← Kenneth A. Mendoza

Preprints & Datasets

Zenodo-deposited research artifacts. Pulled live from the public records API; pre-rendered with the most recent snapshot.

Showing snapshot from 2026-05-07
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Preprint 13 Apr 2026 · v1.0

On Finite Execution and the Rate Limit of Nature’s Laws: A Response to Gödel’s ‘An Example of a New Type of Cosmological Solution of Einstein’s Field Equations of Gravitation’ (1949)

Gödel’s 1949 rotating-universe solution demonstrates that Einstein’s field equations admit spacetimes with no global time function and no universal execution order for dynamical laws. Argues this exposes an unexamined assumption in fundamental physics — that laws enforce themselves instantaneously — and proposes Maxwell’s 1861 displacement current as the first known instance of finite-rate law-execution machinery.

Gödel metric closed timelike curves chronology protection Maxwell’s equations finite-rate dynamics Planck time
DOI 10.5281/zenodo.19549033 · CC BY 4.0
Dataset 10 Apr 2026 · v2.0

First computational upper bound on the infimum for Erdős Problem #1038

First computational upper bound for the sublevel-set infimum of monic polynomials with all real roots in [−1,1]. Main result: inf ≤ 1.837 (N=200 configuration). v2 adds Thomson/Riesz energy mapping — the log-energy minimizer (Saff–Totik weighted potential theory) reproduces the extremal atom weight within 2.1%, demonstrating the atom+cloud architecture is structural, not numerical.

Erdős problems extremal polynomials sublevel sets potential theory Thomson problem Riesz energy
DOI 10.5281/zenodo.19503638 · concept DOI 10.5281/zenodo.19444425 · CC BY 4.0
Dataset 9 Apr 2026 · n=3 to n=14

Computational Verification of the Erdős–Herzog–Piranian Conjecture for Degrees 3 ≤ n ≤ 14

IEEE 1788 interval-arithmetic certified branch-and-bound verification of the EHP conjecture for monic polynomials of degrees 3 through 14. Includes preprint PDF, all result JSONs with SHA-256 checksums, and the closed-form arc-length formula L(zⁿ−1) = 2^(1/n) √π Γ(1/(2n)) / Γ(1/(2n)+1/2). Source code at github.com/MendozaLab/erdos-experiments.

EHP conjecture interval arithmetic certified computation lemniscate Erdős
DOI 10.5281/zenodo.19480329 · concept DOI 10.5281/zenodo.19184467
⚠ Superseded — see canonical record at DOI 10.5281/zenodo.19444427
Preprint 30 Mar 2026

Formal Verification of Sidon Set Upper Bounds in Lean 4 with Mathlib: Erdős Problem 30

A Lean 4 formalization of the two principal upper bounds for Sidon sets (B₂ sets), addressing Erdős Problem 30. 1131 lines of verified Lean 4 code, zero sorry stubs. Proves the Lindström bound (1969) and Balogh–Füredi–Roy bound (2023). Retained for archival continuity; cite the canonical record instead.

DOI 10.5281/zenodo.19324240 · CC BY 4.0
Working Paper 29 Mar 2026

Certified Computation at the Boundary of AI-Assisted Mathematics: A Response to Tao et al. (arXiv:2511.02864)

A direct architectural response to Tao et al. on the Erdős problem space. Three-layer answer: (1) IEEE 1788-certified interval arithmetic for the EHP lemniscate conjecture n=3–13; (2) the Erdős Atlas 3D morphism network; (3) 49 sorry-free Lean 4 proofs. Introduces the Squeeze Lemniscate framework and the ODGAF governance layer.

Erdős conjecture interval arithmetic certified computation AI-assisted mathematics Lean 4 AlphaEvolve
DOI 10.5281/zenodo.19322740 · CC BY 4.0