OP6 — Structural Foundations of the Coherence–Gravity Framework

OP6 — Structural Foundations of the Coherence–Gravity Framework Anthony Dimbleby (2026) This paper establishes the structural foundations of the coherence–gravity framework developed across OP1–OP5. While the earlier papers introduced the statistical, variational, dissipative, and curvature components of the system, OP6 explains why the framework must take this form. It shows that the architecture of OP5 is not a modelling choice but a structural consequence of combining coherence, dissipation, and curvature in a single theoretical system. OP6 demonstrates three foundational results: 1. Irreducible Multi‑Sector Nature The statistical and variational coherence sectors cannot be merged into a single master variable without losing physical meaning. Attempts to reduce the system lead to sign ambiguities, singular behaviour, and the breakdown of the variational structure. The framework is therefore intrinsically multi‑sector. 2. Variational Core and Dissipative Shell The reversible part of the system arises cleanly from a coherence–gravity functional, while the dissipative part cannot be derived from any action principle. This establishes a structural split between a conservative variational core and a phenomenological dissipative shell. 3. Hybrid Conservation Pattern The variational sector obeys covariant conservation of stress–energy, while the dissipative sector exhibits monotone relaxation toward equilibrium. No global invariant unifies both behaviours. The system therefore combines conservation in one channel with irreversible decay in another. These results explain the internal logic of the coherence–gravity framework and clarify why the thermodynamic deviations explored in OP5 arise naturally from its structure. OP6 also discusses the implications of this architecture, including layered temporal behaviour, indirect coupling between dissipation and curvature, and the structural origin of measurable deviations in relaxation rates. This paper completes the theoretical phase of the programme and prepares the ground for a dedicated experimental analysis.