Coarse-threshold and coordinate refinement: conditional κ = 5.2062354654791e-5

.github/workflows/balanced-split.yml

@@ -0,0 +1,25 @@
+name: Balanced split finite witness
+
+on:
+  pull_request:
+    paths:
+      - 'research/balanced-split-reclamation/**'
+      - 'research/pair-assembly/**'
+      - 'scripts/experiments/binary_frame*'
+      - 'references/frame-compiler/pr48/**'
+      - '.github/workflows/balanced-split.yml'
+  workflow_dispatch:
+
+permissions:
+  contents: read
+
+jobs:
+  verify:
+    runs-on: ubuntu-latest
+    timeout-minutes: 45
+    steps:
+      - uses: actions/checkout@v4
+      - uses: actions/setup-python@v5
+        with:
+          python-version: '3.12'
+      - run: make -C research/balanced-split-reclamation verify

research/balanced-split-reclamation/Makefile

@@ -0,0 +1,17 @@
+.PHONY: verify replay test note
+
+verify:
+	python3 -B verify.py --rebuild
+	python3 -B -m unittest discover -s . -p test_witness.py -v
+
+replay:
+	python3 -B verify.py
+
+test:
+	python3 -B -m unittest discover -s . -p test_witness.py -v
+
+note:
+	mkdir -p ../../build/balanced-split-reclamation/pdf
+	pdflatex -interaction=nonstopmode -halt-on-error -output-directory=../../build/balanced-split-reclamation/pdf paper.tex
+	pdflatex -interaction=nonstopmode -halt-on-error -output-directory=../../build/balanced-split-reclamation/pdf paper.tex
+	cp ../../build/balanced-split-reclamation/pdf/paper.pdf paper.pdf

research/balanced-split-reclamation/NOTICE

@@ -0,0 +1,38 @@
+Balanced coarse sums on anchored split frames
+Prepared for huxint with substantial OpenAI Codex assistance, October 9, 2026.
+Distributed under the repository's Apache License 2.0.
+
+The selected finite network composes previously attributed constructions.
+Preserve all repository notices and these source-specific attributions:
+
+eumemic: PR57 joint reversible frame compiler and independent physical replay;
+PR69 balanced coarse column sums, with OpenAI Codex assistance.
+Avi Eisenberg / ikeboy: PR62 interval strips and core-aware pair assembly,
+with Anthropic Claude assistance.
+Rohan Garg / rohangar1: PR59 split-pair operation, with OpenAI Codex assistance.
+Rohan Arun: PR65 schedule/refined arithmetic and PR67 profile-cost compiler,
+with OpenAI Codex assistance.
+Dominik Scholz: PR63 ranked composition and PR68 compatible pending controls,
+with OpenAI GPT-6 Astra / Codex assistance.
+Chafik Boukhalfa: PR60 ranked reclamation and PR71 anchored split graph and
+next-use scoring, with OpenAI Codex assistance.
+
+The original code comments and preserved vendor snapshots retain their own
+attributions. The inherited framework also credits icekylinx, RaD / hipotures,
+James Chang, Zhihao Chen / jacklightChen, Aurel Prosz / Paureel, Swapnil Jain,
+Douglas Colkitt, OpenAI, David Harvey, Joris van der Hoeven, and other
+contributors identified in the root NOTICE and inherited source files.
+
+The new package's finite checks are conditional evidence. They are not a
+complete theorem formalization, an independent human referee report, or a
+practical multiplication benchmark.
+
+The refined witness also uses Thomas DiFiore's PR74 envelope ordering,
+Alejandro Zarzuelo Urdiales's PR70 carry-exchange methodology, Dominik
+Scholz's PR76 composition, Chafik Boukhalfa's PR79 future-compatible unit
+completion and half-plane coarse choice, and Rohan Arun's PR78/82 coordinate
+flags and coordinate-aware pricing. Their original notices and AI-assistance
+disclosures remain applicable. The two-region exchange experiment, shifted
+coarse boundary and selected h25 cyclic flag in this package were evaluated
+by huxint with OpenAI Codex assistance; no global optimum or priority for
+general matroid exchange or coordinate conjugation is asserted.

research/balanced-split-reclamation/README.md

@@ -0,0 +1,106 @@
+# Coarse-threshold and coordinate refinement on anchored split frames
+
+The selected finite construction gives the conditional bound
+
+\[
+T(n)=O\bigl(n(\log n)^{1-\kappa}\bigr),\qquad
+\kappa=\frac{52062354654791}{10^{18}}
+=5.2062354654791\times10^{-5}.
+\]
+
+This is **0.0568021906% above the complete PR82 witness** frozen at
+`3410b940aa26e5876202152dfa7c4f66451ee22c`. Newer community submissions have
+larger reported values. This is a scoped historical comparison, not a claim
+to the latest record, global optimality, or measured multiplication speed.
+The initial PR77 witness `5.1547855889988e-5` remains reproducible at commit
+`83298467291d3bd4b53f76faaef60dbf585be171`.
+
+| Paid quantity | Pinned PR82 | This construction |
+|---|---:|---:|
+| Roles at h=23 | 27,075 | 27,043 |
+| Roles at h=25 | 35,500 | 35,505 |
+| Physical width W | 133,289,600 | 133,224,855 |
+| Complete recursive rank mass | 76,639,673,100 | 76,602,444,725 |
+| Rank deficit | 1,846,900 | 1,846,900 |
+
+The strict bit witness is `26032532642421/(5*10^17)`. The complete old
+PR82 child list, evaluated with its own width, has a rigorous lower moment
+above one at this saving. The new list has an upper moment below one. Both
+the adjacent `10^-18` bit grid point and the next kappa point are rejected.
+
+## Selected construction
+
+Both axes retain the anchored split vector `[1,1,2]`, the original common-point
+envelopes, PR74's envelope ordering, and the inherited reversible compiler.
+The h23 region schedule is `cover-core`; h25 uses `reverse-node`.
+
+- At h23, a coarse cell `(i,j)` uses column sums when `i+j < ng+1`, and row
+  sums otherwise, with zero-based group indices and current group count `ng`.
+  This shifts the earlier half-plane boundary by two. At h25, every cell uses
+  row sums. Both parenthesizations compute the same disjoint edge sum.
+- Independent unit-completion rows are ordered by compatible future uses,
+  as in PR79. Three passes of the inherited improving single carry exchanges
+  are supplemented by legal two-region carry cycles. The selected words use
+  113 such cycles at h23 and 86 at h25. Open two-region reassignment paths
+  were also searched; none was selected in these words.
+- h23 retains rank-ordered retired candidates and insertion-ordered live
+  controls. h25 orders both by actual profile cost against the next use.
+- h23 uses the preserved PR82 coordinate flag. h25 uses the point map
+  `i -> (i+1) mod 25` in both oracle pricing and the final physical word.
+  h23 oracle pricing remains in the original coordinates.
+
+Every selected scalar operation is a literal XOR and every operand promotion,
+center copy, endpoint correction, source growth and cleanup is charged.
+The score is a deterministic discovery heuristic. Only the complete actual
+physical profile decides whether a candidate improves the bound.
+
+The actual width is below `2^27`. The bridge derives wire bits 27, row
+coefficient 843 and degree gap `7007/25`; degree 2000, suffix slope 8000,
+the complex branch and its scalar charge remain unchanged. Stale width
+metadata is rejected.
+
+## Reproduction
+
+From the repository root, using Python 3.11+ and a C++17 compiler:
+
+```sh
+make -C research/balanced-split-reclamation verify
+make -j1 verify
+```
+
+The focused target regenerates both complete words byte-for-byte, checks every
+input/target/arbitrary-dirty basis vector in both orientations, reconstructs
+actual frame transitions, recomputes the bounded-minor/CRT profiles, and
+rebuilds the complete recursive profile and exact certificate. A separately
+evaluated rational logarithm/exponential enclosure confirms the accepted and
+rejected grid points. All 47 strict assembly constraints and seven margins
+are recomputed. Seventeen tests cover malformed or aliased ports, uncharged
+canceling scatter gates, omitted children, adjacent-grid rejection, three
+stale bridge fields, assertion-disabled Python, and read-only pin help.
+
+`selected/` contains the frozen words, profiles and certificates. `SOURCE.json`
+pins consumed sources and deliverables; verification never refreshes it.
+An intentional maintainer update uses `python3 pin.py --record`.
+`generate.py --output <directory>` writes a fresh reconstruction outside the
+selected artifacts. The proof is in [paper.tex](paper.tex) and [paper.pdf](paper.pdf).
+Run receipts, including any environmental interruption of the broad suite,
+are recorded separately in `VALIDATION.json`.
+
+## Scope and credit
+
+The base theorem, all-size residual/frame compiler, fixed finite-alphabet tape
+representation, semantic/analytic reduction, routing, prime setup and exact
+recovery remain inherited hypotheses. These are finite checks and a written
+conditional argument, not a complete formal multiplication theorem or
+independent human expert review.
+
+The initial balanced split/cost-basis experiment and this explicit shifted
+coarse rule, coordinate/cost choice, exchange search and reproducible package
+were prepared for **huxint with substantial OpenAI Codex assistance**.
+Credit eumemic (PR57/69), Avi Eisenberg (PR62), Rohan Garg (PR59), Rohan Arun
+(PR65/67/78/82), Dominik Scholz (PR63/68/76), Chafik Boukhalfa (PR60/71/79),
+Thomas DiFiore (PR74), Alejandro Zarzuelo Urdiales (PR70), and all earlier
+contributors preserved in [NOTICE](NOTICE). Carry exchanges and coordinate
+conjugacy are inherited methods; no general novelty claim is made for them.
+Original licenses, contributor snapshots and AI-assistance disclosures remain
+attached. No contributor endorsement is implied.

research/balanced-split-reclamation/SOURCE.json

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+  }
+}