Copied centers with fixed local bases for conditional κ = 3.886224e-5

.gitattributes

@@ -4,3 +4,6 @@
 *.patch -whitespace
 # Preserve the exact upstream bytes, including original whitespace.
 upstream/** -whitespace
+# Preserve the exact pinned third-party proof snapshots and notices.
+references/copied-centers/pr29/** -whitespace
+references/copied-centers/pr33/** -whitespace

CITATION.cff

@@ -6,18 +6,21 @@ title: "A sharper exponent for integer multiplication"
 authors:
   - family-names: Colkitt
     given-names: Douglas
+  - family-names: Chen
+    given-names: Zhihao
+  - name: eumemic
+  - name: icekylinx
 license: Apache-2.0
 type: software
 repository-code: "https://github.com/CrocSwap/integer-mult-bounds"
 url: "https://github.com/CrocSwap/integer-mult-bounds"
 abstract: >-
-  Exact rational certificates, source patches, and research notes for conditional
-  improvements to OpenAI's integer-multiplication manuscript. Compact dirty-control
-  fields remove the simultaneous layer's spacing penalty. Together with complete
-  temporary reservations, local exceptional repair, a separately sized complex
-  network, and retained refinements, the supplied written proofs support
-  kappa = 83/10^12 > 2^-34. The complete upstream algorithmic theorem is assumed;
-  the new arguments are not independently reviewed or formally verified.
+  Conditional bulk-recursion improvement of the retained integer-multiplication
+  framework, with kappa = 6149999/50000000000000 > 2^-23. Controlled rational
+  projector blocks and whole complex residuals give mixed-width recurrences;
+  a dependency-path guard controls exact intermediate precision. The retained
+  Gaussian scaling enclosure is corrected without changing P=34p. Finite
+  checks and exact certificates do not formally verify the full theorem.
 keywords:
   - integer multiplication
   - computational complexity

CONTRIBUTING.md

@@ -7,7 +7,7 @@ For a mathematical issue, identify the exact proposition, source label, or
 inequality; give a counterexample or the missing implication when possible;
 and distinguish numerical validation from an algorithmic proof obligation.
 For the current result, start with the
-[compact-control review guide](docs/research/compact-control-review.md).
+[batched-recursion review guide](docs/research/batched-review.md).
 The [original audit](docs/audit.md) describes the retained upstream assumptions.
 
 For a parameter improvement, supply exact rational choices, the full dependency
@@ -21,7 +21,7 @@ make verify
 ```
 
 Include regenerated certificates and patches in the same change. If the note
-changes, also run its corresponding PDF target (`make compact-note` for the
+changes, also run its corresponding PDF target (`make batched-note` for the
 current result) and include the updated PDF. Review changes to
 claims in the README and note together. Finite tests should address a mathematical
 identity or a failure mode, rather than simply restating implementation details.

Makefile

@@ -1,6 +1,15 @@
 .PHONY: verify note audit-note tuned-note reuse-note incidence-note dag-note shared-point-note paired-note compact-note fetch
 
 verify:
+	$(MAKE) copied-fixed-check copied-fixed-producer
+	$(MAKE) copied-centers-verify
+	$(MAKE) structured-bulk-verify
+	$(MAKE) endpoint-gauge-producer endpoint-gauge-certificate
+	$(MAKE) partial-swap-producer partial-swap-certificate
+	python3 scripts/prime_field_network.py
+	python3 scripts/complex_network.py
+	python3 scripts/fast_gaussian.py
+	$(MAKE) batched-certificate batched-patch
 	python3 scripts/certify.py
 	python3 scripts/search_network.py
 	python3 scripts/make_patch.py
@@ -54,6 +63,7 @@ verify:
 	git apply --check --directory=upstream patches/h46-shared-point.patch
 	git apply --check --directory=upstream patches/h50-paired-59.patch
 	git apply --check --directory=upstream patches/compact-control-34.patch
+	git apply --check --directory=upstream patches/batched-23.patch
 
 note:
 	mkdir -p artifacts
@@ -93,3 +103,99 @@ compact-note:
 
 fetch:
 	python3 scripts/fetch_upstream.py
+
+.PHONY: batched-certificate batched-patch batched-note
+PDFLATEX ?= pdflatex
+TEX_ENGINE ?= pdflatex
+TECTONIC ?= tectonic
+
+batched-certificate:
+	python3 scripts/controlled_bit_rank_moment.py --output certificates/controlled-bit-rank-moment.json > /dev/null
+	python3 scripts/batched_network.py --output certificates/batched-network.json --summary
+
+batched-patch:
+	python3 scripts/make_batched_patch.py
+
+batched-note:
+	mkdir -p artifacts
+ifeq ($(TEX_ENGINE),tectonic)
+	$(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/batched-23-note.tex
+else
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/batched-23-note.tex
+endif
+
+.PHONY: partial-swap-producer partial-swap-certificate partial-swap-note
+partial-swap-producer:
+	python3 scripts/partial_swap_producer.py
+
+partial-swap-certificate:
+	python3 scripts/partial_swap_network.py
+
+partial-swap-note:
+	mkdir -p artifacts
+ifeq ($(TEX_ENGINE),tectonic)
+	$(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/partial-swap-note.tex
+else
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/partial-swap-note.tex
+endif
+
+.PHONY: endpoint-gauge-producer endpoint-gauge-certificate endpoint-gauge-note
+endpoint-gauge-producer:
+	python3 scripts/endpoint_gauge_producer.py
+
+endpoint-gauge-certificate:
+	python3 scripts/endpoint_gauge_network.py
+
+endpoint-gauge-note:
+	mkdir -p artifacts
+ifeq ($(TEX_ENGINE),tectonic)
+	$(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/endpoint-gauge-note.tex
+else
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/endpoint-gauge-note.tex
+endif
+
+.PHONY: endpoint-gauge-verify
+endpoint-gauge-verify: endpoint-gauge-producer endpoint-gauge-certificate
+	python3 -m unittest discover -s tests -p 'test_endpoint_gauge.py' -v
+
+.PHONY: structured-bulk-producer structured-bulk-certificate structured-bulk-verify structured-bulk-note
+structured-bulk-producer:
+	python3 scripts/structured_bulk_producer.py
+
+structured-bulk-certificate:
+	python3 scripts/structured_bulk_network.py
+
+structured-bulk-verify: structured-bulk-producer structured-bulk-certificate
+
+structured-bulk-note:
+	mkdir -p artifacts
+ifeq ($(TEX_ENGINE),tectonic)
+	$(TECTONIC) -Z search-path=$(CURDIR) --outdir artifacts notes/structured-bulk-note.tex
+else
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex
+	$(PDFLATEX) -interaction=nonstopmode -halt-on-error -output-directory=artifacts notes/structured-bulk-note.tex
+endif
+
+.PHONY: copied-centers-producer copied-centers-certificate copied-centers-verify
+copied-centers-producer:
+	python3 scripts/copied_centers_producer.py
+
+copied-centers-certificate:
+	python3 scripts/copied_centers_network.py
+
+copied-centers-verify: copied-centers-producer copied-centers-certificate
+
+.PHONY: copied-fixed-check copied-fixed-producer
+copied-fixed-check:
+	python3 research/copied-fixed-basis/verify.py
+	git apply --check patches/copied-fixed-basis.patch
+
+copied-fixed-producer:
+	python3 research/copied-fixed-basis/producer.py

NOTICE

@@ -14,3 +14,136 @@ as separate files under patches/; upstream source files remain unchanged.
 The new research note, scripts, certificates, patches, and documentation
 were prepared by Douglas Colkitt with assistance from OpenAI Codex.
 This project is not an official OpenAI release or an OpenAI endorsement.
+
+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 retained centers with fixed local bases, 8 October 2026
+Copyright 2026 Dominik Scholz
+
+The fixed-I+J original-envelope composition at (25,23), complete local replay,
+dimension-specific exactness checks and integration are contributed with
+substantial OpenAI GPT-6 Astra/Codex assistance. This adapts icekylinx's PR36
+at 11817ccacb564bb7f98789c20dc11d3fece207e3 and Dominik Scholz's PR35 at
+9c345a2a11e5f4f3649f7c68214bf9a2a0a3fe9c. Fixed projectors and the local
+profiler originate in icekylinx PR32 at 0ef3aeb61f55cc0b321ce6a0ef00acee25cefe52.
+Copied-center scheduling, the complex producer and semantic assembly remain
+credited to icekylinx; controlled permutations to Zhihao Chen PR29; the corner
+and rational-moment methods to Rohan Arun PR31 and preceding arithmetic;
+parameterization to Dominik Scholz PR33. Paureel/Aurel Prosz, Swapnil Jain,
+Zhihao Chen PR21/23, RaD/hipotures and all preceding authors retain the notices
+above. Original Apache-2.0/CC0 licenses and historical AI disclosures remain.

PATCHING.md

@@ -0,0 +1,32 @@
+# Applying the inherited manuscript patch
+
+This patch is the PR #10 baseline. The current copied-center extension is
+presented in `notes/copied-centers-note.tex`; it is not included
+in this historical combined manuscript patch.
+
+`patches/batched-23.patch` applies to the original manuscript snapshot at
+`adc7f1241b42e322a6451854ab7e4b4c146bf78a`, retained under `upstream/`.
+It includes the PR7 dependencies, batched construction, and corrected Gaussian
+input error enclosure.
+
+To generate a complete copy for review, choose a new destination:
+
+```sh
+python3 scripts/make_batched_patch.py --materialize /tmp/integer-mult-batched-review
+```
+
+The entry point is `/tmp/integer-mult-batched-review/build/main.tex`.
+The bundled `upstream/` stays unchanged. With pdfLaTeX installed, compile from
+that copy's `build/` directory, including BibTeX and the usual reference reruns.
+
+Check applicability without modifying the source:
+
+```sh
+git apply --check --directory=upstream patches/batched-23.patch
+```
+
+The combined patch starts from the original snapshot; historical patches are
+alternatives for the same base. PR7 is pinned at
+`6725c6a17b17871a35353fd29157f4ed851bc114` for the retained producer sources.
+The old uniform recurrences keep their original exponents. The active consumers
+use `lem:batched-chunk-swap` and `prop:batched-simultaneous-layer`.