← Session 13 — Phase 4 completion + draft.tex author block
Now restoring the R-004 tag and updating the ledger.
tool: Edit
input
{
"file_path": "D:\\Python\\Quantum\\research\\results\\R-004-finite-height-li-theorem.md",
"new_string": "Tag: **[PROVED-CONDITIONAL(computational RH-to-height-T\u2080; computational\nfinite verification)]** \u2014 R-bound FULLY TRACED 2026-08-19 (D-056,\ntask 4.5a: reference-point method, A = 6.0, B\u2080 = 40, digamma\nremainder 1.2/|w|\u00b2 proved; E-028 verified, 17\u00d7 slack); N\u2080 = 60 000\n(8.3\u00d7 overlap with Misguich\u2013Voros). M\u2080 remains grid-verified\n(E-023 S1; enters as an additive ~53). Margin convexity: grid-verified\n(E-028), symbolic proof = task 4.5b.\nHistory: tag downgraded then restored same day (D-054 erratum: broken\nD-039/D-036-\u00a71 proofs; D-056 repairs).",
"old_string": "Tag: **[PROVED-CONDITIONAL(computational RH-to-height-T\u2080; computational\nfinite verification; R-bound constants A = 0.9, B\u2080 = 1.0 numerically\nmeasured (E-021, 20\u201330% margin) \u2014 analytic tracing incomplete)]**\nERRATUM (2026-08-19, D-054, task 4.3b): the D-039 digamma proof is\nbroken (Binet tail constant for |W| \u2273 35; recurrence Cauchy estimate\nmisused) and D-036 \u00a71's far-sum bound gives O(|t| log t), not the\ntraced O(log t) \u2014 the reference-point trick is missing. The bound is\ntrue (measured); the tracing is repair task 4.5a. M\u2080 remains\ngrid-verified (E-023 S1; additive ~53). Margins (67 705 at N\u2080,\n2.46\u00d710\u00b2\u2076 at N\u2081) absorb any plausible constant error \u2014 the statement\nis robust.",
"replace_all": false
}
raw content_json (database row)
[{"type":"text","text":"Now restoring the R-004 tag and updating the ledger."},{"type":"tool_use","id":"Edit_152","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\results\\R-004-finite-height-li-theorem.md","new_string":"Tag: **[PROVED-CONDITIONAL(computational RH-to-height-T₀; computational\nfinite verification)]** — R-bound FULLY TRACED 2026-08-19 (D-056,\ntask 4.5a: reference-point method, A = 6.0, B₀ = 40, digamma\nremainder 1.2/|w|² proved; E-028 verified, 17× slack); N₀ = 60 000\n(8.3× overlap with Misguich–Voros). M₀ remains grid-verified\n(E-023 S1; enters as an additive ~53). Margin convexity: grid-verified\n(E-028), symbolic proof = task 4.5b.\nHistory: tag downgraded then restored same day (D-054 erratum: broken\nD-039/D-036-§1 proofs; D-056 repairs).","old_string":"Tag: **[PROVED-CONDITIONAL(computational RH-to-height-T₀; computational\nfinite verification; R-bound constants A = 0.9, B₀ = 1.0 numerically\nmeasured (E-021, 20–30% margin) — analytic tracing incomplete)]**\nERRATUM (2026-08-19, D-054, task 4.3b): the D-039 digamma proof is\nbroken (Binet tail constant for |W| ≳ 35; recurrence Cauchy estimate\nmisused) and D-036 §1's far-sum bound gives O(|t| log t), not the\ntraced O(log t) — the reference-point trick is missing. The bound is\ntrue (measured); the tracing is repair task 4.5a. M₀ remains\ngrid-verified (E-023 S1; additive ~53). Margins (67 705 at N₀,\n2.46×10²⁶ at N₁) absorb any plausible constant error — the statement\nis robust.","replace_all":false},"extra_content":null}]