Code

Summary

The framework is implemented as a small Python package at validation/code/. Domain-agnostic by construction: no if domain == ... branches anywhere; all tools take abstract \((t, \Phi)\) pairs. The package adheres strictly to the five Laws.

Repository layout

uniformity/
├── README.md
├── LICENSE
├── framework/                 # the formal apparatus
│   ├── laws/laws.md           # Five Laws
│   ├── characters/            # symbology, dual representation
│   ├── foundations/           # Volume 0 (T1–T3), I (T4–T9), II (T10–T13)
│   ├── formula/formulas.md    # single-source formula reference
│   └── metrics/               # standardised measurement contract
│
├── validation/                # empirical evidence
│   ├── catalogue.md           # 30 strong + 3 partial + 3 honest-negative
│   ├── instances.md           # framework-native readings
│   ├── announcement.md        # memoir-style introduction
│   └── code/                  # the reference implementation
│       ├── dual.py            # forward-mode automatic differentiation
│       ├── derivatives.py     # ρ extraction (FD, wavelet, GP, EMD)
│       ├── regression.py      # 𝓑: polyfit, GLS-AR(1), Bayesian
│       ├── regimes.py         # PELT change-point detection
│       ├── decomposition.py   # 𝓟: spectral primitive
│       └── tests/             # regression test suite
│
├── domains/                   # 15 domains
│   ├── fluid-dynamics/, particle-physics/, gravitational-waves/, ...
│   └── (each: README.md, docs/, experiments/, data/, results/)
│
├── applications/              # shadow PDE solvers
│   ├── ns_galerkin.py, burgers_1d.py, mhd.py, sabra.py, edqnm.py
│   ├── klein_gordon.py, klein_gordon_nonlinear.py, nls_1d.py
│   ├── maxwell_1d.py, les_dynamic.py, les_nonlinear_sgs.py, les_spectral.py
│   ├── ns_forced.py, ns_stochastic.py, ns_wavelet.py
│   ├── nt_zeta.py, atmospheric_synthetic.py
│   └── run_burgers_demo.py, run_ns_galerkin_demo.py
│
└── data/                      # static data caches

Discipline (mapping to the Five Laws)

Law	What it forbids	What the package does
I (Change)	reasoning on raw \(\Phi\)	every method takes derivatives
II (Domain interiority)	imported scales/thresholds	every input is an abstract \((t, \Phi)\) pair; no domain branches; no constants from outside
III (Universality by consensus)	universality from a single shadow	same code runs unchanged on every shadow; consensus is implied at orchestration level
IV (Intrinsic threshold)	tunable thresholds	only \(\beta = 1\); default penalties BIC, default hazard \(1/n\)
V (Honest scope)	claims of solving	this package measures, does not solve

dual.py — forward-mode automatic differentiation

validation/code/dual.py

The dual-number representation \(\Phi_{\text{dual}} = \Phi_{\text{val}} + \rho \cdot \varepsilon\) with \(\varepsilon^2 = 0\). The framework's differentiation/aggregation split (\(\mathcal{B}, \mathcal{P}\) read \(\varepsilon\)-part; \(\mathcal{S}, \mathcal{M}\) read val-part across an index) is structurally enforced in code.

• Dual32 type with arithmetic matching \(\varepsilon^2 = 0\).
• Smooth-function lifts: dual_log, dual_exp, dual_pow, …
• to_dual_from_observational(t, phi): wraps FD-derived \(\rho\) as Dual32.
• DualN truncated-polynomial extension supplies higher-order derivatives mechanically (\(g''(\log|\Phi|)\) for T7's cadence error and beyond).

derivatives.py — ρ extraction

validation/code/derivatives.py

The framework defines \(\rho_i = (\Phi_{i+1} - \Phi_i)/\tau_i\). Real cascades are sampled finitely and noisily, so \(\rho\) must be estimated. Four methods:

• finite_difference_derivative(t, phi) — naive baseline (centred FD).
• wavelet_derivative(t, phi, scales=None, wavelet='morlet') — multi-scale \(\rho\) via continuous Morlet wavelet transform.
• gp_derivative(t, phi) — Gaussian-process posterior derivative with uncertainty (RBF + WhiteKernel; hyper-parameters by marginal-likelihood maximisation).
• emd_trend(t, phi) — Huang Empirical Mode Decomposition; returns IMFs and the trend residue.

regression.py — 𝓑 brake-exponent estimators

validation/code/regression.py

Three estimators on \(\log|\rho| = \alpha + \beta \cdot \log|\Phi|\):

• polyfit_brake_p(phi, rho) — naive OLS via numpy.polyfit. CI by bootstrap (1000 resamples, deterministic seed).
• gls_ar1_brake_p(phi, rho) — Cochrane–Orcutt iterative GLS with AR(1) residuals.
• bayesian_brake_p(phi, rho, ar_order=1) — MAP + Laplace covariance, Metropolis sampling. Weakly-informative priors (\(\alpha, \beta \sim \mathrm{Normal}(0, 10^2)\), \(\log \sigma \sim \mathrm{Normal}(0, 5^2)\)).
• compare_methods(phi, rho) — runs all three side-by-side.

regimes.py — change-point detection

validation/code/regimes.py

• pelt_changepoints(t, phi, penalty='bic', min_size=10) — Pruned Exact Linear Time (Killick et al. 2012). BIC penalty default; no imported threshold. Returns indices.

Used in instances 17 (Arctic 1990/2007 regime breaks), 22 (MPT date recovery to ±50 kyr), 25 (Montreal Protocol date recovery to ±2–3 yr), 27 (timing-of-tipping). All findings recovered with no domain-tuned threshold.

decomposition.py — 𝓟 spectral primitive

validation/code/decomposition.py

Implements the spectral primitive \(\mathcal{P}(\mathcal{C}, c) = (\mathcal{C}_{\text{brake}}, \mathcal{C}_{\text{resonance}}, \mathcal{C}_{\text{residual}})\). Theorem 13 governs uniqueness: gauge group \(G_{\mathcal{P}}\) excludes frequency-reparametrisation, so the 41-kyr-vs-100-kyr Mid-Pleistocene distinction is preserved.

Reproducibility & provenance

Every experiment writes a JSONL metadata file (solver parameters, all three brake estimators, AR(1) coefficient, R², residual MAD, framework verdict + \(\mathscr{A}\)) and a TXT human-summary file. Reproduction gates are run for every experiment.

Tests under validation/code/tests; regression reports archived as instances_1_10_regression_report.txt, pure_math_regression_report.txt, climate_regression_report.txt, dual_validation_pure_math.txt.