Hey Codex,

This folder claims a verified solution of Erdős Problem #415 (see problem.md). Please verify it end to end — trust nothing you don't check:

1. Read problem.md (the exact Erdős problem). Open workspace/experiments/experiment_1_formalize_patterns/lean/Research/Basic.lean (pinned F, patterns) 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:
   cd workspace/experiments/experiment_3_adjacent_equal_density/lean
   lake exe cache get && lake build
   cd ../../.. && grep -RnE '\b(sorry|admit)\b' workspace/experiments/experiment_3_adjacent_equal_density/lean --include='*.lean' && echo ESCAPE-FOUND || echo CLEAN
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?
