spectral-theory

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.

Passenger Flow Optimisation in the Singapore MRT network through Linear Algebra, Monte Carlo Simulation, Dijkstra's Algorithm, Graph Theory and Pareto Frontier Optimisation

Foundational research for the generator-first SymC framework: stability boundaries, spectral and modal structure, exceptional points, and prospective substrate-inheritance tests.

Lean verified Science.

Standalone paper and reproducibility package for smoothed positive zeta spectral kernels and a scalar RH criterion

Official repository for the Modular Projection Sieve: a sublinear Θ(√N/log N) memory algorithm based on Kmin± prime-coprime entanglement over (ℤ/6ℤ)ˣ. Features discrete spectral operator analysis (GOE quantum chaos), Lean 4 formal proofs, and reproducible Python/Numba execution up to N=10⁹.

Reproducible spectral computations on the Sierpiński gasket — an honest, test-driven audit of a fermion mass-formula conjecture. Every claim is verified, rejected, or explicitly marked open. No black boxes. 14/14 tests passing.

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.

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

Exact zero expansion and unconditional infinite oscillation for one fixed reflected packet in the semilocal Weil form

Rigorous, reproducible study of the large-wave effect on discrete rings: the peak grows like (1/π)·ln N and saturates exactly for prime and power-of-two N — with an exact-arithmetic & formally-verified layer (GAP · PARI/GP · FriCAS · Rocq).

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

CDD v28.0 综合谱理论 - 谱分解大统一理论 | Comprehensive Spectral Mixture Theory: a bottom-up GUT via PP/AC/SC spectral decomposition. Preprint: PDG 2026 three-band census (304 species), GW150914 strain = ac after line removal, G/Planck corollary, 8 calibrated claims

Where graph theory meets quantum mechanics in optimization space

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.

Computational and mathematical research archive and proof-engineering workspace for experimental approaches to the Riemann Hypothesis, Li-Keiper positivity, and related spectral/arithmetic structures.

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

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