The Law of Laws: Canonical Fixed-Point Representation of Persistent Systems

All figures and results in this preprint are reproducible from a frozen software artifact that ships with the engine and a domain test harness. The artifact includes the canonical engine (cce_universal.py) implementing the factorization F=R∘EF=R∘ EF=R∘E with intrinsic contraction/“healing” estimators, plus executable tests covering conservative physics, known-damping recovery, logistic-map bifurcation, time-reversal checks, noise–signal gradients, and real EEG pipelines. cce_universal stress_tests Reproducibility ledger Commit: 5de157b73409790b48e31972eaf3caf04dfe4c9a (tag v1.0.0) Contents: engine, scripted stress tests, and domain harness (see “Files included”) Figures are regenerated by the included scripts; parameterization and SHA-256 checksums are provided in the repository. The preprint’s “Reproducibility and Audit Ledger” section explains the invariance and falsification gates and how to re-run them end-to-end. Files included (core) Engine: cce_universal.py (theory-compliant build; projection–contraction pipeline, intrinsic η/γ estimators). cce_universal Stress tests: stress_tests.py (Hamiltonian λ≈1, known γ recovery, logistic chaos boundary, time-reversal, noise–signal gradient). stress_tests Domain harness: test_nine_laws.py, test_real_data.py, test_neuro_eeg.py (panel across physical, stochastic, quantum, biological regimes). Supporting data/manifests, figures, and SHA-256 ledger. How to reproduce (short) Create a fresh Python 3 environment and install requirements from the repo. Run python stress_tests.py to execute falsification and validation panels; inspect emitted JSON/figures. stress_tests For EEG and other domains, run the corresponding test_* harnesses to regenerate tables and figures. ScopeThe software verifies the necessity/sufficiency structure F=R∘EF=R∘ EF=R∘E, recovers intrinsic contraction ηηη (and γ=−log⁡ηγ=-logηγ=−logη), and validates invariances (averaging, duality, substrate) across domains.