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A Fock-space inequality and the Laughlin spectral gap

OpenAI

For the fermionic Laughlin state at filling 1/3 on the round sphere and flux 3(N−1), the unperturbed V1 Hamiltonian has a uniform gap for all sufficiently large particle numbers N. The released Lean scope gives a 1/25 Fock-space distance estimate and a 1/100 finite spherical gap.

Sources for this record

What was already known

A uniform gap in this growing-particle spherical model was a conjecture.

AI involvement AI-led

OpenAI credits an internal model with the gap manuscripts and Lean artifacts. People selected and released the work; the result-specific interaction history is unavailable.

The institution credits its internal model with producing the manuscripts and artifacts, while human selection and packaging are documented; the exact interaction history for this result is unavailable.

Importance Major

Resolves the selected uniform-gap problem for the unperturbed V1 model.

Limitations

The documented formalization does not cover stability under projected scalar potentials or uniqueness of the perturbed ground state. The source reports the Lean check; no named human proof check or explanation is documented.

Technical verification Formal (Lean 4 kernel and Comparator)

The release's Lean scope page identifies a formalized unperturbed 1/25 inequality and 1/100 spherical gap, with Comparator statements for those exact targets. This is a source-reported machine check of the selected unperturbed result; neither projected-potential stability nor uniqueness of the perturbed ground state is included.

Formal checking

The release's Lean scope page identifies a formalized unperturbed 1/25 inequality and 1/100 spherical gap, with Comparator statements for those exact targets. This is a source-reported machine check of the selected unperturbed result; neither projected-potential stability nor uniqueness of the perturbed ground state is included. The build was not rerun here.

Checker
Lean kernel and Comparator in OpenAI's released Lean library
Scope
Uniform unperturbed Laughlin V1 gap at flux 3(N−1) for sufficiently large N, including the 1/25 distance inequality and reported 1/100 spherical bound
Basis
Reported by the linked checker
Evidence source

Checking a formal statement does not establish that it matches the original problem.

Human understanding Few

Default for missing human explanation: the available release attributes the manuscripts to a model and names no human who explains the central Fock-space or spherical-gap mechanism.

Correction and publication history