The Minimal Explanatory Core: Structural Limits on Explanation Under Physical Admissibility

This work presents a constraint-driven investigation into the structural limits of scientific explanation. Rather than assuming explanatory principles such as unbounded integration, global accessibility, transparent self-modeling, or arbitrary precision, we treat explanatory assumptions as mutable dynamical variables subject only to irreducible physical and informational constraints. Using large-scale ensemble-based computational exploration under finite energy dissipation, irreducible noise, information conservation, causal coherence, signal interference, and finite memory realization, we demonstrate that most commonly assumed explanatory ideals are jointly inadmissible. When enforced, they undergo ordered, spontaneous collapse driven by self-consistency pressure rather than external selection. Crucially, when all explanatory assumptions are removed entirely and only minimal constraints are enforced, the system does not devolve into indeterminacy. Instead, it converges reproducibly to a unique, stable explanatory structure characterized by bounded complexity, finite information flow, constrained causal density, partial self-similarity, and strictly limited accessibility. Topology variance across independent ensemble runs is effectively zero, indicating structural inevitability rather than contingent stabilization. We formalize this result as the Minimal Explanatory Core Theorem, establishing that explanation itself occupies a constrained physical regime. Any attempt to exceed this regime by enforcing additional explanatory assumptions necessarily destabilizes and collapses into inadmissibility, while systems lacking this structure fail to sustain explanatory coherence altogether. These findings reframe explanation not as an arbitrarily extensible ideal, but as a dynamically selected structure governed by intrinsic limits of physical admissibility. Matter, laws, intelligence, and consciousness are interpreted as emergent stabilizations of this minimal explanatory core rather than fundamental primitives.