PK-Trinity: An Empirical Discrimination Framework Built on the Persistence Kernel

PK-Trinity is a deterministic experimental framework built on top of the Persistence Kernel, a minimal structural substrate governing identity, eliminative constraint, admissibility, exhaustion, and collapse. The Persistence Kernel itself is a non-teleological executable reference: it encodes no goals, utilities, rewards, probabilities, optimization criteria, or observer-relative primitives, and exists solely to demonstrate that its invariants admit mechanical realization. PK-Trinity does not modify, extend, or reinterpret those kernel invariants. Instead, it treats the kernel as a fixed reference substrate and constructs an explicit derivative experimental regime around it. The purpose of PK-Trinity is empirical discrimination. It instruments kernel execution with: explicit separation between true admissibility exhaustion and proposal starvation, a structural accumulation parameter (λ) that increments only under irreversible shrinkage of admissible continuation structure and carries explicit shrink witnesses, append-only, irreversible elimination histories, deterministic, replay-verified execution with hash-chained traces, and preregistered falsification criteria. PK-Trinity implements a controlled experimental protocol in which constraint geometry is varied while perturbation schedules and proposal grammars are held fixed. The primary empirical question investigated is whether collapse statistics (e.g., time-to-collapse, λ-at-collapse, elimination locality) track constraint topology rather than perturbation magnitude. All experiments are deterministic, auditable, and reproducible, and all empirical claims are explicitly falsifiable. This framework is not a controller, optimizer, learning system, or predictive dynamics model. It introduces no intelligence, agency, intention, or performance objectives. Its role is to provide an auditable infrastructure for testing whether the structural consequences of the Persistence Kernel survive instantiation in concrete regimes without importing hidden teleology. PK-Trinity is released as an experimental derivative system. The canonical definition and reference implementation of the Persistence Kernel remain unchanged and are cited separately.