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.
An artifact-backed showcase connects a Modal + REBOUND/IAS15 periodic-orbit catalog rung, cardiac signal-processing validation, and a book-to-agents interface. It is a research demo and proposal asset, not an institutional endorsement or deployment claim.
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.
| Domain | The Challenge | H² Solution | Result |
|---|---|---|---|
| Disease Dynamics | Classify disease mechanisms from trajectories | DSO κ classification | Majority of hypotheses validated across archetypes |
| Cardiac Diagnostics | Assess cardiac dynamical state from limited leads | Device-invariant, interpretable review layer | Filed provisional, research-stage |
| Sepsis Monitoring | Track patient trajectory from a single blood draw | White-box host-response signature | Filed provisional, research-stage |
| Climate Detection | Distinguish tipping points from noise | Complexity-drop analysis | Publication and grants track, no patent filing in progress |
| Dynamical Systems | Early warning for critical transitions | Method held pending provisional filing | Filed provisional; strong discrimination, cross-domain transfer under test |
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.
Four 2026 provisional patent applications (patent pending), each addressing a distinct research-stage diagnostic or monitoring problem.
Device-invariant, interpretable ECG review layer that assesses cardiac dynamical state from as little as a single lead.
Objective, blood-based molecular stratification signal for a condition currently diagnosed by symptom criteria and exclusion.
White-box host-response signature plus an interpretable trajectory-review layer, offered alongside clinical judgment.
Interpretable, physically-grounded monitor for critical transitions, positioned as an auditable governance and fallback layer.
Every result in this portfolio follows strict scientific integrity rules:
Lean 4 statements merged into google-deepmind/formal-conjectures. Each merged record is a statement in the library, not a Lean proof.
Lean 4 formalization of Borsuk's conjecture on decomposition of n-dimensional sets into pieces of smaller diameter, including a one-dimensional test statement and formal_proof metadata referencing the Alexeev–Aristotle Lean 4 formalization.
Statement-level Lean 4 contribution for the equilateral-triangles-in-six-space problem family, including the Clemen–Dumitrescu–Liu any-size variant with explicit proof-status boundaries.
Additive update to the distinct-distances entry: an Erdős–Moser grid upper-bound variant and reference cleanup complementing the Guth–Katz lower-bound line.
Erdős–Rado upper-bound variant recorded as a Lean-facing formal-conjectures statement. This is a known extremal-combinatorics bound, not a solution of the open sunflower conjecture. Statement in the library, not a Lean proof.
Statement in the library, not a Lean proof. Theorem body remains sorry with a literature citation.
Statement in the library, not a Lean proof. Theorem body remains sorry with a literature citation.
Statement in the library, not a Lean proof. Theorem body remains sorry with a literature citation.
google-deepmind/formal-conjectures
Seeking collaborators in applied category theory, information geometry, formal mathematics, and cross-domain validation. Open to academic partnerships, licensing discussions, and adversarial review.
[email protected]