OAI/Combinatorics/HoneycombChords/BridgeLaplace.lean
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).
- def
OAI.CriticalHoneycomb.bridgeLaplaceline 19Source documentation
The height Laplace transform of the strict bridge mass.
noncomputable def bridgeLaplace (s : ℝ) : ℝ := …
- lemma
OAI.CriticalHoneycomb.bridgeMass_toReal_boundsline 22 - lemma
OAI.CriticalHoneycomb.bridgeLaplace_summableline 33 - theorem
OAI.CriticalHoneycomb.bridgeLaplaceEstimateline 43Source documentation
The height Laplace transform is comparable to
s^(-3/4)for0 < 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