A single mathematical spine — the Shannon → Von Neumann → Riemannian entropy hierarchy — producing validated predictions across five maximally distant domains. When it works on materials AND pure mathematics, the "overfitting" dismissal fails.
Every H² result traces to a single insight: entropy is not one thing — it's a hierarchy. Each level embeds the previous, and each embedding adds predictive power.
This is not metaphor. Von Neumann named Shannon's quantity "entropy." The Koopman-von Neumann formalism (1931) lifts classical dynamics into Hilbert space. MDL (Rissanen 1978) selects the shortest description. The hierarchy is real, testable, and computationally exploitable.
Paul Erdős (1913–1996) posed 1,179 open problems across combinatorics, number theory, and discrete geometry. We're systematically translating them into MDL — the first such mapping ever attempted.
K. Mendoza. Target: Physical Review E / Chaos. Introduces δ = |Ffwd − Fbwd| as a novel operator-theoretic EWS diagnostic. AUC = 0.935 with MI-k10 feature selection.
K. Mendoza. Target: arXiv math.CO. All 6 lemmas machine-proved in Lean 4 by Aristotle (Harmonic AI). Cramér bound emerges from MDL without RH assumption.
K. Mendoza. Target: arXiv math.NT. Empirical validation on 108 primes. CV = 0.006, 3.7× improvement over Granville refinement.
| Domain | The Challenge | H² Solution | Result |
|---|---|---|---|
| Immune System | Prevent premature activation on noise | Multi-threshold hysteresis | 90% false alarm reduction |
| Quantum Computing | Prevent false syndrome detection | Dwell-time hysteresis filter | 895% improvement (hardware) |
| Materials Science | Predict phase transitions without simulation | Information-theoretic classification | 91% accuracy, 86,000× speedup |
| Climate Detection | Distinguish tipping points from noise | Entropy-gradient thresholding | AMOC complexity-drop validated |
| Dynamical Systems | Early warning for critical transitions | Koopman channel asymmetry δ | AUC = 0.935; cross-domain 1.000 |
| Pure Mathematics | Maximal prime gap distribution | MDL parsimony (no Riemann Hypothesis) | CV = 0.006 on 10&sup8; primes |
| AI Systems | Prevent optimization oscillation | Entropy clamping + stability control | Active (experiments in progress) |
"This cross-domain insight wouldn't have emerged from staying within traditional disciplinary boundaries. Sometimes the best solution to a physics problem comes from biology — and the best validation of both comes from pure mathematics."
Each domain application is protected by patent filings. The core mathematical framework is held as trade secret; domain-specific implementations are patent-backed.
Hardware-validated on IBM Quantum. Multi-threshold dwell-time hysteresis reduces false syndrome triggers.
107–108× speedup vs DFT simulation. Early warning for thermal runaway and dendrite formation.
Hallucination reduction via entropy-guided optimization. Music analysis using thermodynamic feature extraction.
Tipping point detection via entropy gradients. Geophysical inversion for subsurface imaging.
Danger Theory–inspired immune state estimation. Psychoneuroimmunology for mental health early warning.
Biomimetic apoptosis defense. Deepfake detection via entropy inversion signatures.
Every result in this portfolio follows strict scientific integrity rules:
Seeking collaborators in applied category theory, information geometry, formal mathematics, and cross-domain validation. Open to academic partnerships, licensing discussions, and adversarial review.
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