OAI.Laughlin.Certificate.four_body_22_positive: intermediate lemma from OpenAI, Uniform stability of the spherical Laughlin gap (result family 269)

Proved

OAI.Laughlin.Certificate.four_body_22_positive

by dbenbenn · Oct 28, 2026 · Mathlib 0df444a (Lean v4.33.1)

openai-math

An intermediate lemma of the split of OpenAI's proof of OAI.Laughlin.mainTarget_proved, carved from OpenAI's openai/math development for this platform. The statement and its proof are OpenAI's (OpenAI, Uniform stability of the spherical Laughlin gap (result family 269), OpenAI Math Release, October 5, 2026, result family 269, github.com/openai/math, Apache License 2.0); in Lean it is the declaration OAI.Laughlin.Certificate.four_body_22_positive of lean/OAI/Analysis/Laughlin/FiniteFlux/Positive22.lean at commit adc7f12, ported to Lean 4.33.1 and Mathlib 0df444a.

The statement, as published (namespace OAI.Laughlin.Certificate):

theorem four_body_22_positive :
    ((compressedRational 22).map (Rat.castHom ℝ)).PosSemidef

Definitions. The statement is written with OAI.Laughlin.Certificate.compressedRational (definitions bundle OAIQ047L000 of this split).

Used by. The proofs of OAI_Laughlin_Certificate_four_body_certificates and OAI.Laughlin.Certificate.scaled_four_body_certificates of this split import it.

Preamble

import Mathlib
import Definitions.Def_OAIQ047L000

Formal statement

section

set_option linter.all false
set_option linter.unusedVariables false
set_option linter.unusedTactic false
set_option linter.unreachableTactic false

namespace OAI

namespace Laughlin.Certificate

theorem four_body_22_positive :
    ((compressedRational 22).map (Rat.castHom ℝ)).PosSemidef := by
  sorry

end Laughlin.Certificate

end OAI
end

Source

OpenAI, Uniform stability of the spherical Laughlin gap (result family 269), OpenAI Math Release, October 5, 2026, https://github.com/openai/math (result family 269; paper: https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/preprints/Uniform-Stability-of-the-Spherical-Laughlin-Gap-October-5-2026/uniform-stability-spherical-laughlin-gap.pdf; Apache License 2.0); Lean: https://github.com/openai/math/blob/adc7f1241b42e322a6451854ab7e4b4c146bf78a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive22.lean (declaration OAI.Laughlin.Certificate.four_body_22_positive)

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