Partial-swap networks for a conditional kappa = 1.884586e-6 bound

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 +1,11 @@
 .PHONY: verify note audit-note tuned-note reuse-note incidence-note dag-note shared-point-note paired-note compact-note fetch
 
 verify:
+	$(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 +59,7 @@ 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 +99,42 @@ 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

NOTICE

@@ -14,3 +14,56 @@ 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.

PATCHING.md

@@ -0,0 +1,32 @@
+# Applying the inherited manuscript patch
+
+This patch is the PR #10 baseline. The current partial-swap extension is
+presented in `notes/partial-swap-note.tex` and its PDF; 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`.