Dedicated deep-dive site
A standalone site is published for this domain at pure-math.senuamedia.com — with the per-instance results, walkthroughs, and downloadable data behind every reading on this page.
Same framework, applied to Pure-Math Universality
The framework's value lies in its universality across disparate domains. The brake operator \(\mathcal{B}\), dispersion \(\mathcal{S}\), consensus \(\mathcal{M}\), spectral primitive \(\mathcal{P}\), anti-shadow detector \(\mathfrak{A}\), and scope-reporter \(\mathscr{A}\) — together with Theorems 1–13 — are applied here exactly as on every other domain. Source code: github.com/senuamedia/uniformity. No per-domain calibration. No imported threshold. No bespoke fit.
Cross-domain catalogue — \(\beta\)-strip
Every brake-exponent reading across every domain. The same operator \(\mathcal{B}\) produced every point. This domain's points are highlighted; the rest of the catalogue is visible for cross-domain context.
Click any point for the full reading: instance, domain, \(\beta\) value, and a link to the source code.
What the framework provides for pure-mathematical universality classes
Universality classes in mathematical physics are conventionally identified through analytical machinery specific to each class: KPZ via Hopf–Cole, Ising via conformal bootstrap, Wigner–Dyson via Selberg integrals, Ricci flow via Hamilton–Perelman classification, stochastic homogenisation via Gloria–Otto. The framework recovers all five universality signatures in a single dimensionless language, often with cross-shadow dispersions tighter than within-shadow noise — empirical universality calls in framework-native form.
Headline results (catalogue instances 11–15)
Five strong validations
- 11. KPZ universality (1+1D). 3 microscopic models (BD, RSOS, TASEP); \(\beta = 0.316\) (target 1/3) with \(\sigma_{\text{cross}} = 0.004\); \(\alpha = 0.505\) (target 1/2); \(z = 1.64\) (target 3/2).
- 12. 3D Ising critical exponents. Wolff cluster MC; \(T_c = 4.51235\) (0.02% error vs literature 4.51153); \(\beta_{\text{mag}} = 0.318 \pm 0.021\); \(\gamma/\nu = 1.93 \pm 0.04\) (1.7% error).
- 13. Wigner–Dyson RMT. 5 entry distributions at \(N = 1000\); \(\sigma_{\text{cross}} = 0.006\); KS distance to Wigner-GOE surmise = 0.0064. 5% of within-shadow sample noise — universality signature.
- 14. Ricci-flow neckpinch. Type-I \(\beta = 1.083\)/\(1.086\); Type-II \(\beta = 1.164\); within-Type-I \(\sigma = 0.0015\), gap \(+0.080\) — 50× separation, sharpest in catalogue.
- 15. Stochastic homogenisation rates. 2D divergence-form elliptic, 3 coefficient ensembles; σ-dispersion brake-p \(\beta = 1.02 \pm 0.05\) (target \(d/2 = 1\)) — recovers Gloria–Otto rate.
Experiments
Scripts: domains/pure-math/experiments/ (5 scripts + C kernels).
kpz_universality.pyising_3d_critical.pyrmt_universality.pyricci_neckpinch.pystochastic_homogenisation.py
Framework reading
These are the framework's strongest empirical patterns: structurally different microscopic realisations of a universality class agree on the universal exponent to a tightness smaller than their own within-realisation sample noise. That cross-shadow agreement is the framework's universality call, demonstrated on five of the most-studied universality classes in mathematical physics. Theorem 11 (cross-shadow convergence rate) is the formal statement: \(\sigma_{\text{cross}} \sim 1/\sqrt{K \log N_{\text{eff}}}\). Wide per-shadow log-range \(K\) drives \(\sigma_{\text{cross}}\) sharper — wide-\(K\) instances (KPZ \(W(L,t)\) growth across many decades) reach 0.4% precision; \(K\)-limited instances (Ricci flow's clean self-similar window) demonstrate the K-limited regime instead of the N-limited one.