Bad Geometry Must Resolve: A Solver-Based Falsification Framework for Near-Closure Astrophysical Phenomena

This paper presents a solver-based, falsification-oriented framework for evaluating claims related to primordial black holes (PBHs) and other near-closure astrophysical phenomena. Rather than proposing new physical mechanisms or asserting the existence of PBHs, the work addresses a persistent methodological problem: many PBH-related claims conflate distinct physical regimes—near-closure compression, horizon-level causal structure, and core-level breakdown of spacetime description—rendering such claims ill-posed and resistant to empirical resolution. The framework enforces admissibility across three independent channels: (i) linguistic typing (explicit separation of dynamical “verbs” from static or non-temporal domains), (ii) mathematical consistency under energy-first (eBase) and proper-time accounting, and (iii) geometric closure analysis. When these constraints are applied, all admissible interpretations collapse into exactly three mutually exclusive resolution paths: successful geometric closure into a black hole, verb-dominant dynamical release (“flare”) without nucleosynthesis, or transient near-closure configurations often labeled as PBHs, which are shown to be pre-resolution states rather than stable objects. A central result of the framework is that permanently ill-posed (“bad”) geometry cannot persist as a terminal state: unresolved structure necessarily forces either closure or release. The paper formalizes this conclusion through explicit admissibility postulates and a finite falsification matrix grounded in persistent observables, including heavy-element abundance patterns, isotopic proper-time signatures, and multi-messenger emission characteristics. The work is intended as a methodology and hypothesis-structuring contribution rather than a discovery paper. It demonstrates how solver discipline can convert ambiguous or rhetorically framed astrophysical claims into well-posed, decidable questions, and it is designed to be compatible with standard general relativity, semiclassical gravity, and existing PBH phenomenology without assuming any particular resolution of the black-hole information problem.