Published August 29, 2026
| Version 0.2.0-candidate
Preprint
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Extremes do not always maximise: a minimal monotone reversible counterexample
Authors/Creators
Description
Unrefereed theorem candidate. This release gives an exact, cardinality-minimal four-state counterexample to the general monotone-reversible clause of AIM Markov-chain mixing problem 1.6(1), together with a classification of an endpoint-symmetric two-spin heat-bath family.
The separate zero-field Ising question, AIM questions 1.6(2) and 1.6(3), historical priority, independent reconstruction, formal verification, external specialist review, peer review and downstream impact are not established.
The deposit contains a six-page PDF, the complete replay/source ZIP, and SHA-256 checksums. It is mixed-licence: article, original prose and structured research records are CC0-1.0; original Python code is MIT. See LICENSES.md in the ZIP.
Notes
Producer proof and exact replay passed internal release gates and public CI. The release remains an anonymous, unrefereed theorem candidate; publication is not independent validation or peer review.
Files
extremes-do-not-always-maximise-v0.2.0-candidate.pdf
Additional details
Related works
- Is supplement to
- https://github.com/ipitchford/extremes-do-not-always-maximise/releases/tag/v0.2.0-candidate (URL)