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Bras-Amorós genus-monotonicity conjecture

It is proved that $n_{g+1}\ge n_g$ for every $g\ge0$ , without restrictions on multiplicity or conductor. A partial injection leaves a specified family of source semigroups; unused targets are then shown to be numerous enough to cover it. Exact transfer computations bound relaxed source counts for $1\le g\le836$ , and generating-function estimates handle $g\ge837$ . This is not an enumeration of all numerical semigroups through genus 836. The stronger Fibonacci inequality $n_{g+1}\ge n_g+n_{g-1}$ and fixed-multiplicity monotonicity are not proved.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 30, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-co-developed. 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: Bras-Amorós genus-monotonicity conjecture · Numerical semigroup monotonicity

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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VibeMathed
registry · event recorded by

GPT-6 Astra
model · ai model contributor · OpenAI

Fable 5.1
model · ai model contributor · Anthropic

Mingchang Liu
human · human collaborator

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VibeMathed record: Bras-Amorós genus-monotonicity conjecture

specialist registry · passed

No independent mathematician has checked this yet. Checked by this site on 7 October 2026: the statement matches Conjecture 2 of Kaplan's survey (arXiv 1707.02551), which also says the weak form was open and that Zhai's asymptotics leave only finitely many genera to settle. From a fresh clone at commit b1b6fb8, all five shipped checkers passed: capacity recurrences through degree 1500, the omitted-pivot multiplier below 0.221715, the guarded mass assembly, the analytic join (comparison fails at genus 836, holds from 837), and all 836 finite rows with nonnegative slack (smallest 1, at genera 1 and 2). A separate enumeration written here of all numerical semigroups through genus 23 reproduced the known counts and confirmed that each certified slack is at most the true difference $n_{g+1}-n_g$ for $g\le 22$ . These are arithmetic checks only. The coefficient arrays were not regenerated from the C++ sources, and the combinatorial and analytic arguments that connect them to the theorem (about 2,000 lines of the manuscript) were not read. No Lean formalisation.