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

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

Physics-based computation at scale — Hamiltonian dynamics, spectral theory, and statistical mechanics powering optimization, drug discovery, genomics, molecular proof, and agentic commerce.

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

Lean verified Science.

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.

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

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.

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).

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.

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

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

Fixed-parameter Galerkin, relative trace, smoothed spectral, and certified interlacing results for semilocal zeta operators

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

A 25-page rigorous, proof-based expository monograph covering foundational Real Analysis, Riemann integration theory, and Spectral Linear Algebra.

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.