Synthetic Falsifier Tests for the Laws of Persistence and Coherence (Sznajd-like) v1.2

This emonstrates that the triadic conservation framework can reliably distinguish conserving from non-conserving dynamics across spatial, oscillatory, and chaotic regimes (R² ≈ 0.80 in-band, collapsing to ~0.05 in nulls and controls), providing a rigorous, falsifiable proof-of-concept prior to empirical testing in natural systems.”xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxv1.2 extends the earlier Ising–Kuramoto–Lorenz suite (v1.1) with a more rigorous, multi-seed replication and additional falsification checks:• 6-seed replication for statistical robustness  • Shuffle nulls (all systems) and phase-randomized surrogate nulls (Kuramoto, Lorenz)  • Parameter sweeps (Ising → T, Kuramoto → K, Lorenz → ρ)  • Window-size sensitivity analysis (stability check of R² plateaus)  • Residual diagnostics (Durbin–Watson, Ljung–Box, QQ plots)  • Additive-law control (Sznajd-like): multiplicative form fails (low R²); additive fit succeeds and correctly recovers α, β.  Interpretation:  Across Ising, Kuramoto, and Lorenz regimes, the proportional law y = dA ≈ −(dB + dC) remains valid in-band with slope ≈ 1 (95 % CI includes 1) and R² ≈ 0.8, while both nulls collapse R² → 0.05–0.1. The additive control confirms falsifiability by rejecting the multiplicative model and reproducing the expected coefficients of the additive ground-truth system.Included files  – Ising_synthetic.csv  – Kuramoto_synthetic.csv  – Lorenz_synthetic.csv  – Sznajd_additive_control.csv  – SUMMARY_metrics.csv  – diagnostics/*.png  – README.txt  This v1.2 record supersedes v1.1 by adding null controls, additive validation, and multi-seed replication.  It serves as the final synthetic proof-of-principle prior to empirical Phase-2 tests.xxxxxxxxChange log (v1.2 → v1.1): Adds shuffle + phase-randomized nulls, introduces multi-seed averaging, includes additive-law (Sznajd) falsifier, and expands diagnostics (parameter sweeps, window-sensitivity, residual checks). Strengthens reproducibility and falsifiability of the proportional conservation result (slope ≈ 1, R² ≈ 0.8 ± 0.05).