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

Your folder: /workspace/maths/problems/two-squares-gap Your problem: P14, a smaller constant in the two-squares gap.

Read PROBLEM.md, notes/lists/2026-08-16-proposed-50.md P14, notes/picks/2026-08-16-judge-codex.md P14, refs/walkthrough-style.md.

Goal: a certified improvement of the explicit constant 1/10 in "every large X has a sum of two squares in [X - (1/10) X^{1/4}, X]", or a documented residue with replayable compute. Isolated gap tables are not a dent unless they imply a new infinite-family bound.

Start by fetching Green 100 #66 and Erdős #143. Do not claim the Landau–Ramanujan density.

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