This arXiv preprint (v1, May 2026) introduces Lean-QEC, the first machine-checked formalization in Lean 4 of stabilizer-code theory that certifies code distance for industrially relevant qLDPC families. The work directly confronts the NP-hard barrier of distance verification, which has long forced reliance on unverified solvers or non-scalable hand proofs. By encoding the distance condition as a verified Boolean satisfiability reduction and flattening representations via BitVec and compact error-location variables, the pipeline delivers Lean-checked proofs for codes such as the [[90, 8, 10]] and [[70, 6, 9]] bivariate bicycle instances—sizes that matter for near-term hardware roadmaps. Unlike typical theoretical papers, this is explicitly a preprint rather than peer-reviewed work; the authors note external SAT solving scales to 144 qubits while the Lean kernel handles smaller instances. What original coverage often misses is the deeper linkage to the broader verifiable-quantum-hardware imperative: without formally certified distance, claims of fault tolerance remain provisional, echoing past gaps in classical hardware verification before tools like Coq and Lean became standard. Related efforts include the 2024 IBM-led bivariate bicycle code constructions (Nature, 2024) that supplied the code families now formalized here, and the 2023 arXiv survey on qLDPC decoding thresholds (arXiv:2305.09745), which highlighted exactly the trust deficit Lean-QEC targets. Limitations remain evident: the approach still depends on external SAT solvers for larger instances, and full end-to-end verification of decoders or physical error models is left for future library extensions. The synthesis reveals a pattern across quantum engineering—formal methods are migrating from classical to quantum precisely where hardware claims require cryptographic-grade assurance rather than empirical benchmarking.