# 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

Article · Xavier Callens

- Archive id: doi:10.5281/zenodo.23478812
- Published: 2026-10-19
- Venue: Zenodo (CERN European Organization for Nuclear Research)
- DOI: https://doi.org/10.5281/zenodo.23478812
- Citations: 0
- Source URL: https://doi.org/10.5281/zenodo.23478812
- Provenance: openalex

## 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 reproduced under CC-BY (publisher license, via OpenAlex)._

Topics: [Neutral-Atom & Trapped-Ion Quantum Computing](https://space-kitty.com/topics/atoms-and-ions)

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