← Session 13 — Phase 4 completion + draft.tex author block
thinking (1065 chars)
Now update NGUYEN.md ledger #6 tag and add Phase 4 task states. Also add 4.5a–d to the checklist. Let me do NGUYEN.md edits now (part of fixes), then move to E-027.
Ledger #6 in NGUYEN.md:
"| 6 | Explicit finite-height Li theorem: λ_n > 0 for all n ≤ N₁ = (T₀−1)² ≈ 9.0×10²⁴ (T₀ = 3×10¹² Platt–Trudgian); conservative window N₁* = 2.73×10²¹; first assembled explicit chain (S_∞ elementary lower bound + traced contour constants + margin convexity + finite verification) | [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification)] (digamma proved D-039) | R-004, D-037, D-039, E-023 |"
Update tag: [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification; R-bound constants measured (E-021), tracing open → 4.5a)] (D-054 erratum: D-039 proof broken).
Also Phase 4 checklist: 4.1 [x] (D-052), 4.2 [x], 4.3 [~] (4.3a gate pass D-053; 4.3b independent review D-054 — tags downgraded, repairs opened), 4.4 pending E-027. Add 4.5a–d tasks. I'll finalize NGUYEN.md at session end (after E-027) to include 4.4 status. But the ledger tag fix should go now.
Updating the NGUYEN.md ledger tag for #6 (erratum), then moving to E-027.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\NGUYEN.md",
"new_string": "| 6 | Explicit finite-height Li theorem: \u03bb_n > 0 for all n \u2264 N\u2081 = (T\u2080\u22121)\u00b2 \u2248 9.0\u00d710\u00b2\u2074 (T\u2080 = 3\u00d710\u00b9\u00b2 Platt\u2013Trudgian); conservative window N\u2081* = 2.73\u00d710\u00b2\u00b9; first assembled explicit chain (S_\u221e elementary lower bound + traced contour constants + margin convexity + finite verification) | [PROVED-CONDITIONAL(computational RH-to-T\u2080; finite verification; R-bound constants E-021-measured \u2014 analytic tracing open \u2192 task 4.5a)] (D-054 erratum 2026-08-19: D-039 proof broken, bound true) | R-004, D-037, D-054, E-023 |",
"old_string": "| 6 | Explicit finite-height Li theorem: \u03bb_n > 0 for all n \u2264 N\u2081 = (T\u2080\u22121)\u00b2 \u2248 9.0\u00d710\u00b2\u2074 (T\u2080 = 3\u00d710\u00b9\u00b2 Platt\u2013Trudgian); conservative window N\u2081* = 2.73\u00d710\u00b2\u00b9; first assembled explicit chain (S_\u221e elementary lower bound + traced contour constants + margin convexity + finite verification) | [PROVED-CONDITIONAL(computational RH-to-T\u2080; finite verification)] (digamma proved D-039) | R-004, D-037, D-039, E-023 |",
"replace_all": false
}
raw content_json (database row)
[{"type":"thinking","thinking":"Now update NGUYEN.md ledger #6 tag and add Phase 4 task states. Also add 4.5a–d to the checklist. Let me do NGUYEN.md edits now (part of fixes), then move to E-027.\n\nLedger #6 in NGUYEN.md:\n\"| 6 | Explicit finite-height Li theorem: λ_n > 0 for all n ≤ N₁ = (T₀−1)² ≈ 9.0×10²⁴ (T₀ = 3×10¹² Platt–Trudgian); conservative window N₁* = 2.73×10²¹; first assembled explicit chain (S_∞ elementary lower bound + traced contour constants + margin convexity + finite verification) | [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification)] (digamma proved D-039) | R-004, D-037, D-039, E-023 |\"\n\nUpdate tag: [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification; R-bound constants measured (E-021), tracing open → 4.5a)] (D-054 erratum: D-039 proof broken).\n\nAlso Phase 4 checklist: 4.1 [x] (D-052), 4.2 [x], 4.3 [~] (4.3a gate pass D-053; 4.3b independent review D-054 — tags downgraded, repairs opened), 4.4 pending E-027. Add 4.5a–d tasks. I'll finalize NGUYEN.md at session end (after E-027) to include 4.4 status. But the ledger tag fix should go now.","signature":""},{"type":"text","text":"Updating the NGUYEN.md ledger tag for #6 (erratum), then moving to E-027."},{"type":"tool_use","id":"Edit_49","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\NGUYEN.md","new_string":"| 6 | Explicit finite-height Li theorem: λ_n > 0 for all n ≤ N₁ = (T₀−1)² ≈ 9.0×10²⁴ (T₀ = 3×10¹² Platt–Trudgian); conservative window N₁* = 2.73×10²¹; first assembled explicit chain (S_∞ elementary lower bound + traced contour constants + margin convexity + finite verification) | [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification; R-bound constants E-021-measured — analytic tracing open → task 4.5a)] (D-054 erratum 2026-08-19: D-039 proof broken, bound true) | R-004, D-037, D-054, E-023 |","old_string":"| 6 | Explicit finite-height Li theorem: λ_n > 0 for all n ≤ N₁ = (T₀−1)² ≈ 9.0×10²⁴ (T₀ = 3×10¹² Platt–Trudgian); conservative window N₁* = 2.73×10²¹; first assembled explicit chain (S_∞ elementary lower bound + traced contour constants + margin convexity + finite verification) | [PROVED-CONDITIONAL(computational RH-to-T₀; finite verification)] (digamma proved D-039) | R-004, D-037, D-039, E-023 |","replace_all":false},"extra_content":null}]