OP5 — Dissipation and the Unified Coherence Framework in Curved Spacetime

OP5 — Dissipation and the Unified Coherence Framework in Curved Spacetime develops the next stage of the Coherence‑Time programme by unifying statistical coherence, variational coherence, dissipation, and gravitational coupling within a single phenomenological framework. Building on OP1–OP4, this paper introduces a three‑variable architecture \((\eta, C, \phi)\) and a phenomenological mapping \(C = \alpha \phi^2\) that links the irreversible statistical sector to the reversible variational sector. A dissipative evolution equation for \(C\) is formulated in curved spacetime, and this induces a well‑defined dissipative correction to the evolution of the variational field \(\phi\) while preserving its action‑derived dynamics and stress‑energy tensor. The resulting chain, dissipation → C → φ → T\{\mu\nu} → G\{\mu\nu}, shows how dissipation can influence curvature indirectly, without modifying Einstein’s equations or the variational structure established in OP4. OP5 assembles these components into a unified dynamical system describing coherence in curved spacetime under both reversible and irreversible processes. The framework is intentionally minimal and phenomenological, serving as a conceptual and mathematical bridge toward the Unified Coherence Equation to be developed in OP6.