Hey Codex,

This folder claims a verified solution of Erdős Problem #1189 (see problem.md). Please verify it end to end — trust nothing you don't check:

1. Read problem.md (the exact Erdős problem). Open Research/FinalClaimsAudit.lean inside the pinned project; workspace/shared/LEAN_REPRODUCE.md documents the exact steps. The count theorem carries the published BBMST enumeration as explicit named hypotheses (BBMSTLowerDatum/BBMSTUpperHypothesis); the max/min/reciprocal/divisor theorems have no external hypotheses. and judge for yourself that the formal statement faithfully encodes the problem — quantifiers, ranges, and edge cases. check_answer/README.md documents the encoding choices; be skeptical and check them.
2. Reproduce the verification from a cold start by running, from this folder:
   mkdir erdos1189-lean && cd erdos1189-lean && tar -xzf ../workspace/shared/erdos1189_lean_source.tar.gz
   lake exe cache get && lake build
   lake env lean Research/FinalClaimsAudit.lean
   cd ../check_answer && cargo test --release && cargo run --release -- fixtures/classic_k5.txt
3. Scan the proof sources yourself for escape hatches (sorry, admit, added axioms, native_decide) — scoped to the proof project, excluding .lake build dirs.
4. The axiom audit must list only [propext, Classical.choice, Quot.sound]. Confirm the build/verifier output shows it.

Then give your verdict: does this bundle contain a complete, faithful, kernel-checked solution of the stated problem?
