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. 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.

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Materials Science

High accuracy on large-scale phase transition datasets. Orders-of-magnitude speedup over density functional theory. Majority of hypotheses validated.

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Medical Monitoring

Dramatic false alarm reduction with sensitivity preserved. Patient-specific thresholds outperform population averages.

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Climate Tipping Points

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

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Dynamical Systems

Koopman channel asymmetry reliably discriminates near-transition from stationary dynamics. Cross-domain transfer to industrial fault detection 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. 1,190 problems mapped.

5
Validated Domains
16
Verified Lean 4 Files
1,190
Erdős Problems Mapped
19
Patents Portfolio
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 1,190 Erdős problems. 1,090 problems mapped to MDL morphisms (91.6% 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).

1,190
Erdős Problems Catalogued
1,090
MDL Morphisms
16
Lean 4 Files (0 sorry)
4
New Proofs of Open Problems
Full Research Details →

Intellectual Property

14

Legacy Patents (Proteomics, 2005-2020)

Arbor Vita Corporation

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

New Provisionals (2025)

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 1,190 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 high accuracy across large-scale phase transition datasets with orders-of-magnitude speedup over density functional theory. In dynamical systems, Koopman channel asymmetry yields strong discriminative performance 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

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 with Mathlib (0 sorry). Target: arXiv math.CO.

Manuscript Complete

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

K. Mendoza (2026). Near-zero coefficient of variation on large prime datasets. Outperforms all tested classical baseline models. No Riemann Hypothesis assumption. Target: arXiv math.NT.

In Preparation

Koopman Channel Asymmetry as an Early Warning Signal for Critical Transitions

K. Mendoza (2026). δ = |Ffwd − Fbwd| as operator-theoretic early warning signal diagnostic. Validated on benchmark datasets with cross-domain transfer. Target: Physical Review E / Chaos.

In Preparation

Information-geometric methods for ductile-vs-brittle classification in crystalline materials

K. Mendoza (2026). Manuscript in preparation. Details available to NDA-gated collaborators pending provisional patent filing.

In Preparation

Methodology: Honest Accounting

All experiments use real data with SHA-256 checksums. Falsified hypotheses are reported openly. Key formalizations are rigorously machine-checked in Lean 4 to ensure logical correctness without relying on unverified heuristics. Reproducibility scripts and data to be published on GitHub.

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 computational screening of materials databases. HPC-compatible pipelines for crystalline phase classification. Seeking allocations and collaborators for systematic benchmarking 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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