Published August 8, 2026
| Version 0.3-candidate
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The bordered Jacobian of binary-form multiplication: an integral foundation for the degree-difference principle
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Description
Status: unrefereed candidate. Candidate manuscript and exact evidence package for an integral bordered-Jacobian identity for binary-form multiplication. Producer-side replay passes, including negative controls; the all-degree result rests on the manuscript proof. Independent reproduction, complete formal verification, editorial peer review, and an absolute novelty or priority determination are not claimed.
Original non-code content is dedicated under CC0 1.0; original code is MIT.
Notes
Repository maintainer and publisher: Ian Pitchford. Scholarly attribution: Anonymous. Publication mechanics and producer-side replay are not independent mathematical verification.
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bordered-jacobian-foundations-v0.3-candidate.zip
Additional details
References
- Subsequent unrefereed work: Anonymous. (2026). Exact Smith Invariants and Affine Determinant Lines of Binary-Form Factorisation (Version 0.1.0-candidate). This is a separate child extension, not a correction to or strengthening of the present release. https://evidencepress.org/releases/exact-smith-invariants-affine-determinant-lines/
- Immutable archive of the subsequent unrefereed child candidate: doi:10.5281/zenodo.21861347. https://doi.org/10.5281/zenodo.21861347
- Anonymous. (2026). The degree-difference principle and affine slices of binary-form factorisation spaces, 0.1-candidate. https://doi.org/10.5281/zenodo.21647593
- Anonymous. (2026). A counterexample to the Jacobian conjecture. https://www.ulam.ai/research/jacobian.pdf
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- Gelfand, I. M., Kapranov, M. M., & Zelevinsky, A. V. (1994). Discriminants, Resultants, and Multidimensional Determinants. https://doi.org/10.1007/978-0-8176-4771-1
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- Levinson, J. (2026). The Jacobian conjecture counterexample, via classical projective geometry. https://levjake.wordpress.com/2026/07/22/the-jacobian-conjecture-counterexample/
- Lezeau, P. (2026). feat: add Jacobian disproof, formal-conjectures PR #4474. https://github.com/google-deepmind/formal-conjectures/pull/4474
- Lou, A. (2026). Deriving an explicit polynomial counterexample to the Jacobian conjecture. https://aaronlou.com/jacobian_counterexample_derivation.pdf
- Mathlib contributors. Polynomial resultants and universal factorisation rings. https://leanprover-community.github.io/mathlib4_docs/Mathlib/RingTheory/Polynomial/UniversalFactorizationRing.html
- Speyer, D., & contributors. (2026). The new counterexample to the Jacobian conjecture. https://sbseminar.wordpress.com/2026/07/20/the-new-counterexample-to-the-jacobian-conjecture/
- Tao, T. (2026). A digestion of the Jacobian conjecture counterexample. https://terrytao.wordpress.com/2026/07/21/a-digestion-of-the-jacobian-conjecture-counterexample/