A Geometric Companion to Stochastic Rupture: Fisher Geometry, the Flash Map, the Born Rule, and the Protection of Lorentz Symmetry

GUILHERME ZAMBUZI

Published Jul 10, 2026• 0 citations

Abstract

This companion collects results of the Stochastic Rupture (SR) framework that are absent from the main paper. Its organising claim is that a single geometric object—the Fisher–Rao metric, unique by Chentsov’s theorem—supplies the pruning rate, the noise, and the barrier of the collapse sector, leaving that sector with no free choice of its own. We derive rather than posit. The barrier V = γ0/(1−χ) is the Fisher transport of the Casini relative entropy, which fixes the inverse-square exponent as the product of a logarithmic divergence and the Chentsov metric; the noise temperature is Teff = ℏγ0/kB, saturating the Feller condition as an identity. We construct the flash map, identifying pruning events with Wright–Fisher fixations: a martingale argument gives P(k) = |ak|², supplying the branch→effect map that Busch’s theorem requires, so that Born becomes a theorem conditional on one hypothesis-and Born exactness becomes equivalent to neutrality of the race, hence falsifiable. That hypothesis, that the quantum phase is the tangent orientation, is promoted to an elimination theorem: of the four compact angular variables the substrate possesses, Wallstrom’s condition leaves exactly one, with Poincar´e–Hopf supplying the integer winding. On the field-theoretic side we concede that friction is a relevant operator and show its coefficient is nevertheless fixed: multiplicative noise vanishes in vacuum, leaving Γ0 = Λ, so the wave regime (z = 1) holds for all observable physics and diffusive scaling is confined to super-Hubble scales. Transverse traceless gravitons preserve areas at linear order and do not inherit the friction; we accordingly retract an earlier gravitational-wave damping estimate and replace it with a polarisation-selective prediction. The MSRJD action, having no free choices, selects Itˆo by covariance and causality; its quantum lift is the Drude–Lorentz bath, satisfying KMS with analyticity strip 1/γ0 and saturating both the Planckian dissipation and Maldacena-Shenker-Stanford chaos bounds. Throughout, the epistemic status of each claim-derived, assumed, or open-is stated in the text. Two founding premises remain declared rather than derived: the master equation itself, and relational parsimony. Results here are internally verified, symbolically or numerically; they have not been subjected to independent review, which we invite.

DOI: 10.5281/zenodo.21297786

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