Source authenticated

The Stable Coordinate Conjecture in ambient dimension five

Corollary 1.2: the explicit $H\in P=\mathbb C[p,s,u,F,J]$ is a coordinate of $P[w]$ (by the Dutta-Lahiri theorem, since $H$ is a residual coordinate over $\mathbb C[p]$ ) but not a coordinate of $P$ , because otherwise $P/(H)\cong\mathbb C^{[4]}$ , contradicting Theorem 1.1. So the conjecture fails over $\mathbb C$ in ambient dimension five after one stabilization. Lower ambient dimensions are not addressed. A four-variable counterexample, the first possible dimension, was given in a later OpenAI math release manuscript (5 October 2026), see stable-coordinate-conjecture-four-variables.

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Sep 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: The Stable Coordinate Conjecture in ambient dimension five · Stable Coordinate Conjecture, dimension 5

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Unreleased internal OpenAI model
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Named evidence

VibeMathed record: The Stable Coordinate Conjecture in ambient dimension five

specialist registry · passed

No independent mathematician has checked this yet. Checked here: the abstract, the introduction and Corollary 1.2 with its proof, read against the conjecture as the manuscript cites it. The deduction is two lines given Theorem 1.1 and the published Dutta-Lahiri theorem. Not Lean-checked as stated: the release's Lean scope note says the stable-coordinate consequence is not formalized; only the non-polynomiality and stabilization of P/(H) are (Comparator challenge ComplexCancellation), and the step that H itself is a coordinate of P[w] is not in the formal statement.

Source ↗

The Dolgachev-Weisfeiler affine-fibration conjecture

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Makar-Limanov, van Rossum, Shpilrain, Yu 2004, Comment. Math. Helv. 79

specialist registry · pending

problem-record link supplied by the VibeMathed registry.

Source ↗

Stronger result in the OpenAI math release

witness · pending

other link supplied by the VibeMathed registry.