Catalogue

Thirty strong validations across fifteen domains. Every instance with its dataset, the framework's primitive call, and the result. Linked to source.

Summary

The catalogue records every instance the framework has been applied to, with its dataset, methods, and verdict. 30 strong validations + 3 partial + 3 honest-negative, plus open-direction targets organised in tiers A–D and a pure-math research tier. Source: validation/catalogue.md.

Strong validations (instances 1–30)

Physics & astronomy

  • 1. Fluid turbulence — NS-Galerkin DNS, Burgers, MHD, Sabra (Re=10³–10¹⁰), EDQNM closure. ~190 cells, \(\varepsilon > 0\) universally, K41 within 0.022 of literature. domain page · scripts
  • 2. Particle physics — CMS H→ZZ*→4ℓ Record 5200, 278 events. Z @ +8.6σ at 92 GeV, Higgs @ +2.6σ at 128 GeV. domain page · cms_higgs_test.py
  • 3. Binary black hole mergers — LIGO GW150914 + GW151226. GW150914 @ +23.6σ (37 ms), GW151226 @ +3.7σ (25 ms) via cross-detector consensus. ligo_gw150914_test.py
  • 4. Exoplanet transits — TESS WASP-43 + HD 209458. WASP-43b period 0.81336 d (true 0.81348, 0.015% error). tess_exoplanet_test.py
  • 5. Seismology — USGS Tohoku 2011 (1716 \(M \ge 4.5\) events over 14 days). Omori–Utsu \(p = 1.184\), \(R^2 = 0.916\). seismic_omori_v2.py
  • 6. Nuclear / \(E = mc^2\) — AME2020, 2,545 isotopes. Median residual \(3 \times 10^{-9}\), max \(1 \times 10^{-7}\). emc2_test.py
  • 7. Medical / cancer biomarkers — Wisconsin Breast Cancer (UCI ML, 569×30). 6/7 literature-consensus biomarkers in framework's top 7 by Cohen's \(d\). medical_bump_hunt.py
  • 8. NANOGrav nanohertz GWB — 15-yr Bayesian free-spectrum (Lamb-Taylor-van Haasteren 2023). \(\gamma = 4.11 \pm 0.39\) — within 1σ of SMBH-binary regime (13/3 ≈ 4.33). nanograv_spectral_slope.py
  • 9. LIGO O3 sub-threshold discrimination — GW190521 → consensus_signal (+5.76σ); GW190426_190642 → consensus_noise (matches LIGO demotion). ligo_subthreshold_search.py
  • 10. CHIME/FRB repeater periodicity — 21 repeaters, 326 bursts. FRB 20180916B period 16.33 d (0.01% error, MC \(p = 0.005\)). scripts

Pure-math universality classes

  • 11. KPZ universality (1+1D) — BD + RSOS + Corner Growth/TASEP. \(\beta = 0.316\), \(\sigma_{\text{cross}} = 0.004\) (target \(1/3\)).
  • 12. 3D Ising critical exponents — Wolff cluster MC, \(L \in \{16,24,32,48\}\). \(T_c = 4.51235\) (0.02% error); \(\beta_{\text{mag}} = 0.318\) (2.8% error); \(\gamma/\nu = 1.93\).
  • 13. Wigner–Dyson RMT — 5 entry distributions at \(N = 1000\). \(\sigma_{\text{cross}} = 0.006\); KS distance to Wigner surmise = 0.0064.
  • 14. Ricci-flow neckpinch (S³) — 3 initial-data profiles. Type-I \(\beta = 1.083\)/\(1.086\); Type-II \(\beta = 1.164\); within-Type-I \(\sigma = 0.0015\), gap \(+0.080\) — sharpest separation in catalogue.
  • 15. Stochastic homogenisation rates — 2D divergence-form elliptic, 3 coefficient ensembles. \(\sigma\)-dispersion brake-p \(\beta = 1.02 \pm 0.05\) (target \(d/2 = 1.0\)). Recovers Gloria–Otto rate.

Climate (instances 16–30)

15 instances across CMIP6 ensembles, observational records, paleoclimate proxies, and energy budgets. Highlights:

  • 16. CMIP6 tipping cross-shadow consensus — Arctic 21/21 robust; AMOC partially-robust; Amazon NPP inconclusive.
  • 17. Arctic sea-ice (NSIDC 1979–2025) — Theorem 3 precision-floor empirical confirmation.
  • 18. Earth-system energy-budget conservation-decomposition — Trenberth–Fasullo "missing energy" reproduced from first principles, 78% closure.
  • 22. Mid-Pleistocene Transition — resonance-shift 41-kyr → 100-kyr (T9, T13 anchor).
  • 23. Atmospheric CO\(_2\) multi-cadence — anthropogenic vs natural separated at 5.7σ; within-paleo \(\sigma_{\text{cross}} = 0.024\) at 100-millennial cadence.
  • 25. Stratospheric ozone (Montreal Protocol) — T10 anchor: \(\mathfrak{A} = 22.4\) anti-shadow detection.
  • 26. Permafrost carbon cascade — cross-model first-break warming +0.36 ± 0.12 K (far below literature ±1.5–2.0 °C tipping window).
  • 27. Cross-model timing-of-tipping prediction — \(\beta = 1\) crossing-year extrapolation. Framework beats naive baseline (20-25 yr error vs 38-41 yr).
  • 30. Tropical cyclone cross-basin — T10 anchor: wind-vs-pressure shadow disagreement 5/6 basins.

Full list at catalogue.md Part 1; experiment scripts under domains/climate/experiments/ (45 scripts).

Partial validations (instances 31–33)

  • 31. Binary neutron star merger — LIGO GW170817. Framework primitive does not match templated matched-filter at this SNR.
  • 32. TESS unconfirmed exoplanet search — bump-hunt yields candidates; follow-up needed.
  • 33. Solar wind — correctly out of scope. Open-system violation of cascade closure assumption; framework reports verdict honestly under Law V (Theorem 12 anchor).

Honest negative findings (instances 34–35)

  • 34. Biology / ECG (PhysioNet MIT-BIH) — cascade-style primitives do not improve domain-standard arrhythmia analysis.
  • 35. TESS ultra-short-period search — sample selection issue; redo proposed in Tier A1.

Open-direction targets

Tier A (highest leverage): TESS USP M-dwarf sample, sub-threshold LIGO O4 sweep. Tier B: anomalous cosmic-ray spectra, neural avalanche statistics. Tier C: solar superflares, tropical-cyclone energy dissipation, dark-matter direct detection, genomic variant detection. Tier D: cold-atom turbulence, ocean internal-wave spectra, earthquake foreshock detection, climate tipping early-warning. Pure-math: Liouville Quantum Gravity / SLE, Mean Field Games regularity.