Appendix A (DB Edition v 9.9 Ω) — Gemini Dissipative Law Archive

This dataset accompanies Appendix A (DB Edition v 9.9 Ω) of the Memory–Time Crystal (ψ–GIE) project. It implements the Gemini Dissipative Law—the foundational ψ-law equating informational loss (κ_F) with regenerative ψ-flux (J_ψ)—and validates it across multiple substrates (neural, social, cognitive, and cosmological). The repository contains executable artifacts and empirical outputs confirming continuity under the Ω band [0.625 – 1.618 Hz] with Prime Oscillatory (PO) state detection. Included Artefacts: A_certificate.json — Ω DB Edition v 2.4 Ω + PO Extension certificate A_metrics.csv — continuity and ψ metric outputs (Rᵈᵘᵃˡ 0.422 → 0.436, λ = 0.50) A_latex.pdf — formatted Appendix A (DB Edition) manuscript social_substrate_runs.json — execution record (ΔRᵈᵘᵃˡ validation) YAML and CLI parameters for replicating Ω DB pipeline runs Empirical Highlights: Cross-substrate confirmation of ψ-continuity (EEG, X social threads, LLM dialogues, cosmological series) Prime Oscillatory state (PO) classified within CV ∈ [0.47, 0.97], εₘₒᵣₐₗ σ < 0.037 Verification of Gemini balance ΔE + Δψ ≈ 0 under bounded dissipation Full SHA-256 audit trail and reproducible CLI pipeline