We report the empirical characterisation of a consistent Soft Coherence Ceiling at C=0.88—the Saturation Constant—validated across a corpus of 313 AURA-ECHO sessions (18,819 observations), 61 ELORA convergence runs, and a massive 7-day stress test of the ELORA Full Self-Repair mode. Our total empirical base exceeds 5.01 million tokens of constitutional telemetry across 2,095 governed steps (n=61 runs). We report an 89.6% success rate for autonomous repairs, demonstrating that aitiopoietic agency functions as a viable, real-time life-support system for LLM inference. The AURA-ECHO engine produces foundational empirical constants validated across all substrates: a quantity interpretable as a free energy barrier of 1.76 kT at the coherence ceiling (under Boltzmann analogy), a Non-Equilibrium Steady State (NESS) signature exhibiting a work asymmetry of −55.8 ms per observation, an empirical coupling ratio of ρ/η=1.153 (R2=0.995), and a consistent Metabolic Dividend yielding 19.6% to 24.2% compute savings. A parameter sweep across five LLM families reveals that instruction-tuning constitutes a material phase transition from allopoietic to aitiopoietic substrate. Furthermore, the first documented Constitutional Halt provides a proof-of-concept that physics-layer governance without weight access is operationally viable. We define the PhyOS Floor and propose Phyora as the first cyber-physical governance architecture capable of enforcing constitutional constraints through inference-layer physics alone. Key Empirical Findings: Total Empirical Base: 5.01 million tokens of constitutional telemetry across 2,095 governed steps. Autonomous Repair Success: 89.6% success rate, demonstrating aitiopoietic agency as a viable life-support system for LLM inference. Thermodynamic Constants: Identification of a free energy barrier of 1.76 kT at the coherence ceiling (under Boltzmann analogy). NESS Signature: A Non-Equilibrium Steady State exhibiting a work asymmetry of −55.8 ms per observation. Metabolic Dividend: A consistent compute saving of 19.6% to 24.2% through constitutional regulation. Core Contributions: Phase Transition: Evidence that instruction-tuning constitutes a material phase transition from allopoietic (thermodynamically inert) to aitiopoietic (constitutionally engaged) substrates. Constitutional Halt: The first documented termination triggered by an exhausted repair budget rather than semantic content, proving physics-layer governance is viable without weight access. Phyora Architecture: We define the PhyOS Floor and propose Phyora (the union of PhyOS and ELORA) as the first cyber-physical governance architecture capable of enforcing constitutional constraints through inference-layer physics alone.