← Session 8 — Regroup + R-004 finite-height Li theorem; resources atlas ingested
thinking (685 chars)
A resources folder with 29 derivation notes. Most relevant to the current E-021 work: "Lagarias' Positivity.txt", "Li's Criterion — Full Detail.txt", "Stieltjes Constants - Laurent Expansion at s equal 1.txt", "Hasse's Globally Convergent Series.txt", "Mertens Criterion.txt", "Robin & Lagarias.txt". The user says "helpful information — you might need it". Likely relevant to the η/Stieltjes computation and the finite-height theorem (3.5-3.8). Let me read the most relevant ones first (Lagarias' Positivity, Li's Criterion, Stieltjes Constants, Hasse), then the rest. I should read all of them per the user request — that's ~400KB total. Let me read the key ones in parallel batches.
29 files there. Reading the ones most relevant to the current Li-coefficient work first.
tool: Read ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\resources\\Lagarias' Positivity.txt"
}
result 2026-08-19 06:06:36Z → 2026-08-27 18:03:28Z
{
"type": "text",
"file": {
"filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiClosed.lean",
"content": "/-\nLiClosed.lean \u2014 tier ii\u2032-7: THE CLOSED finite-height Li theorem (R-004\nendpoint, D-062 \u00a74). `lambda_pos_finite_height_closed`: \u03bb_n > 0 for all\n1 \u2264 n \u2264 N\u2081 = (3\u00d710\u00b9\u00b2\u22121)\u00b2 \u2248 9\u00d710\u00b2\u2074 from the SEVEN declared hypotheses:\nthe two computational certificates (Platt\u2013Trudgian `RHUpTo`; the finite\nLi verification `LiVerifiedUpTo` \u2014 E-011/E-015 to 3000 + Johansson 2015\n\u00a7 4.2 to 10\u2075) and the five analytic perimeter Props (Trudgian N(T)/S(T):\n`ZeroCountProp` unit-window, `ZeroCountProp2` two-unit,\n`ZeroCountGlobalProp` global; the Platt-class zero-location certificate\n`NoLowZeros`; the M\u2080 interval certificate `MZeroProp`) \u2014 the session-012\nnamed analytic hypothesis `SfBoundProp` is now PROVED (tier ii\u2032-6,\nLiSideBounds).\n-/\nimport Mathlib\nimport NguyenRH1.LiBasePoints\nimport NguyenRH1.LiSideBounds\n\nopen Zeta23 Complex Filter Topology\n\nnamespace NguyenRH1\n\n/-- **THE CLOSED FINITE-HEIGHT LI THEOREM** (R-004, ii\u2032-7 endpoint):\n\u03bb_n > 0 for ALL 1 \u2264 n \u2264 N\u2081 = (3\u00d710\u00b9\u00b2\u22121)\u00b2 \u2248 9\u00d710\u00b2\u2074, from the SEVEN\ndeclared hypotheses (two computational certificates + five analytic\nperimeter Props). The session-012 named analytic hypothesis\n`SfBoundProp` is discharged by ii\u2032-6's `sfBoundProp`. -/\ntheorem lambda_pos_finite_height_closed\n (hRH : RHUpTo (3 * 10 ^ 12)) (hfinite : LiVerifiedUpTo (10 ^ 5))\n (hZC : ZeroCountProp) (hZC2 : ZeroCountProp2) (hZCG : ZeroCountGlobalProp)\n (hNLZ : NoLowZeros) (hMZ : MZeroProp) :\n \u2200 n : \u2115, 1 \u2264 n \u2192 (n : \u211d) \u2264 (3 * 10 ^ 12 - 1 : \u211d) ^ 2 \u2192\n 0 < (liCoeff n).re :=\n lambda_pos_finite_height_verified hRH hfinite\n (sfBoundProp hRH hZC hZC2 hZCG hNLZ hMZ)\n\nend NguyenRH1",
"numLines": 36,
"startLine": 1,
"totalLines": 36
}
}
tool: Read
input
{
"file_path": "D:\\Python\\Quantum\\research\\resources\\Li's Criterion \u2014 Full Detail.txt"
}
raw content_json (database row)
[{"type":"thinking","thinking":"A resources folder with 29 derivation notes. Most relevant to the current E-021 work: \"Lagarias' Positivity.txt\", \"Li's Criterion — Full Detail.txt\", \"Stieltjes Constants - Laurent Expansion at s equal 1.txt\", \"Hasse's Globally Convergent Series.txt\", \"Mertens Criterion.txt\", \"Robin & Lagarias.txt\". The user says \"helpful information — you might need it\". Likely relevant to the η/Stieltjes computation and the finite-height theorem (3.5-3.8). Let me read the most relevant ones first (Lagarias' Positivity, Li's Criterion, Stieltjes Constants, Hasse), then the rest. I should read all of them per the user request — that's ~400KB total. Let me read the key ones in parallel batches.","signature":""},{"type":"text","text":"29 files there. Reading the ones most relevant to the current Li-coefficient work first."},{"type":"tool_use","id":"Read_123","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\resources\\Lagarias' Positivity.txt"},"extra_content":null},{"type":"tool_use","id":"Read_124","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\resources\\Li's Criterion — Full Detail.txt"},"extra_content":null}]