← Session 27 — ii′-5c/5d: Davenport disc + FE-reflection bounds
thinking (624 chars)
Session 027: ii′-5e-i — the γ-gap circles. Per STATE.md's NEXT ACTION:
**ii′-5e-i** — the γ-gap circles (D-068 §2): radius R_k ∈ [4k+5/2, 4k+3] with |R_k − γ| ≥ 1/(6·C0hat(8k+6))-ish for ALL zero ordinates γ, via the ×2-RESCALE TRICK on ii′-4's exists_avoiding_midpoint (at a = 8k+5 on the ×2-scaled ordinate finset; count input = ZeroCountProp on [4k+2, 4k+3] ∪ [4k+3, 4k+4]); then R_k/2 ∈ [2k+5/4, 2k+3/2] ⟹ dist(R_k/2, ℤ) ≥ 1/4.
First I need to look at ii′-4's exists_avoiding_midpoint and exists_zero_avoiding_T in LiContour.lean, and the ×10-rescale trick in LiDisc.lean (exists_collection_radius). Let me read those.
Session 027: ii′-5e-i — the γ-gap circles. Let me first study the existing pigeonhole machinery (ii′-4's `exists_avoiding_midpoint`/`exists_zero_avoiding_T` and 5c's ×10-rescale trick).
tool: Bash
input
{
"command": "grep -n \"exists_avoiding_midpoint\\|exists_zero_avoiding_T\\|ZeroCountProp\\|C0hat\\|zeroWindow\" /d/Python/Quantum/research/lean/NguyenRH1/NguyenRH1/LiContour.lean | head -25",
"description": "Locate the ii\u2032-4 pigeonhole declarations"
}
raw content_json (database row)
[{"type":"thinking","thinking":"Session 027: ii′-5e-i — the γ-gap circles. Per STATE.md's NEXT ACTION:\n\n**ii′-5e-i** — the γ-gap circles (D-068 §2): radius R_k ∈ [4k+5/2, 4k+3] with |R_k − γ| ≥ 1/(6·C0hat(8k+6))-ish for ALL zero ordinates γ, via the ×2-RESCALE TRICK on ii′-4's exists_avoiding_midpoint (at a = 8k+5 on the ×2-scaled ordinate finset; count input = ZeroCountProp on [4k+2, 4k+3] ∪ [4k+3, 4k+4]); then R_k/2 ∈ [2k+5/4, 2k+3/2] ⟹ dist(R_k/2, ℤ) ≥ 1/4.\n\nFirst I need to look at ii′-4's exists_avoiding_midpoint and exists_zero_avoiding_T in LiContour.lean, and the ×10-rescale trick in LiDisc.lean (exists_collection_radius). Let me read those.","signature":""},{"type":"text","text":"Session 027: ii′-5e-i — the γ-gap circles. Let me first study the existing pigeonhole machinery (ii′-4's `exists_avoiding_midpoint`/`exists_zero_avoiding_T` and 5c's ×10-rescale trick)."},{"type":"tool_use","id":"Bash_223","name":"Bash","input":{"command":"grep -n \"exists_avoiding_midpoint\\|exists_zero_avoiding_T\\|ZeroCountProp\\|C0hat\\|zeroWindow\" /d/Python/Quantum/research/lean/NguyenRH1/NguyenRH1/LiContour.lean | head -25","description":"Locate the ii′-4 pigeonhole declarations"},"extra_content":null}]