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.

Where graph theory meets quantum mechanics in optimization space

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.

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

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.

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

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

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

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

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.