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

Your folder: /workspace/maths/problems/cosine-zeros Your problem: P16, zeros of integer cosine sums.

Read PROBLEM.md, notes/lists/2026-08-16-proposed-50.md P16, notes/picks/2026-08-16-judge-codex.md P16, refs/walkthrough-style.md.

Goal: a certified improvement of either the universal lower bound (currently (log log n)^{1-o(1)}) or the construction-side upper barrier (O(n^{2/3} log^{2/3} n)), with an independent verifier. Isolated root tables are not a dent.

Start by fetching Green 100 #82 and Bedert arXiv:2312.04454. Adjacent work tonight: problems/chowla-cosine has an explicit K(n) >= n^{1/7}/18; do not overwrite that folder.

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