[{"type":"thinking","thinking":"Oops — my edit replaced the opening and left \"E-021 2026-08-19: **A = 0.9...\" — wait, the old_string ended with \"TIGHTENED by\" and new_string ends with \"TIGHTENED by\", so the continuation \"E-021 2026-08-19...\" follows. But the original had \"TIGHTENED by\\nE-021...\" on the next line. My new_string ends with \"TIGHTENED by\" (no newline), so the file now has \"...TIGHTENED by\\nE-021...\" — preserved. Good.\n\nNow D-049 erratum and D-050 note.","signature":""},{"type":"text","text":"Now the D-049/D-050 errata for T-3."},{"type":"tool_use","id":"Edit_37","name":"Edit","input":{"file_path":"D:\\Python\\Quantum\\research\\derivations\\D-049-valley-theorem-proof.md","new_string":"# D-049 — The valley theorem: full write-up (B1–B3 closed)\nDate: 2026-08-19 | Session: 008 | Task: valley theorem rigor (D-048 B1–B3)\nStatus: **ERRATUM (2026-08-19, D-054 task 4.3b).** Upper bounds stand\n(with m_γ fix, F11); lower bounds BROKEN as written:\n (F9) B1 lower: Lemma D's 4C₀/g_γ² term was dropped in the assembly;\n with g_γ ≥ 4/a it contributes Θ(C₀a²), so the method yields a\n CONSTANT floor ~0.65–0.9, not 1 − 1/(2a) − C(1+log γ)/a². Repair via\n node-killing test functions or averaged-density lemma = task 4.5c.\n (F10) B3: correct profile argument is sinc²((z−γ)a), not\n sinc²((z−γ)a/2) — the printed envelope is an overclaim.\n (F11) B1 upper: K(γ,γ) ≤ 1/m_γ under RH alone; \"= 1\" uses\n Platt–Trudgian simplicity (γ ≤ T₀).\n (F12, D-050) δ_crit = π/(2a): existence of a negative direction for\n δ > π/(2a) proved; the converse (\"iff\") open.\n Form-domain note: v₀ IS admissible via the zero-side domain\n (Σ m_γ|v̂₀(γ')|² converges); the operator-form/zero-side domain\n identification = write-up item (task 4.5d). Sign slip: localization\n at +γ needs v₀ = e^{−iγx} with v̂(z) = ∫v e^{izx}.\n Measured phenomenology (E-022 family) unaffected.\nOriginal status: complete under RH; finite-height version modulo named estimate\nT2 (Lemma T). Tag: [PROVED-CONDITIONAL(RH)] main form;\n[PROVED-CONDITIONAL(RH-to-T₀) modulo T2] finite form.\nSupersedes D-048 (skeleton).","old_string":"# D-049 — The valley theorem: full write-up (B1–B3 closed)\nDate: 2026-08-19 | Session: 008 | Task: valley theorem rigor (D-048 B1–B3)\nStatus: complete under RH; finite-height version modulo named estimate\nT2 (Lemma T). Tag: [PROVED-CONDITIONAL(RH)] main form;\n[PROVED-CONDITIONAL(RH-to-T₀) modulo T2] finite form.\nSupersedes D-048 (skeleton).","replace_all":false},"extra_content":null}]