← Session 27 — ii′-5c/5d: Davenport disc + FE-reflection bounds
thinking (1218 chars)
The user wants to work on ii′-5d. Per the session start protocol, I've read STATE.md. Now let me review the relevant materials:
1. The NEXT ACTION section in STATE.md describes ii′-5d in detail:
- FE-reflection of the loose R-bound to σ ∈ [−5/2, 1/2], |t| ≥ 10
- ζ′/ζ(s) = −ζ′/ζ(1−s) − [ΓR′/ΓR(1−s) + ΓR′/ΓR(s)]
- Zero-sums cancel exactly (FE-symmetric zeros)
- ΓR-bracket bound via digamma + StirlingVert
- Conclusion: |R(s)| ≤ |R(1−s)| + C·log|t| + O(1)
- Also: left-plane uniform digamma bound |ψ(w) − log w| ≤ C away from poles (needed in 5e)
- Also (can slip): zeroMult(−2n) = 1 for ALL n (generalize ii′-4c)
2. I should read journal-024 for gotchas mentioned in STATE.md, and D-067 for the design doc.
3. Then look at LiDisc.lean to see what exists (logDeriv_riemannZeta_sub_nearZeros_le), and LiContour.lean for zeroMult_neg_two.
Let me start by reading the relevant files:
- research/journal/session-024.md (gotchas)
- research/derivations/D-067-*.md (design doc §3 left half + §6)
- research/lean/NguyenRH1/NguyenRH1/LiDisc.lean (current state, capstone)
This is a long multi-step task, so I should create a task list. Let me first gather context.
Let me read the files in parallel.
Starting session 025 — ii′-5d. Let me load the design doc, journal gotchas, and the current Lean state.
tool: Bash
input
{
"command": "ls D:/Python/Quantum/research/derivations/ | tail -20 && ls D:/Python/Quantum/research/journal/ | tail -5 && ls D:/Python/Quantum/research/lean/NguyenRH1/NguyenRH1/",
"description": "List derivations, journal, and Lean package files"
}
raw content_json (database row)
[{"type":"thinking","thinking":"The user wants to work on ii′-5d. Per the session start protocol, I've read STATE.md. Now let me review the relevant materials:\n\n1. The NEXT ACTION section in STATE.md describes ii′-5d in detail:\n - FE-reflection of the loose R-bound to σ ∈ [−5/2, 1/2], |t| ≥ 10\n - ζ′/ζ(s) = −ζ′/ζ(1−s) − [ΓR′/ΓR(1−s) + ΓR′/ΓR(s)]\n - Zero-sums cancel exactly (FE-symmetric zeros)\n - ΓR-bracket bound via digamma + StirlingVert\n - Conclusion: |R(s)| ≤ |R(1−s)| + C·log|t| + O(1)\n - Also: left-plane uniform digamma bound |ψ(w) − log w| ≤ C away from poles (needed in 5e)\n - Also (can slip): zeroMult(−2n) = 1 for ALL n (generalize ii′-4c)\n\n2. I should read journal-024 for gotchas mentioned in STATE.md, and D-067 for the design doc.\n\n3. Then look at LiDisc.lean to see what exists (logDeriv_riemannZeta_sub_nearZeros_le), and LiContour.lean for zeroMult_neg_two.\n\nLet me start by reading the relevant files:\n- research/journal/session-024.md (gotchas)\n- research/derivations/D-067-*.md (design doc §3 left half + §6)\n- research/lean/NguyenRH1/NguyenRH1/LiDisc.lean (current state, capstone)\n\nThis is a long multi-step task, so I should create a task list. Let me first gather context.\n\nLet me read the files in parallel.","signature":""},{"type":"text","text":"Starting session 025 — ii′-5d. Let me load the design doc, journal gotchas, and the current Lean state."},{"type":"tool_use","id":"Bash_1","name":"Bash","input":{"command":"ls D:/Python/Quantum/research/derivations/ | tail -20 && ls D:/Python/Quantum/research/journal/ | tail -5 && ls D:/Python/Quantum/research/lean/NguyenRH1/NguyenRH1/","description":"List derivations, journal, and Lean package files"},"extra_content":null}]