Stochastic Rupture as an Information-Bounded Mechanism for Objective Wave-Function Collapse: Field Dynamics, Trigger Regime, and the Arrow of Time

Stochastic Rupture (SR) proposes that objective wavefunction collapse is triggered when the local von Neumann entropy saturates a fraction η of the holographic Bousso bound. This version (v8) substantially advances the mathematical foundations of the framework through four new derivations. (1) Fisher Information Action. The spatial coupling in the SR field equation — previously an ad-hoc assumption — is derived from a Fisher Information Action over the network transition probabilities. The kinetic term 12 g µν∂µχ ∂νχ emerges from contracting the Fisher tensor Iµν = β 2∂µχ ∂νχ with the second-moment tensor Qµν; the β-factors cancel exactly, yielding a universal (scale-independent) kinetic term. Newton’s law follows as the geodesic of the Fisher metric, without postulating E = mΓ. (2) Dyson Brownian Motion and the holographic UV fixed point. The SR spectral dynamics is shown, via Itˆo calculus, to be exactly a Dyson BrownianMotion: the network noise generates eigenvalue repulsion 2Γζ/(λk − λj ) at secondorder. The stationary distribution satisfies a Dyson singular integral equation. Its explicit solution gives spectral dimension ds ≈ 2 robustly across mappings — the holographic dimension, and the known ultraviolet fixed point of Asymptotic Safety and CDT. Classical 4D spacetime is then an infrared phenomenon requiring a dimensional flow ds : 2 → 4, whose RG derivation is open.(3) Thermodynamic cycle: Schr¨odinger complements pruning. Numerical experiments confirm that pruning alone fragments the network (ds → 0).The full SR dynamics requires a restoration term: pruning generates Unruh heat that exits as the gravitational field, cooling the region; Schr¨odinger evolution then restores connections when χ < η. The complete cycle drives ds → 3–4. 1 (4) Tomita-Takesaki foundation. The Casini relative entropy anchor for η is extended beyond the Gaussian approximation via the Tomita-Takesaki modular operator K = − log ∆D, which is well-defined for arbitrary quantum states.The framework has two logically independent sectors. The collapse sector (SR mechanism, GHZ/Bell separation, η calibration) is self-contained and makes falsifiable predictions independent of the emergent geometry. The geometric sector (gravity, Einstein equations) is conditional on a dimensional flow: the SR saddle point gives the ultraviolet fixed point ds ≈ 2 (the holographic dimension, also the Asymptotic Safety and CDT UV value), and classical 4D spacetime must emerge in the infrared via a flow ds : 2 → 4. We are explicit throughout about which results belong to which sector.The framework makes fourteen falsifiable predictions, including a GW dispersion vg ≈ 1 + 3 2 αk2testable with LISA, a collapse time ratio τBell | τGHZ ∼ N1–2 testable on NISQ processors, and gravitational corrections to the Born rule near black hole horizons.