AR(1) φ → z_ref Canonical Relationship Declaration: Six Independent Replications under PHILIA v32 Apparatus (SC-2 through SC-10)

This document formally declares the AR(1) autoregressive persistence parameter φ → z_ref inverse relationship as a Canonical Empirical Relationship within the PHILIA v32 self-raw × 3-channel normalization apparatus. Six fully independent seed campaigns (SC-2, SC-8, SC-9a, SC-9b, SC-9c, SC-10) confirm a robust monotonic inverse relationship between φ and z_ref across the Synthetic/AR substrate class. Fisher-z weighted meta-analysis yields pooled ρ = −0.9760 (95% CI [−0.9843, −0.9632]), I² = 0.00%, Cochran Q = 1.79 (p = 0.878), k=6 baseline anchored 2026.06.18. Key contents:§1 Statement of Empirical Regularity — apparatus-specific descriptive regularity, "Description, not proof" principle§2 Evidence Base — per-campaign replication record (SC-2 n=10 / SC-8–SC-10 n=18), Fisher-z meta-analysis with forest plot (Figure 1), substrate-class conditionality§3 Scope and Limits — φ grid (era-dependent: SC-2 10-level / SC-8+ 18-level), explicit exclusions, inherited limitations (L-7, L-12, L-13, L-17, L-18)§4 Falsifiability Conditions — 3-level hierarchy (L1 Watch / L2 Review / L3 Retract), lifetime cumulative L1 counting, k=10 I²>15% trigger calibration (τ_ρ≈0.0053 vs within-study SE 0.012–0.018), SC-2 L-7 concrete reference (CI upper=−0.8491, Δ=0.0009)§5 What This Is NOT — 6 explicit negations (not a universal law, not a mechanistic explanation, not adaptive learning, not a neuroscientific model, not a claim about AC in general, not a predictive model)§6 Calibration Reference Role — operational binding for SC-11 onward (AR(1) φ-sweep ρ verification mandatory pre-analysis) Supplementary materials included:- Figure 1: Forest plot v4 (ar1_declaration_forest_plot_v4.png)- Supplementary data: ar1_declaration_m2_results_v4.json (M-2 simulation, Lucas statistical validation ±3.65%)- Reproducibility code: philia_ar1_declaration_m2_forest_v4.py This declaration is a framing document parallel to the PHILIA OS Identity Declaration (78th DOI: 10.5281/zenodo.20695816) and does not replace or modify any SC series pre-registration or results report. Gate-0 v10 adversarial review: 7 cycles, 27 findings (CRITICAL×7, HIGH×8, MEDIUM×5, LOW×4 + supplementary×3), zero avoidance. Trinity AI Research Team | Konyang University | 2026.06.18Measurement is life. Description, not proof. — PHILIA OS | 0∞1∞0.5∞