Adèlic spectral frameworks for computational number theory: exploring exact discrete bounds for pattern avoidance via CP-SAT, and quantum-physical realizations of automorphic L-function zeros.

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.

"Spectral Determinant of a Cutoff-Regularized Hamiltonian and the Riemann Zeta Function" - preprint

Certified log-concavity of the Riemann-Jacobi kernel with Arb/FLINT ball-arithmetic certificates. Source-critical audit of the Polya-type real-zero criterion. No unconditional RH claim.

Numerical experiments for defect eigenvalues and localization in finite discrete Schrödinger / tight-binding chains with a single on-site defect.

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.

Where graph theory meets quantum mechanics in optimization space

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

Multi-route Riemann Hypothesis research atlas with public scripts, certificates, and Zenodo records

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

唯一の公理¬∃→∃と明示された同定公理から、宇宙論的定数（120桁問題を連続パラメータゼロで抑制、誤差1.71%）・CMB音響ピーク・標準模型の群構造を導出する反証可能な統一理論。新等式 α·ln n* = R(S^(n*-1))·π を含む。/ A falsifiable unified theory deriving Λ, CMB peaks, and the SM gauge group from a single axiom with zero fitted parameters.

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.

The Spectral Gap-Statement: when the negative subspace of attention transport is a well-posed invariant

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.

GirkoNet_MPNN: Deep Learning vs. Random Matrix Theory. Sfruttare le Message Passing Neural Networks e l'Explainable AI (XAI) per prevedere il raggio spettrale e smascherare l'illusione delle euristiche topologiche locali.

We carry out a complete formalization of the spectral theorem in Lean, for both bounded and unbounded linear operators over some Hilbert space H.