KEN MENDOZA

Information theory → cross-domain science. MDL parsimony, Koopman operators, and entropy hierarchies applied to pure mathematics, materials science, dynamical systems, and climate detection.

Independent researcher. Formal proofs in Lean 4. Validated predictions across five domains. 19-patent portfolio spanning quantum error correction to materials phase transitions.

Cross-Domain Research

One mathematical framework. Five domains. Validated independently on each. When the same theory works on materials phase transitions AND 90-year-old number theory, it's not luck.

Materials Science

Materials Science

91% accuracy on 12,525 phase transitions. 86,000x speedup vs density functional theory. 5 of 5 hypotheses validated.

Medical Diagnostics

Medical Monitoring

90% false alarm reduction with 100% sensitivity maintained. Patient-specific thresholds beat population averages.

Climate Detection

Climate Tipping Points

AMOC complexity-drop detection validated. One hypothesis falsified and openly retracted — honest accounting matters.

Dynamical Systems

Dynamical Systems

Koopman channel asymmetry: AUC = 0.935 on benchmark, AUC = 1.000 on cross-domain transfer with zero retraining.

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Pure Mathematics

Cramér bound (1936) derived from MDL parsimony — 90-year-old conjecture, no Riemann Hypothesis needed. Erdős Problem #233 proved in Lean 4. 1,179 problems mapped.

5
Validated Domains
14
Experiments Run
1,179
Erdős Problems Mapped
9
Lean 4 Proofs
Explore Research Portfolio →

Pure Mathematics

Applying Minimum Description Length (MDL) parsimony to extremal combinatorics and analytic number theory. All proofs verified in Lean 4 against Mathlib.

Erdős MDL Mapper

Systematic information-theoretic reinterpretation of 1,179 Erdős problems. 498 problems mapped to MDL morphisms (42.2% coverage). No prior art exists for this mapping.

Verified Results (Lean 4)

16 Lean files, 64 declarations, 0 sorry. New proofs: #1, #18, #233 (product sets), #420. Disproof: #198. Formalizations and partial results: #20 (ALWZ sunflower bound), #30 (Sidon coding), #228 (Rudin-Shapiro), #389, #396.

Cramér-MDL Conjecture

The Cramér bound O((log N)²) for maximal prime gaps derived from MDL parsimony alone—no Riemann Hypothesis required. Validated on 10⁸ primes (CV = 0.006). Beats Hardy-Littlewood, Gallagher, Granville, PNT, and geometric models.

Erdős-Moser Problem

2-adic squeeze mechanisms and 4|pn filter for the Erdős-Moser conjecture on consecutive prime sums. Lemmas 1–9 formally verified. Active collaboration interest with Pieter Moree (MPIM Bonn).

1,179
Erdős Problems Catalogued
498
MDL Morphisms
16
Lean 4 Files (0 sorry)
4
New Proofs of Open Problems
Full Research Details →

Intellectual Property

14

Issued Patents (Proteomics)

Arbor Vita Corporation

  • ▸ Drug target identification and validation
  • ▸ Molecular modeling and computational biology
  • ▸ Laboratory information management systems
2025
5

Provisional Patents Filed

Entropy & Hysteresis Framework

  • ◆ Quantum error correction (hardware-validated)
  • ◆ Climate tipping point detection
  • ◆ Materials phase prediction
  • ◆ AI optimization & music analysis
  • ◆ Quantum sensing
Full Patent Portfolio →

About

Ken Mendoza

Ken Mendoza is an independent researcher applying information-theoretic methods—Minimum Description Length (MDL), Koopman-von Neumann operators, and the Shannon–von Neumann–Riemannian entropy hierarchy—to problems across pure mathematics, materials science, dynamical systems, and climate detection.

His current focus is the Erdős MDL Mapper: a systematic information-theoretic reinterpretation of 1,179 Erdős problems, with formal proofs verified in Lean 4 (Mathlib). Related work includes the Cramér bound derived from MDL parsimony without the Riemann Hypothesis, and the Erdős-Moser problem via 2-adic squeeze mechanisms.

In materials science, his framework achieves 91% accuracy on 12,525 phase transitions with 86,000× speedup over density functional theory. In dynamical systems, Koopman channel asymmetry yields AUC = 0.935 on benchmark with perfect cross-domain transfer.

Background: 25 years in computational biology and software architecture, including 14 issued patents in proteomics (Arbor Vita Corporation) and roles spanning bioinformatics, drug target identification, and systems integration. 5 additional provisional patents filed in 2025 covering quantum error correction, climate detection, and materials science.

19
Patents (Issued + Provisional)
25+
Years in Computational Science
276
Experiments Run

Papers & Preprints

Product Set Bounds via Minimum Description Length: An Information-Theoretic Approach to Erdős Problem #233

K. Mendoza (2026). All 6 lemmas machine-proved in Lean 4 by Aristotle (Harmonic AI). Target: arXiv math.CO.

Submission-Ready

The Cramér-MDL Conjecture: Prime Gap Bounds from Information-Theoretic Parsimony

K. Mendoza (2026). CV = 0.006 on 10⁸ primes. Beats 5 classical models. No Riemann Hypothesis assumption. Target: arXiv math.NT.

Data Complete

Koopman Channel Asymmetry as an Early Warning Signal for Critical Transitions

K. Mendoza (2026). δ = |Ffwd − Fbwd| as operator-theoretic EWS diagnostic. AUC = 0.935. Target: Physical Review E / Chaos.

Manuscript Complete

Discrete Harmonic Basins in Elastic Eigenvalue Ratios Predict Ductile vs. Brittle Mechanical Response

K. Mendoza (2026). 90.1% accuracy on quaternary alloys, p < 10−7. 12,259 materials from Materials Project. Target: Physical Review Materials.

In Preparation

Methodology: Honest Accounting

All experiments use real data with SHA-256 checksums. Falsified hypotheses are reported openly. Key results verified in Lean 4 by Aristotle (Harmonic AI). Adversarial review via Feynman Team protocol. Reproducibility scripts and data to be published on GitHub.

Applied Research & Ventures

PhaseEntropy Materials Science

PhaseEntropy

Materials science platform: ductility prediction via discrete harmonic basins in elastic eigenvalue ratios. 90.1% accuracy on quaternary alloys. API and dashboard for computational materials teams.

phaseentropy.com →
EtioDynamics Clinical

EtioDynamics

Dynamical disease classification using HS(p) metrics. 5 disease archetypes (frustrated attractor, hyperbolic runaway, crystalline lock, holonomic drift, KvN bridge failure). Clinical trial rescue and patient stratification.

Coming 2026
DangerTheory Immunology

DangerTheory.org

Computational immunology research platform exploring Polly Matzinger's Danger Theory: context-dependent immune activation as an information-theoretic optimization problem.

dangertheory.org →

Collaboration Interests

Open to academic partnerships, adversarial review, and co-authorship in the following areas.

Extremal Combinatorics & Number Theory

MDL morphisms for Erdős problems. Erdős-Moser conjecture (2-adic methods). Formal verification in Lean 4 / Mathlib. Interested in working with researchers in additive combinatorics, analytic number theory, and automated theorem proving.

Applied Category Theory & Information Geometry

Cross-domain morphisms as functors. Information-geometric structure of the entropy hierarchy. Compositional approaches to dynamical systems. Seeking collaborators in the applied category theory and information geometry communities.

Computational Materials Science & HPC

Large-scale eigenvalue ratio computation on HPC clusters. Validation on expanded materials databases. NERSC allocation for systematic materials screening beyond the Materials Project.

Contact

For research collaboration, preprint requests, or Lean proof files: reach out directly. Open to adversarial review of any result on this site.

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