Capacity Overflow, Effective Stochasticity, and Phase-B Invariants: Critical Deficit, Markov Closure, and Invariant Selection under Finite Projection
Yining Wu · PhilPapers (PhilPapers Foundation) · 2026
Official website: distinctiontheory.orgPublic portal for the start guide, papers, claim status, failure registry, prior-art boundary, and citation resources. Canonical GitHub repository:https://github.com/yiningwu-research/Distinction-Theory FDS-T3 develops a finite-capacity bridge model for effective stochasticity under capacity overflow. Building on FDS-T1, FDS-O1, and FDS-O2, this paper abstracts a common mechanism: when task-relevant distinction demand exceeds accessible capacity, a finite observer or finite system can no longer track all distinctions required for full-fidelity prediction, control, or persistence. The central thesis is that effective stochasticity is structured dynamics viewed after finite projection. Even when dynamics on a larger state space is deterministic, the induced dynamics on the accessible record space can become stochastic because multiple inaccessible states map to the same visible state while having different successors. The missing distinctions re-enter the accessible description as coarse-graining, stochastic kernels, hysteresis, false invariants, externalization demand, semantic drift, or failure. This version strengthens the phase-transition layer of the theory. It defines the T3 overflow deficit, predictive susceptibility, transition-entropy susceptibility, non-injective projection loss, Markov closure error, informational hysteresis, observer hierarchy, and a maintenance-cost selection score for Phase-B invariants. Phase-B invariants are modeled as coarse variables that remain cheap to update, slow to forget, and approximately Markovian after microstate tracking fails. The paper also introduces a selection principle for post-overflow structure: law-like variables that survive finite projection are not necessarily the most detailed variables, but those with favorable ratios of predictive persistence to update cost, maintenance cost, and residual memory burden. In this sense, stable law-like structure is treated as the residue of distinctions that remain cheap, predictive, and slow to forget under overflow. The accompanying replication package includes deterministic synthetic simulations, figures, CSV outputs, LaTeX source, and Python code. The simulations illustrate projection-induced stochastic kernels, critical capacity deficit and predictive susceptibility, Markov closure and invariant selection, informational hysteresis after temporary overload, observer-capacity-relative stochasticity, Phase-A to Phase-B transition, and semantic drift in finite-context AI-like systems. Scope and boundary. This paper does not claim that all randomness is epistemic, that quantum randomness is derived, that stochastic models are unnecessary, that topology is required for all persistence, or that fundamental conservation laws are reduced to observer capacity. Its narrower contribution is an operational finite-capacity model: effective stochasticity can arise when finite non-injective projection hides distinctions that are dynamically relevant to prediction.