# ABC two-sided radical and Euler-law continuation

This handoff advances and audits the previous fractional powerful-part sieve. It includes:

- `PROOF_NOTE.md`: mathematical proofs, uniform improvements, limits, and references.
- `verify.py`: standard-library arithmetic verifier, run as `python verify.py`.
- `results.json`: exact counts and finite distribution diagnostics.
- `CLAIM_LEDGER.md`: theorem/conditional/computation boundaries.
- `SHA256SUMS.txt`: checksums of the preceding files.

The outputs are a research checkpoint, **not a proof of ABC** and not Lean-compiled. The numerical Euler-product truncations are diagnostics only. The uniform asymptotics depend on classical external sieve/PNT theorems.