses: actions/checkout@3d3c42e5aac5ba805825da76410c181273ba90b1
+        with:
+          persist-credentials: false
+      - uses: actions/setup-python@5fda3b95a4ea91299a34e894583c3862153e4b97
+        with:
+          python-version: ${{ matrix.python-version }}
+      - run: python -m pip install -r research/e8-coupled-bit-retiming/requirements.txt
+      - name: Install exact arithmetic headers
+        run: |
+          if ! test -f /usr/include/boost/multiprecision/cpp_int.hpp; then
+            sudo apt-get update
+            sudo apt-get install -y libboost-dev
+          fi
+      - name: Replay both suppliers, controls, finite invoices and record
+        run: python -B research/e8-coupled-bit-retiming/verify.py "${RUNNER_TEMP}/e8-coupled"
+      - name: Check repository candidate record
+        run: python -B research/e8-coupled-bit-retiming/record.py
+      - run: git diff --exit-code
+      - uses: actions/upload-artifact@v4
+        if: always()
+        with:
+          name: e8-coupled-${{ matrix.python-version }}
+          path: ${{ runner.temp }}/e8-coupled

CONTRIBUTORS.md

@@ -23,6 +23,45 @@ not import every numerical refinement from the source527 branch. Original
 commits, licenses and AI-assistance disclosures are preserved. Douglas Colkitt
 performed the maintainer review and integration with OpenAI Codex assistance.
 
+### October 11 pending E8 extension
+
+ai-nanachi, with substantial OpenAI Codex assistance, adds two exact two-donor
+complex helper substitutions, 55 clean-reset bit helper reuses, 54 subsequent
+bit frame moves and complete changed supplier admission. The combined shared
+response-space construction has conditional κ
+`40750673324589432209923/40000000000000000000000000`.
+The new bit component lifts the previous bit bottleneck; the combined complex
+component determines the headline. Three independently derived, scoped exact
+structural obstructions are included in the structural-frontiers appendix.
+applecrusher supplies PR376's equal-helper aliases and frame repairs; Dugongue
+supplies PR390's prefix restoration; Rohan Arun supplies PR395's signed
+extension. Dugongue also supplies PR401's two-sided bank normalization and
+PR404's shared-donor response spaces; applecrusher supplies the additional
+target201 frame refinement. The exact selected source pins and original notices are retained
+in the [extension notice](research/e8-clean-reuse-extension/NOTICE.md).
+All credits of the frozen PR389 package below remain. Maintainer acceptance
+and all-size proof obligations remain pending.
+
+### October 11 preceding PR389 candidate
+
+ai-nanachi, with substantial OpenAI Codex assistance, contributes connected
+one-, two- and three-gate frame coalescence (98 changed bit gates), complete
+pinned supplier replay and a separate exact candidate record. The conditional
+κ is `998634658090834606116833/1000000000000000000000000000`.
+The headline improvement applies applecrusher's #376 assembly refinement to
+Zhihao Chen's #377 nine-stage complex supplier; it is not attributed to the
+new bit frames. Dylan Crow supplies the #370 E8 bit word; applecrusher supplies
+the #376 helper reuse; DaysSky supplies #375's full replay and #381's unsplit
+degree-two layout; Rohan Arun supplies #380's common-envelope comparison.
+Chafik Boukhalfa's #384 supplies the far-retimed complex unit and dated preceding
+witness. Rohan Arun's #385 supplies the complete retimed-complex derivation
+procedure. This package freshly checks the #384 unit's physical word, new
+Clifford frames and finite invoice, and adopts #387's smaller beta backoff.
+#387 is the final preceding witness. The
+[package notice](research/e8-coupled-bit-retiming/NOTICE.md) records exact pins,
+AI disclosures, retained licenses and the complete predecessor lineage.
+Maintainer acceptance and general all-size proof obligations remain pending.
+
 ### Historical source527 checkpoint
 
 **eumemic's [#210](https://github.com/CrocSwap/integer-mult-bounds/pull/210),

Makefile

@@ -54,6 +54,27 @@ source527-verify: source527-record-check
 	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-source527.XXXXXX"); \
 	python3 -B research/five-stage-source527-banks/verify.py --output "$$work/replay"
 
+.PHONY: e8-coupled-record-check e8-coupled-verify
+.PHONY: e8-clean-reuse-record-check e8-clean-reuse-verify
+.PHONY: e8-structural-verify
+e8-structural-verify:
+	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-e8-structural.XXXXXX"); \
+	python3 -B research/e8-structural-frontiers/verify.py "$$work/replay"
+
+e8-clean-reuse-record-check:
+	python3 -B research/e8-clean-reuse-extension/record.py
+
+e8-clean-reuse-verify: e8-clean-reuse-record-check
+	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-e8-clean-reuse.XXXXXX"); \
+	python3 -B research/e8-clean-reuse-extension/verify.py "$$work/replay"
+
+e8-coupled-record-check:
+	python3 -B research/e8-coupled-bit-retiming/record.py
+
+e8-coupled-verify: e8-coupled-record-check
+	@work=$$(mktemp -d "$${TMPDIR:-/tmp}/integer-mult-e8-coupled.XXXXXX"); \
+	python3 -B research/e8-coupled-bit-retiming/verify.py "$$work/replay"
+
 verify-community: community-audit-check community-followup-check copied-reversed-producer copied-reversed-check copied-fixed-reversed-producer copied-fixed-reversed-check
 	$(MAKE) copied-fixed-verify
 	$(MAKE) climbed-48-verify

README.md

@@ -3,6 +3,86 @@
 **Community research maintained by Douglas Colkitt — conditional on the original
 OpenAI #109 framework.**
 
+## New conditional candidate: shared E8 response spaces and clean reuse
+
+The extension candidate gives **κ = 0.001018766833114735805248075**, with maintainer review
+pending. It composes Dugongue's shared-donor response spaces from
+[#404](https://github.com/CrocSwap/integer-mult-bounds/pull/404), the exact
+two-sided dirty-bank normalization from
+[#401](https://github.com/CrocSwap/integer-mult-bounds/pull/401), and
+applecrusher's new frame improvement with our independent R779 substitutions.
+It also composes PR409's ordered entrance promotions, PR410's enlargements
+and PR412's checker-clean re-pivoting. The unchanged original gx and gxcore
+checker families both pass the reconstructed word.
+The combined word has 202 entrance gauges of rank mass 360 and 734 mixed
+banks per stage. All 1,019 independent dirty columns, both orientations,
+every old and new Gaussian child pair, physical owners and the finite
+invoice are checked. The source-specific gains are recomputed together.
+
+The separate bit contribution reuses 55 retired helpers by cancelling their
+clean content and rebuilding compensation for their actual independent dirt.
+After 54 further frame moves it has 767 helpers; full local and seven-stage
+column, geometry, whole-bank and finite checks are rerun. Its coarse saving
+also lifts a new bit bottleneck: keeping the preceding bit supplier with this
+same complex supplier gives κ = 0.001016774267814750149837485. The combined
+construction is limited by the complex supplier.
+The requested 0.002 research target has not been achieved.
+
+[Exact pending record](certificates/candidates/e8-clean-reuse-extension.json) ·
+[Construction and scope](research/e8-clean-reuse-extension/PROOF.md) ·
+[Sources](research/e8-clean-reuse-extension/NOTICE.md) ·
+[Research record](research/e8-clean-reuse-extension/RESEARCH.md)
+
+```sh
+python3 -m pip install -r research/e8-clean-reuse-extension/requirements.txt
+make e8-clean-reuse-verify
+```
+
+Both full predecessor supplier suites, the intermediate signed R779 supplier,
+and the changed response-space/bit/assembly checks run from pinned source.
+All-size theorem interfaces remain conditional. This candidate does not
+replace the maintainer-reviewed selected result below.
+
+[Three exact structural obstructions](research/e8-structural-frontiers/README.md)
+are included independently: the frozen center basis cannot lower copied
+frame rank; any rank-eight completion still needs source span at least seven;
+and the fixed first-frame family misses 0.002 for every bank count. These
+results state their restrictions and leave changed centers, words, joint
+endpoints and geometries open. Run `make e8-structural-verify` to reproduce.
+
+## Preceding PR389 candidate: coupled E8 frames and refined assembly
+
+The October 11 candidate gives
+**κ = 998634658090834606116833 / 1000000000000000000000000000
+= 0.000998634658090834606116833**, with maintainer review pending.
+It improves the public [#387](https://github.com/CrocSwap/integer-mult-bounds/pull/387)
+witness by approximately `9.58198606116833e-13`.
+
+ai-nanachi's connected frame search changes 98 scalar-gate frames after
+applecrusher's [#376](https://github.com/CrocSwap/integer-mult-bounds/pull/376)
+helper reuse. The composition uses DaysSky's unsplit degree-two bit geometry
+from [#381](https://github.com/CrocSwap/integer-mult-bounds/pull/381) and
+Zhihao Chen's complete nine-stage complex supplier from
+[#377](https://github.com/CrocSwap/integer-mult-bounds/pull/377), with Chafik
+Boukhalfa's far-retimed unit from #384. The new unit's physical, Clifford and
+finite checks are fully rerun, following Rohan Arun's #385 derivation. The headline
+κ improvement comes from applying #376's exact assembly refinement to this
+new complex supplier, with #387's smaller positive beta backoff; the separate bit improvement is recorded independently
+because the composition is complex-bound. Both complete supplier suites,
+physical columns, mutation controls, finite invoices and the 47 assembly
+inequalities are freshly replayed. General all-size interfaces remain
+conditional; finite replay is not a formal proof of the complete theorem.
+
+[Candidate record](certificates/candidates/e8-coupled-bit-retiming.json) ·
+[Proof and scope](research/e8-coupled-bit-retiming/PROOF.md) ·
+[Sources and attribution](research/e8-coupled-bit-retiming/NOTICE.md) ·
+[25-trial exploration](research/e8-coupled-bit-retiming/campaign/REPORT.md)
+
+```sh
+python3 -m pip install -r research/e8-coupled-bit-retiming/requirements.txt
+make e8-coupled-verify
+```
+
 ## Current reviewed result: gen4 circuits and common-delivery frames
 
 The composition of **DreamingOfClouds' [#276](https://github.com/CrocSwap/integer-mult-bounds/pull/276)**

certificates/candidates/e8-clean-reuse-extension.json

@@ -0,0 +1,95 @@
+{
+  "absolute_gain": "10066087511950599565621/500000000000000000000000000",
+  "assistance": "Substantial OpenAI Codex assistance",
+  "bit_R": 767,
+  "bit_coarse": "104575879789097/100000000000000000",
+  "bit_component_gain": "13974823961493/500000000000000000",
+  "bit_finite_coefficient": 55762535482200,
+  "bit_global_columns": 1487,
+  "bit_live": 10409,
+  "bit_local_columns": 1007,
+  "bit_profile": {
+    "1": 115983,
+    "14": 1680,
+    "2": 42875,
+    "20": 1680,
+    "28": 1680,
+    "3": 23275,
+    "34": 1680,
+    "4": 15729,
+    "5": 8036,
+    "6": 1680,
+    "7": 4046,
+    "8": 882
+  },
+  "bit_reuse_kappa_gain": "199256529998565541059/100000000000000000000000000",
+  "complex_R": 779,
+  "complex_all_fresh_phase_pairs": 6482,
+  "complex_bank_boundary_adapters": 29088,
+  "complex_banks_per_stage": 734,
+  "complex_chronological_entrance_shears": 551,
+  "complex_coarse": "254951444354246755323/250000000000000000000000",
+  "complex_entrance_rankmass": 360,
+  "complex_finite_invoice": {
+    "C0_exponent": 210000,
+    "E_exponent": 100000,
+    "G_exponent": 30000,
+    "adapter_groups": 303184,
+    "compiler": 25934336,
+    "explicit_bank_boundary_adapters": 29088,
+    "group_bits": 2628,
+    "halving_degree": 2,
+    "induction_gap_multiple_B": 49,
+    "literal_bits": 35284,
+    "live": 14286,
+    "local_bound": 7862875808976,
+    "logical_bits": 2677,
+    "outside_groups": 2412664,
+    "pervertex": 628697897898302,
+    "physical": 15075,
+    "physical_stock_bits": 2642,
+    "real_primitives_all_calls": 5799984,
+    "retained_row": 20161,
+    "router_bits": 7984,
+    "row": 15445
+  },
+  "complex_gauges": 202,
+  "complex_live": 14286,
+  "complex_local_columns": 1019,
+  "complex_physical": 15075,
+  "complex_profile": {
+    "1": 178830,
+    "16": 3840,
+    "2": 47520,
+    "3": 30960,
+    "32": 3840,
+    "4": 8568,
+    "48": 3840,
+    "5": 15768,
+    "6": 15840,
+    "7": 4536,
+    "8": 7488,
+    "9": 576
+  },
+  "complex_unchanged_original_checkers": [
+    "gx.check1",
+    "gxcore.mirror"
+  ],
+  "conditional": true,
+  "contributor": "ai-nanachi",
+  "date": "2026-10-11",
+  "fair_old_bit_kappa": "203354853562950029967497/200000000000000000000000000",
+  "format": "conditional-candidate-record/1",
+  "kappa": "40750673324589432209923/40000000000000000000000000",
+  "kappa_decimal": "0.001018766833114735805248075",
+  "manifest_sha256": "197f02bb6ee45a2ca338611fbe5357af86e54ebebbff2f71f03c6be16e6f8e82",
+  "package": "research/e8-clean-reuse-extension",
+  "prior_pr389": "998634658090834606116833/1000000000000000000000000000",
+  "prior_pr389_commit": "b3c45822ca847aec8c0c019bb04db30881fc2966",
+  "review_status": "Pending maintainer review",
+  "scope": "Finite conditional witness. Full theorem, all-size compiler, recursive supplier, compressed Clifford windows, dirty banking/cover, restored-row, routing, fixed tape, precision/recovery and analytic interfaces remain assumed.",
+  "source_pins_sha256": "18ace817f2f9af22511bb303e99656ed114e534b87f3dd95a65ca4ca670baf2f",
+  "status": "PASS_FRESH_E8_SHARED_RESPONSE_AND_CLEAN_REUSE_COMPOSITION",
+  "upstream_main": "12a4934d15006e8c10f9b2264f13f8f341be802b",
+  "verification": "make e8-clean-reuse-verify"
+}