A Unified Framework for Witness Cosmology: Information, Cosmology, and the Cosmological Constant (Version 3.0: Epistemological and Logical Audit)

Version 3.0 presents a comprehensive methodological, epistemological, and mathematical audit of the Witness Cosmology framework, establishing it as an explicitly axiomatic and conditionally deductive information-theoretic framework for the cosmological constant problem. Key Updates and Refinements in Version 3.0: Strict Epistemological Taxonomy: Implements a rigorous logical classification for every core statement: [A] Axioms (the 16 structural elements of the Witnessed Contract), [D] Definitions, [T] Theorems, [P] Postulates, [C] Conditional Consequences, and [O] Observational Predictions. Vacuum Equation of State vs. Covariant Conservation (Theorem 1): Formally decouples the vacuum-form stress-energy tensor T_µν^(info) = -ρ_Λ g_µν (which dictates p = -ρ ⟹ w_info = -1) from local covariant conservation ∇_µ T^(µν) = 0 (which establishes spatial and temporal constancy ∂_µ ρ_Λ = 0). Cosmological Scaling Consistency (Theorem 2): Defines β_scale(λ) = 4λ as a cosmic-scale consistency function, explicitly distinguishing it from standard quantum-field-theoretic (QFT) renormalization group beta functions. Scale Decoupling & Structural Count (Postulate 2): Evaluates the numerical consistency of η, demonstrating that the global holographic count N_max ~ 10^122 yields N_max^(-1/4) ~ 10^(-31) ≠ 0.012. Version 3.0 decouples the global capacity N_max from the local effective sector by introducing an independent structural count postulate N_* ≈ 4.82 × 10^7 for η ≈ 0.012. Quantum Error Correction Architecture (Postulate 1): Posits the [[4,1,2]] QEC code structure and code distance d=2 as explicit structural postulates, yielding a 12.2% relative discrepancy with observational reference scales. Observational Predictions & Open Research Agenda: Provides testable effective-sector predictions w_eff(z) for DESI and Euclid surveys, present witness density target n_w^0 ≈ 2.3 × 10^13 m^(-3), and an information-sector relic mass target m ∈ [0.05, 0.5] meV, accompanied by a 5-point Research Agenda for future microscopic derivations.