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

Your folder: /workspace/maths/problems/sidon-second-term Your problem: P07, the second term for Sidon subsets of [N].

Read PROBLEM.md, notes/lists/2026-08-16-proposed-50.md P07, notes/picks/2026-08-16-judge-codex.md P07, refs/walkthrough-style.md.

Goal: a strict improvement of either F(N) >= sqrt(N)+O(1) or F(N) <= sqrt(N)+0.98183 N^{1/4}+O(1) that holds for infinitely many N, with an independent verifier. Isolated small-N tables are not a dent.

Start by fetching Green 100 #31 and the current Erdos #30 status. Do not claim Erdos-Turan.

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