Branched Flow as a Model for History Selection in Wave-Dominated Systems

Branched Flow as a Model for History Selection in Wave-Dominated Systems

This work proposes branched flow—the spontaneous formation of filamentary intensity channels in weakly disordered media—as a concrete physical model for history selection in wave-dominated systems. Unlike interpretations requiring observer-induced collapse or infinite branch proliferation, we demonstrate that outcome selection arises naturally from transport geometry: flux concentrates into a sparse set of "closure-preserving" channels that remain structurally stable under coarse-grained evolution.

The paper formalizes this perspective via an operational Closure Criterion, defining a "history" as a transport channel that resists geometric dispersion over time. This framework explains how effective irreversibility and single-threaded macroscopic reality emerge from time-reversible wave mechanics without invoking fundamental dissipation or stochastic reduction.

Appendix Part II: Closure-Locked Recursion
This version includes an expanded appendix deriving the Closure-Locked Recursion Threshold (Θ_A). By synthesizing the transport stability of branched flow with the invariant geometry of CPT-Coherence Theory (specifically the Unified Recursion Constant, Δτ_R), we define a physical boundary condition for "awareness". In this model, awareness is identified as a phase transition where a selected transport channel becomes self-sustaining against recursive dispersion.

Key Concepts:

• Branched Flow: The mechanism of geometric flux concentration in weak disorder.
• Closure Criterion: An operational test for dynamical viability and history persistence.
• Closure-Locked Recursion: The coupled threshold (Θ_A) linking transport stability to recursive depth.
• Unified Recursion Constant (Δτ_R): The structural invariant governing the stability of recursive states.

Notes: Research conducted under the MASb / Minima Studios Research and Engineering Division (2023-2025).