H² Research Framework

A single mathematical spine — the Shannon → Von Neumann → Riemannian entropy hierarchy — producing validated predictions across multiple maximally distant domains. When it works on materials AND disease dynamics AND dynamical systems, the "overfitting" dismissal fails.

The Entropy Hierarchy

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.

Level 0: Clausius entropy (1865) — thermodynamic, S = ∫dQ/T
↓ embeds into
Level 1: Shannon entropy (1948) — information, H = −Σp log p
↓ embeds into
Level 2: Von Neumann entropy (1932) — quantum, S = −Tr(ρ log ρ)
↓ connected by Koopman-von Neumann bridge
Level 3: Riemannian geometry — curvature, holonomy, geodesic structure
↓ unified by
MDL: Minimum Description Length — Nature's parsimony principle

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.

Validated Results

Materials Science (H2m)

High accuracy · Orders-of-magnitude speedup
Phase transition classification across thousands of material pairs. A zero-parameter formula predicts phonon frequencies with single-digit error. Majority of hypotheses validated. Golden Ratio universality hypothesis honestly downgraded after data showed limited support.

Medical Monitoring (H2d-Med)

Dramatic false alarm reduction · Sensitivity preserved
Dwell-controlled state machines for rare physiological event detection. Patient-specific thresholds outperform population averages. Majority of hypotheses validated.

Dynamical Systems (KvN Channel Asymmetry)

Strong early warning · Cross-domain transfer
Koopman channel asymmetry δ reliably discriminates near-transition from stationary dynamics with high statistical significance. Spectral gap mechanism identified. The same frozen pipeline transfers to industrial bearing fault detection with zero retraining.

Climate Tipping Points (H2Clime)

AMOC complexity-drop validated
AMOC/CESM slices show higher complexity-drop rates than empirical/paleoclimate under matched contracts. One general hypothesis (V7 holonomy improves detection) was falsified and openly retracted. Honest accounting is a feature, not a bug.

Disease Dynamics (H2-EtioDynamics)

Perfect classification · Multiple disease archetypes
Dynamical disease classification via DSO κ (differential structural overlap). Multiple archetypes identified: frustrated attractor, hyperbolic runaway, crystalline lock, holonomic drift, KvN bridge failure. Majority of hypotheses validated. Clinical trial rescue and patient stratification applications.

One Problem, Many Domains, Same Solution

Domain The Challenge H² Solution Result
Disease Dynamics Classify disease mechanisms from trajectories DSO κ classification Perfect classification across archetypes
Quantum Computing Prevent false syndrome detection Dwell-time hysteresis filter Order-of-magnitude improvement (hardware)
Materials Science Predict phase transitions without simulation Information-theoretic classification High accuracy, orders-of-magnitude 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 Strong discrimination, cross-domain transfer

The same entropy hierarchy predicts phase transitions in steel, false alarms in ICU monitors, tipping points in climate systems, and disease dynamics classification. If a single framework works across maximally distant domains, the framework is measuring something real.

Patent-Backed Innovation

Each domain application is protected by patent filings. The core mathematical framework is held as trade secret; domain-specific implementations are patent-backed.

Quantum Error Correction

Hardware-validated on IBM Quantum. Multi-threshold dwell-time hysteresis reduces false syndrome triggers.

Materials & Battery Safety

Orders-of-magnitude speedup vs DFT simulation. Early warning for thermal runaway and dendrite formation.

AI & Music

Hallucination reduction via entropy-guided optimization. Music analysis using thermodynamic feature extraction.

Climate & Geoscience

Tipping point detection via entropy gradients. Geophysical inversion for subsurface imaging.

Immune & Mental Health

Danger Theory–inspired immune state estimation. Psychoneuroimmunology for mental health early warning.

Cybersecurity

Biomimetic apoptosis defense. Deepfake detection via entropy inversion signatures.

Explore Full Patent Portfolio →

Methodology: Honest Accounting

Every result in this portfolio follows strict scientific integrity rules:

Collaborate

Seeking collaborators in applied category theory, information geometry, formal mathematics, and cross-domain validation. Open to academic partnerships, licensing discussions, and adversarial review.

ken@kenmendoza.com