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.

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.

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

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

Conditional Riemann Hypothesis research atlas with public scripts, certificates, Zenodo records, and proof-audit status boundaries

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.

Book II of Dark Geometry: the Standard Model gauge group, particle masses, couplings and mixing angles derived from d=3 and the Planck mass alone — zero free parameters. ~170 predictions, ~80 sub-percent (Koide leptons, v_H to 22 ppm, m_p/m_e=6π⁵). Verification code + master table.

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

Canonical-lane closure package for the invariant subspace problem: admissible-class formulation, projection gates, local-to-global bridge, and carried remainder.

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.

Canonical-lane closure package for the Hodge Conjecture: admissible-class formulation, projection gates, local-to-global bridge, and carried remainder.

Integration tests proving all 12 Rust metal libraries work together as a coherent system