spectral-gap

This repo contains the code for the QHack 2024 challenge "Bridging the gap".

Scale-coherence rigidity and the orbitwise gap in Collatz dynamics. Paper D: from population mixing to individual orbits. Does not claim a proof of the Collatz conjecture.

Spectral amplification by one-bit inflow in Collatz dynamics. Paper C: numerical phase diagram and open gap problem. Does not claim a proof of the Collatz conjecture.

Uniform spectral gap for the Syracuse (3n+1) mod-2^k transfer operator, proved elementarily for all scales (cert <= 0.8536). The earlier cycle-elimination claim is retracted (3x-1 control) - see README/THEOREM.md. Not a proof of Collatz.

Demo pack for the BSD Operator–Fredholm: Sage/Python scripts (principal part, finite Hecke gap, R×R renorm, leading coefficient).

ALL my project in ONE place Lichen‑Universe est le point d’entrée unifié de l’écosystème Lichen : un univers de projets open source autour de nouveaux formats de données, d’architectures cognitives, d’expérimentations quantiques et de temps universel, conçu pour explorer des systèmes informatiques réellement symbiotiques

Spectral Atomicity of the Admissible Sector: Scaled Coercivity and Mosco Compactness without Nash Inequalities

Eigenforensic framework — AEMDAS audit sequence, six disciplines, eigenvalue decomposition of institutional suppression. I-80 corridor investigation. by Steven Crawford-Maggard (EVEZ)

Reproducibility artifact for orbit-resolved spectra and dynamical accessibility in multi-register covering Hamiltonians

Projective Resolution Dynamics on Variable-Valence Relaxation Graphs

A Lean 4 formalization of fundamental theorems in matrix analysis, including the Courant-Fischer min-max theorem, Singular Value Decomposition (SVD), Frobenius norm properties, and the Eckart-Young theorem.

🔍 Verify and certify analytic bounds related to the Yang–Mills mass gap problem using reproducible computer-assisted scripts.