Point-Carré: Full Source, Audit Archive, and Release Materials for a Finite PL/ZFC Proof Manuscript of the 3-Dimensional PL Poincaré Theorem

Start-2 calibration note. This archive also belongs to a broader staged research program. In that program, Start-2 is the correction-and-calibration layer: the part where the system stops expanding and begins testing whether its own translations, audits, proof objects, and residual classifications are sharp enough to survive hostile use. Start-2 has proven more difficult than expected. Its sensitivity is the point: a weak calibration layer would turn small inconsistencies into false certainty. For that reason, the current strategy is not to force premature closure of Start-2, but to stabilize its precision through adjacent hard problems first. In practical terms, this means that several “smaller” millennium-scale or boundary-case problems are being completed, archived, and audited before the core Start-2 layer is locked. These problems are not side quests. They are being used as calibration instruments. Each one supplies stress tests, failure modes, symbolic normalization cases, proof-packaging constraints, and audit patterns that improve the eventual precision of Start-2. The working hypothesis is that solving and packaging these difficult adjacent problems will produce a stronger final correction layer than attacking Start-2 directly too early. The present Point-Carré archive is therefore both a self-contained proof manuscript archive and a high-sensitivity calibration object for the later Start-2 phase. The archive should be read in that spirit: not as a claim of external institutional certification, and not as a notebook-based proof, but as a stable public record of a written ZFC/PL proof manuscript, its audit companion, and the calibration data it provides for the next correction layer. This repository archives the source text, PDF renderings, executable audit companion, verification reports, and release materials for the manuscript: “Point-Carré: A Finite PL/ZFC Proof Manuscript for the 3-Dimensional PL Poincaré Theorem.” The manuscript presents a written ZFC/PL proof manuscript over finite piecewise-linear objects. The proof rail proceeds through puncturing, finite PL encoding, active spine extraction, finite obstruction classification, PL-realizable moves, well-founded descent, terminal collapse, the PL terminal-to-ball bridge, and final gluing. The archive includes the full source text of the proof, generated PDF versions, an executable Colab/Jupyter audit notebook, verification reports, and scientific release materials. The executable files are conformity-audit companions only. They verify finite consistency properties such as source loading, section presence, hash correspondence, critical-marker presence, dependency ordering, and artifact coherence. They do not replace the written definitions, lemmas, theorems, or proofs in the manuscript. No external institutional certification is claimed. No notebook, script, boolean flag, or generated certificate is claimed to prove the theorem independently of the written proof. The repository is intended to provide a stable, citable public archive for the manuscript, its source, and its audit/release materials.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-05-22
DOI
https://doi.org/10.5281/zenodo.20345020
Primary Topic
Logic, programming, and type systems
Type
preprint
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preprint

Point-Carré: Full Source, Audit Archive, and Release Materials for a Finite PL/ZFC Proof Manuscript of the 3-Dimensional PL Poincaré Theorem

Son David Bolduc
Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
preprint

Point-Carré: Full Source, Audit Archive, and Release Materials for a Finite PL/ZFC Proof Manuscript of the 3-Dimensional PL Poincaré Theorem

Son David Bolduc
preprint en

Abstract

Start-2 calibration note. This archive also belongs to a broader staged research program. In that program, Start-2 is the correction-and-calibration layer: the part where the system stops expanding and begins testing whether its own translations, audits, proof objects, and residual classifications are sharp enough to survive hostile use. Start-2 has proven more difficult than expected. Its sensitivity is the point: a weak calibration layer would turn small inconsistencies into false certainty. For that reason, the current strategy is not to force premature closure of Start-2, but to stabilize its precision through adjacent hard problems first. In practical terms, this means that several “smaller” millennium-scale or boundary-case problems are being completed, archived, and audited before the core Start-2 layer is locked. These problems are not side quests. They are being used as calibration instruments. Each one supplies stress tests, failure modes, symbolic normalization cases, proof-packaging constraints, and audit patterns that improve the eventual precision of Start-2. The working hypothesis is that solving and packaging these difficult adjacent problems will produce a stronger final correction layer than attacking Start-2 directly too early. The present Point-Carré archive is therefore both a self-contained proof manuscript archive and a high-sensitivity calibration object for the later Start-2 phase. The archive should be read in that spirit: not as a claim of external institutional certification, and not as a notebook-based proof, but as a stable public record of a written ZFC/PL proof manuscript, its audit companion, and the calibration data it provides for the next correction layer. This repository archives the source text, PDF renderings, executable audit companion, verification reports, and release materials for the manuscript: “Point-Carré: A Finite PL/ZFC Proof Manuscript for the 3-Dimensional PL Poincaré Theorem.” The manuscript presents a written ZFC/PL proof manuscript over finite piecewise-linear objects. The proof rail proceeds through puncturing, finite PL encoding, active spine extraction, finite obstruction classification, PL-realizable moves, well-founded descent, terminal collapse, the PL terminal-to-ball bridge, and final gluing. The archive includes the full source text of the proof, generated PDF versions, an executable Colab/Jupyter audit notebook, verification reports, and scientific release materials. The executable files are conformity-audit companions only. They verify finite consistency properties such as source loading, section presence, hash correspondence, critical-marker presence, dependency ordering, and artifact coherence. They do not replace the written definitions, lemmas, theorems, or proofs in the manuscript. No external institutional certification is claimed. No notebook, script, boolean flag, or generated certificate is claimed to prove the theorem independently of the written proof. The repository is intended to provide a stable, citable public archive for the manuscript, its source, and its audit/release materials.

Zenodo (CERN European Organization for Nuclear Research)
Logic, programming, and type systems
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