We present the Special Theory of Curvature (SC): five foundational canonical equations forming a compact kernel for the ACORN (Alternating Curvature Ontology of Nature) framework. The canon consists of coupled curvature dynamics and closure constraints governing two curvature participation channels, mNE(T) and meq(T), evolving over an invariant internal parameter T. Together these canonicals generate quantised loop closure, emergent proper time, relativistic invariance (within the admissible stable-mode domain), and a restricted stable particle spine (electron, proton, and α), while naturally extending toward bulk matter behaviour, defect-like weakly coupled modes (neutrino-sector candidates), electromagnetically silent closed states (dark-matter-like signatures), and quantum-mechanical projection effects. We provide an intermediate-accessible presentation of the five canonicals, an admissible hyperbolic solution family, and a concise consequence summary library. A full 5 × 5 matrix appendix is included to make explicit the higher-dimensional geometric setting. Although ACORN is fundamentally five-dimensional, it is not conceptually difficult: the additional curvature-time channel is hidden from direct observation yet remains dynamically active as a curvature exchange and accounting engine. In this view, a universe describedby only two curvature channels, one invariant closure-time parameter, and two universal constants (h and c) provides a minimal starting point capable of recovering large domains of established physics. The SC kernel presented here also motivates a later extension to a General Theory of Curvature (GC) with additional geometric scope.
Morrow et al. (2026) studied this question.