OAI/Combinatorics/HoneycombChords/BridgeLaplace.lean

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4 declarations, 0 contain sorry, 0 declared as axioms

Height Laplace estimates for critical strict bridges

Formalized from Critical honeycomb chords with prescribed boundary endpoints (OpenAI, September 26, 2026).

  1. def OAI.CriticalHoneycomb.bridgeLaplace line 19

    Source documentation

    The height Laplace transform of the strict bridge mass.

    noncomputable def bridgeLaplace (s : ℝ) : ℝ :=
    …
  2. lemma OAI.CriticalHoneycomb.bridgeMass_toReal_bounds line 22
  3. lemma OAI.CriticalHoneycomb.bridgeLaplace_summable line 33
  4. theorem OAI.CriticalHoneycomb.bridgeLaplaceEstimate line 43

    Source documentation

    The height Laplace transform is comparable to s^(-3/4) for 0 < s ≤ 1.

    theorem bridgeLaplaceEstimate : ∃ c C : ℝ, 0<c ∧ 0<C ∧ ∀ s : ℝ, 0<s → s≤1 →
        c*s^(-(3:ℝ)/4) ≤ bridgeLaplace s ∧ bridgeLaplace s ≤ C*s^(-(3:ℝ)/4) := by
    …

    Mentions: OAI.CriticalHoneycomb.bridgeLaplace