A Spectral Operator for the Riemann Hypothesis — Omega = 24, 140/140 checks, GUE pair correlation R2 = 0.026 at N = 5M

Principia Fractalis: Fractal Resonance Ontology. A 1000+ page work exploring how mathematics, consciousness, and physical reality connect through a unified structure. Formally triple-verified in Lean 4, Coq, and L4L

Physics-based computation at scale — Hamiltonian dynamics, spectral theory, and statistical mechanics powering optimization, drug discovery, genomics, molecular proof, and agentic commerce.

Lean verified Science.

Watkins Temperature Theorem: conservation-law constrained optimization on the golden-ratio simplex

The Riemann Hypothesis: A Gauge-Theoretic Proof via Even Dominance and Spectral Stability. Zenodo DOI: 10.5281/zenodo.19035845

A modular harmonic sieve for detecting nontrivial Riemann zeta zeros through phase-locked resonance, leveraging the interplay of base-3 and base-π spirals to isolate precise zero locations without statistical approximation. Ideal for mathematical research, numerical experiments, and algorithm development.

Research project exploring operator-theoretic approaches to the Riemann Hypothesis, combining spectral theory and computational analysis. Includes English (main) and Portuguese versions.

Where graph theory meets quantum mechanics in optimization space

Decoding cognitive states from fMRI brain networks using Spectral Graph Signal Processing (GSP) and High-Resolution Graph Fourier Transforms. Analysis of 88 subjects from the HCP S1200 dataset.

Exploring the relationship between conformal rigidity, spectral properties, and genus of graphs.

The Hodge Conjecture via Hodge-class persistence and rigidity on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The invariant subspace problem via operator-spectral persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

3D Navier-Stokes global regularity via dissipative persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

The Riemann Hypothesis via self-adjoint spectral persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

First explicit curvature correction formula for fractional Laplacians on curved manifolds. Complete proof via heat kernel expansion, validated computationally on S². Applications in anomalous diffusion, thermal field theory, and curved spacetime physics.

Yang-Mills existence and mass gap via self-adjoint gauge persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

Machine-checked proof that the persistent sheaf Laplacian is independent of simplex orientation. Kernel dimension, characteristic polynomial, and eigenvalue spectrum are invariant. Formalized in Lean 4 with Mathlib.

Archimedean kernel rigidity (AKCL) framework for RH via coercivity and defect control

Experimental extensions of the Yang–Mills spectral wall: non-radial modes, higher k, and alternate discretizations.