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.

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.

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

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

Where graph theory meets quantum mechanics in optimization space

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

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

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.

The Hodge Conjecture via Hodge-class persistence and rigidity 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.

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.

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

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

The Birch-Swinnerton-Dyer Conjecture via analytic-arithmetic persistence on the manifold-constrained canonical lane. Reproducible local-to-global theorem package.

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

Spectral floor normalization and Hermite-basis structural analysis for Gaussian-Laguerre operator models