The Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere

Theorem 1.1: for every $0<\gamma<\gamma_*=4616733319001/10^{14}>1/25$ there is $Q_\gamma$ with $H_Q^2\ge\gamma H_Q$ on the full lowest-Landau-level fermionic Fock space for $Q\ge Q_\gamma$ , independently of particle number. Corollary 1.2: $H_{N,3(N-1)}\ge\frac1{25}(1-P_{\mathrm L,N})$ for $N\ge N_0$ . Section 7 proves the planar analogue at $\gamma_*$ , the fermionic cubic case of Rougerie's Conjecture A.1. The companion adds stability under bounded projected scalar potentials. Thresholds are existential; bosonic and other fillings are not treated.

Exact FrontierDelta

Prior state unknown→proved

Scope and record

Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: lean-checked. 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 Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere · Laughlin spectral gap conjecture

Confidence: Not scored

Registry verification: lean checked · announcement · candidate

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Attribution

VibeMathed
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Unreleased internal OpenAI model
model · ai model contributor · OpenAI

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Named evidence

VibeMathed record: The Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere

specialist registry · passed

No independent mathematician has checked this yet. Checked here: Theorem 1.1 and Corollary 1.2 of the Fock-space manuscript were read against the conjecture: $H_Q^2\ge\gamma H_Q$ on the whole Fock space for every $\gamma<\gamma_*\approx0.0462$ and large $Q$ , hence a gap of $1/25$ above the Laughlin state at $Q=3(N-1)$ for large $N$ . lean/formalization.yaml lists Laughlin.json (declaration OAI.Laughlin.mainTarget_proved, file OAI/Analysis/Laughlin/Main.lean). The statement Laughlin.lean was read here; not rebuilt here. It encodes antisymmetric states in a number basis, the $V_1$ energy through explicit pair coefficients and the Laughlin vector through its polynomial, and states energy at least $1/100$ times squared distance to the Laughlin line for all $N\ge N_0$ at flux $3(N-1)$ : a uniform positive gap, the headline (with a weaker constant than the paper's 1/25, which LaughlinGap.lean states). Fidelity of the pair-coefficient encoding to $P^{(1)}$ was not audited. Permitted axioms: propext, Quot.sound, Classical.choice.

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The Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere

witness · pending

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

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Companion: Uniform Stability of the Spherical Laughlin Gap

paper · pending

paper link supplied by the VibeMathed registry.

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Lean proof (OAI.Laughlin.mainTarget_proved)

lean artifact · pending

lean-proof link supplied by the VibeMathed registry.

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Artifacts and verifiers

Lean proof (OAI.Laughlin.mainTarget_proved)

lean artifact · pending

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This event attributed to Unreleased internal OpenAI model

Lean proof (OAI.Laughlin.mainTarget_proved) evidence for this event

The Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere parent of this event

Companion: Uniform Stability of the Spherical Laughlin Gap evidence for this event

The Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere evidence for this event

VibeMathed record: The Laughlin spectral gap conjecture for the V1 pseudopotential on the sphere evidence for this event

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