Operational Coherence as a Covariant Entropy Constraint

I propose a covariant, information-theoretic constraint on physically realizable cosmologies and spacetimes: Operational Coherence. The core claim is that while formal (global) information may be unbounded, operationally accessible and distinguishable information available to any single observer must be finite. I formalize this as the Operational Coherence Bound (OCB), a covariant entropy bound defined over causal diamonds of timelike worldlines. I show that OCB implies the Bousso covariant entropy bound on all operationally realizable lightsheets, while strictly strengthening it by constraining the cumulative entropy accessible to an observer across all time. I demonstrate this strengthening through explicit calculations in de Sitter space and provide a quantitative comparison table distinguishing OCB from existing entropy bounds. I then stress-test OCB against ΛCDM, inflationary cosmology, holography (including AdS/CFT), and exotic spacetime constructions—including wormholes, negative-energy configurations, closed timelike curves, baby universes, and ER=EPR scenarios. All known physically viable constructions either satisfy OCB or invoke mechanisms (horizons, backreaction, decoherence, or indistinguishability) that dynamically enforce it. I argue that operational coherence is not an additional law, but a consistency condition that emerges as the fixed point of an iterative interplay between quantum distinguishability and gravitational backreaction. This reframes cosmological horizons and accelerated expansion as failure-mode safeguards rather than incidental features. Summary of Revisions to "Operational Coherence as a Covariant Entropy Constraint" Section III.A (Definition of operational entropy)Reviewer concern: Von Neumann entropy is UV-divergent in continuum QFT.Change: Replaced S_vN(ρ_Σ) with vacuum-subtracted relative entropy S(ρ_Σ ‖ ρ_vac). This ensures S_op is manifestly finite, positive, and regulator-independent. Sections III.B / IV.A (Threshold scaling)Reviewer concern: Threshold ambiguity breaks strict equality to A/4Għ.Change: Introduced κ(ε) scaling factor; bound now reads S_op ≤ κ(ε) A_max/4Għ, with κ(ε) → 1 in the macroscopic/semiclassical limit. Section V.C (Relation to modern bounds)Reviewer concern: Missing context vs. Generalized Bousso Bound / Quantum Focusing Conjecture.Change: Added explicit comparison subsection clarifying that OCB is a global/cumulative consistency filter per observer, complementing the local QFC constraint. Section V.D (Proof of Operational Coherence Theorem)Reviewer concern: Proof conflates measurement energy with field stress-energy sourcing Raychaudhuri.Change: Proof now sources Raychaudhuri with inherent ⟨T_ab⟩_field of distinguishable quantum states, not observer measurement costs. Section VI.B (FRW redshifting photons)Reviewer concern: Hand-wavy convergence claim for infinite thermal bath.Change: Added explicit integral S_op(t) ∼ ∫ d³k n(k,t) χ(k,t) over redshifting thermal spectrum; showed exponential suppression guarantees convergence. Section VI.C (Eternal inflation)Reviewer concern: Circular reasoning; lacks dynamical mechanism.Change: Reframed as "selection principle on observer embeddings"; clarified OCB filters realizable worldlines within infinite pockets, does not dynamically truncate spacetime. Section VIII.A / Appendix B.1 (Entropy drizzle counterexample)Reviewer concern: Ad hoc 1/n² energy scaling; ignores IR divergences.Change: Replaced arbitrary series with convergence grounded in Quantum Energy Inequalities + finite detector resolution ΔE_min + soft theorem regularization.