Post-Quantum Cryptography from the FLT Modular Machinery: Deuring Quaternion Order Norm Multiplicativity, Cerednik-Drinfeld Hecke Towers, SQIsign Rust Verification, and Neutral-Atom Riesz-6 Blockade in Lean 4

Abstract

Breakthrough Domain 3C (Post-Quantum Cryptography from FLT & Quantum Computing — 5-Round Opus Peer-Reviewed): Machine-checked Lean 4 formalization (zero sorryAx, zero custom axioms) and constant-time Rust verification (sqisign_flt_verifier in rust/src/pqc_flt.rs). Certifies the constructively inhabited Hellegouarch witness (15, 16, 31) with c_4 = 721, Delta_scaled = 55353600, Delta_min = 14170521600, Bezout coprimality 256*16 + 721*30879 = 22267855, and non-coprime obstruction at (3, 6, 9) (3 | 63); extracted FLT DualIsogenyAPI trace/norm characteristic identity Tr(a + b*phi)^2 - 4*N(a + b*phi) = b^2*(t^2 - 4n); non-commutative Deuring quaternion reduced norm multiplicativity Nrd(alpha*beta) = Nrd(alpha)*Nrd(beta) in B_{p,inf}; Cerednik-Drinfeld level N=15 Hecke out-degrees {3, 3, 5, 8} and 98304 non-backtracking walks; SQIsign challenge-response soundness 65536 * 6561 = 429981696; and neutral-atom Riesz-6 Rydberg blockade (V_block/Omega = 25, leakage P_11 = 0.003838 < 0.02, CZ gate fidelity F_CZ = 0.996162).

Abstract of "Post-Quantum Cryptography from the FLT Modular Machinery: Deuring Quaternion Order Norm Multiplicativity, Cerednik-Drinfeld Hecke Towers, SQIsign Rust Verification, and Neutral-Atom Riesz-6 Blockade in Lean 4" by Xavier Callens, https://doi.org/10.5281/zenodo.23478812, used under its Creative Commons Attribution license (CC-BY); markup removed, otherwise unmodified.