Closure Theory: A Geometric Recovery Framework for Relativity, Electromagnetism, Constants, and Matter

Closure Theory (CT), developed from the earlier ACORN framework, investigates whether major sectors of known physics may arise from a comparatively compact set of invariant geometric principles organised around closure, recurrence, propagation, projection, and admissibility. The framework extends the geometric programme of relativity by treating mass, charge, quantisation, and matter structure as possible manifestations of recurrence-supported curvature closure rather than as fundamentally disconnected physical primitives. Within the present formulation, the framework develops: recovery of relativistic invariant structure, geometric embedding of gravitation, Maxwellian propagation structure, recurrence-supported matter organisation, atomic recurrence hierarchy, conservation laws, and projection-based interpretations of quantum behaviour. Several non-trivial numerical structures also emerge, including: a geometric route to the fine-structure constant, recurrence-supported proton–electron hierarchy, and defect structures associated with imperfect closure compatibility. The work is intentionally conservative in tone. Closure Theory does not seek to discard successful existing theories, but rather investigates whether special relativity, general relativity, electromagnetism, recurrence quantisation, and matter structure may represent different projection sectors of a common invariant closure geometry. The paper further identifies several open mathematical programmes, including: tensorial reduction to general relativity, electromagnetic tensor recovery, closure spectral classification, and projection-theoretic approaches to quantum behaviour. Closure Theory is therefore presented not as a completed final theory, but as a structured geometric recovery framework intended for further mathematical and experimental investigation.