# Reproducing the unconditional BBMST lower formalization

Archive: `erdos1189_bbmst_lower_lean_source.tar.gz` (Lean 4.31.0, pinned Mathlib manifest).

```bash
mkdir bbmst-lower && cd bbmst-lower
tar -xzf ../erdos1189_bbmst_lower_lean_source.tar.gz
lake exe cache get
LEAN_NUM_THREADS=8 lake build
lake env lean Research/BBMSTLowerAudit.lean
```

Key declarations:

- `BBMSTLower.explicitLowerDatum`
- `BBMSTLower.exists_eventual_omegaLowerDatum`
- `BBMSTLower.eventually_bbmstScale_le_omegaExponent`
- `BBMSTLower.eventually_log_irreducible_count_lower`

The last theorem states an unconditional `exp(Omega(k^(3/2)/sqrt(log k)))` lower bound for the actual strong irreducible-modulus-set count along the explicit dense frame sizes. The finite datum has fiber bound one. `bbmst_lower_build.log` records a full build; `bbmst_lower_axioms.log` records that only standard Mathlib axioms (`propext`, `Classical.choice`, `Quot.sound`) occur.

