Capacity Overflow, Effective Stochasticity, and Phase-B Invariants: Critical Deficit, Markov Closure, and Invariant Selection under Finite Projection

FDS-T1 defines finite-observer distinguishability budgets. FDS-O1 turns those budgets into measurement capacity, and FDS-O2 turns finite record update into register time. This paper(FDS-T3) abstracts the common mechanism: capacity overflow. When task-relevant distinction demand exceeds accessible capacity, a finite observer or finite system cannot track all distinctions needed for full-fidelity prediction. The missing distinctions re-enter the accessible description as coarse-graining, effective stochasticity, hysteresis, false invariants, externalization demand, or failure. This paper formulates effective stochasticity as structured dynamics viewed through non-injective finite projection. Even when dynamics on a larger state space is deterministic, the induced dynamics on the accessible record space can be stochastic because multiple inaccessible states map to the same visible state while having different successors. This version strengthens the phase-transition layer: it defines the overflow deficit, predictive susceptibility, effective Markovian closure error, informational hysteresis, observer hierarchy, and a maintenance-cost selection score for Phase-B invariants. Phase-B invariants are coarse variables that remain cheap to update, slow to forget, and approximately Markovian after microstate tracking fails. Deterministic simulations illustrate projection-induced stochastic kernels, critical deficit susceptibility, Markov closure, invariant selection, irrecoverable post-overflow loss, capacity-relative stochasticity, Phase-A/Phase-B transition, and semantic drift in finite-context AI-like systems. The paper does not claim that all randomness is epistemic, that quantum randomness is derived, that topology is required for all persistence, or that fundamental conservation laws are reduced to observer capacity. Its narrower contribution is a finite-capacity bridge model: effective stochasticity is the shadow cast by finite projection, and law-like structure is the residue of distinctions that remain cheap, predictive, and slow to forget under overflow.