Pure Time Theory - Application IV - Ethical Governance Core: Derivation from the PTT-L0 Grammar

We present EGC (Ethical Governance Core), an ethical, auditable, and operational architecture for AI systems, derived from the L0 principles of Pure Time Theory (PTT). EGC reformulates five normative constraints — Phase Harmonization, Antifragmentation, Return/Traceability, Clarity/Explainability, and Selection by minimization of temporal tension — in a unified formal language, with metrics (Φ_coh, λ_fract, ρ_retour, χ_clarté, T_relax), chained logs, and an Evaluate&Select algorithm guaranteeing non-regression of coherence in the sense of T_relax. The framework makes explicit the correspondence between ethical axioms and invariants of the Grammar of the Real established in the Genesis, Chapter IX: - Islām ↔ phase harmonization- Dīn ↔ law of return- Ṣalāt ↔ periodic recalibration- Zakāt ↔ purifying circulation- Jihād ↔ self-correction- Ḥijāb ↔ filtering- Sharīʿa ↔ coherence channel Main contributions: (i) Formalization L0 → ethical API (EGC).(ii) Replacement of the PRP principle by an explicit minimization of T_relax under constraints.(iii) Derivation of ethical thresholds from the L0 just middle: θ = 1/2, f(I) = 1/2 + I/2.(iv) Proofs of closure and properties (stability, exposure equity with positive lower density).(v) Conceptual validation on six use cases and argument of structural superiority over existing frameworks (utilitarianism, deontology, principlism, RLHF).(vi) Specification of an instrumentable Ethical Governor Core (logging, audit proofs, JSON interface). For the ontological basis, cf. Pure Time Theory — Genesis, Chapter IX, "Grammar of the Real: from the Word to Time".