Read /workspace/maths/notes/supergrok-2026-08-17/house.md and follow it.

Your folder: /workspace/maths/problems/two-smooth-summands Your problem: P12, two smooth summands for every integer.

Read PROBLEM.md, notes/lists/2026-08-16-proposed-50.md P12, notes/picks/2026-08-16-judge-codex.md P12, refs/walkthrough-style.md.

Goal: a certified finite residue cover or an explicit ε with a checkable covering template. Isolated small-N tables are not a dent.

Start by fetching Green 100 #59 and Erdős #334.

Work until you have a verified dent or a documented residue. Write ATTACK.md as you go. Finish with WALKTHROUGH.md and RESEARCH.md.