The Admissibility Frontier: Bounded Cumulative Inference, Indexical Reference, and the Structural Dependency Beneath Symbolic Persistence

Abstract This paper examines the boundary beyond the declared-regime core of the Identity–Persistence Program. The forcing theorem establishes that coherent identity-persistence claims require a Tier-1 structural regime; this paper asks what can be forced before such a regime is explicitly declared for bounded systems that preserve reference across memory, communication, compression, replay, audit, or other broken-thread recurrence. The unrestricted claim that all stable reference forces the full persistence stack is refuted by causal and indexical tracking. The paper therefore narrows the theorem class to bounded cumulative symbolic inference and subjects the resulting claim to adversarial analysis. It derives a forced admissibility kernel from boundedness and non-idleness, distinguishes that kernel from richer induced structure, and identifies the remaining frontier as a structured admissibility problem rather than a single undifferentiated dependency. The principal contribution is a closure map. Admissibility sufficient for bounded cumulative symbolic inference must be quotient-relative and drift-bounded; exact preservation is the minimal admissibility regime; conflict without declared governance forces partiality; and, once a finite conflict poset is fixed, lawful determinate resolutions form the lattice of refinements rather than an arbitrary rule. The paper leaves OPEN whether the invariant basis alone induces the relevant preservation relation or conflict poset, and whether metric, stochastic, nonstationary, or broader governance structures admit analogous closure.