Same framework, applied to Seismology
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 seismology
Aftershock decay is described in seismology by the Omori–Utsu law \(n(t) = K/(t + c)^p\), where \(p\) is fitted per sequence. The framework recovers the same exponent in framework-native log-log primitives, with no domain-specific machinery — and reads it through Theorem 1 as Type-II asymptotic decay (\(\beta > 1\)).
Headline results (catalogue instance 5)
- Omori-Utsu \(p = 1.184\), \(R^2 = 0.916\) (literature range 1.0–1.3).
- Dataset: USGS catalog Tohoku 2011, 1716 \(M \ge 4.5\) events over 14 days post-mainshock.
- Theorem 1 reading: \(\beta > 1\) is Type-II slow asymptotic decay — matches the physical reality of long aftershock tails.
Experiments
Scripts: domains/seismology/experiments/ (3 scripts).
Framework reading
Cascade-brake form applies to seismic energy decay. The framework's universal brake form recovers the Omori-Utsu \(p\)-exponent without imported per-sequence calibration. \(\beta = 1.184 > 1\) places this cascade in Theorem 1's Type-II class — the system approaches but does not attain rest in finite time, which matches the seismological reality that aftershock sequences decay slowly without ever abruptly terminating.