Hyperbolic–Liquid
Fractal Buoy Formalism

Reproducible finite numerical witness for the Poincaré metric, hyperbolic growth, synthetic fractal scaling, Kuramoto coherence, buoy residual, contraction bound, and Weyl spectral stability.

First-principles spine

dκ(z,w)=2/κ artanh |(z−w)/(1−z̄w)|
Vκ(r)=2π(cosh(κr)−1)/κ²
A(ℓ)=Cℓ^α  ⇔  log A=log C+α log ℓ
R=|(1/N)Σ exp(iθj)|,  0≤R≤1
ε=sup ||Φ∘F−F̂∘Φ||
eₙ≤ε(1−Lⁿ)/(1−L), 0≤L<1
maxᵢ|λᵢ(A+E)−λᵢ(A)|≤||E||₂

Reproduction

The September 30 reproduction preserves the historical HLFB-IND-20260730 record and adds an immutable executable witness. It is calibration, not a replacement of the July run.

MC-HLFB-RUN-B-REPRO-20260930-001 · PASS_WITH_CALIBRATION

Evidence boundary

Finite typed mathematical and numerical witness only. A finite buoy residual and finite contraction bound do not establish high-fidelity equivalence. No universal physical, consciousness, or propulsion identification is certified.