← Session 31 — ii′-5f: tight R-bound 10.5/48 (piece 3 + pinch)
thinking (1769 chars)
PASSES in 20s (with just the three sorry warnings)! The fix is confirmed: write the division terms as `c * (b / d)` with explicit parens everywhere in the goal lambdas, matching `mul_left`'s grouping.
So in farGLeftMaj_combo_summable (and everywhere else with the same pattern), I must write `0.433 * (Real.log X / D²)` instead of `0.433 * Real.log X / D²`.
The affected spots in §17: every occurrence of the pattern `0.433 * Real.log (...) / (...)` and `0.886 * Real.log (...) / (...)` in:
1. farGLeftMaj_combo_summable's statement.
2. farGLeftMaj_shift_le's RHS.
3. farGLeftMaj_series_le's hle (tsum_le_tsum with the combo) and heval + hdecomp.
4. The mul_left calls feeding them.
Also — hmm — wait: the hABC goal's C-term: `0.886 * Real.log (Real.log X) / D²` — same fix → `0.886 * (Real.log (Real.log X) / D²)`.
But ALSO the shift_le's tsum_le_tsum (hle in series_le): Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) — its conclusion: ∑'[L] (i), f i ≤ ∑'[L] (i), g i — used as `hle` — fine.
And heval's decomposition e1/e2 with Summable.tsum_add (f := ...)(g := ...) — the f/g ascriptions — need the same paren fixes. And the tsum_mul_left rewrites afterward.
Let me apply a global paren-fix across §17: replace `0.433 * Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2` → `0.433 * (Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2)` and `0.886 * Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2` → `0.886 * (Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2)` — everywhere in the farGLeftMaj region. Also the x-variant (hdecomp uses x instead of ℓ).
Also — IMPORTANT: this same precedence landmine likely affects §18 (right tail) plans — I'll use parens from the start there.
Let me do a careful sed over the farGLeftMaj region.
Fix confirmed. Applying the paren-grouping fix throughout the farGLeftMaj region.
tool: Bash
input
{
"command": "cd D:/Python/Quantum/research/lean/NguyenRH1 && python - <<'EOF'\np = 'NguyenRH1/LiTightR.lean'\nsrc = open(p, encoding='utf-8').read()\nn = 0\nfor a in [\"\u2113\", \"x\"]:\n old1 = f\"0.433 * Real.log (({a} : \u211d) + 14) / ((({a} : \u211d) + 14) + 10) ^ 2\"\n new1 = f\"0.433 * (Real.log (({a} : \u211d) + 14) / ((({a} : \u211d) + 14) + 10) ^ 2)\"\n n += src.count(old1)\n src = src.replace(old1, new1)\n old2 = f\"0.886 * Real.log (Real.log (({a} : \u211d) + 14)) / ((({a} : \u211d) + 14) + 10) ^ 2\"\n new2 = f\"0.886 * (Real.log (Real.log (({a} : \u211d) + 14)) / ((({a} : \u211d) + 14) + 10) ^ 2)\"\n n += src.count(old2)\n src = src.replace(old2, new2)\nopen(p, 'w', encoding='utf-8').write(src)\nprint(\"fixed\", n, \"occurrences\")\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiTightR.lean 2>&1 | head -25",
"description": "Apply paren fix and recompile",
"timeout": 420000
}
raw content_json (database row)
[{"type":"thinking","thinking":"PASSES in 20s (with just the three sorry warnings)! The fix is confirmed: write the division terms as `c * (b / d)` with explicit parens everywhere in the goal lambdas, matching `mul_left`'s grouping.\n\nSo in farGLeftMaj_combo_summable (and everywhere else with the same pattern), I must write `0.433 * (Real.log X / D²)` instead of `0.433 * Real.log X / D²`.\n\nThe affected spots in §17: every occurrence of the pattern `0.433 * Real.log (...) / (...)` and `0.886 * Real.log (...) / (...)` in:\n1. farGLeftMaj_combo_summable's statement.\n2. farGLeftMaj_shift_le's RHS.\n3. farGLeftMaj_series_le's hle (tsum_le_tsum with the combo) and heval + hdecomp.\n4. The mul_left calls feeding them.\n\nAlso — hmm — wait: the hABC goal's C-term: `0.886 * Real.log (Real.log X) / D²` — same fix → `0.886 * (Real.log (Real.log X) / D²)`.\n\nBut ALSO the shift_le's tsum_le_tsum (hle in series_le): Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) — its conclusion: ∑'[L] (i), f i ≤ ∑'[L] (i), g i — used as `hle` — fine.\n\nAnd heval's decomposition e1/e2 with Summable.tsum_add (f := ...)(g := ...) — the f/g ascriptions — need the same paren fixes. And the tsum_mul_left rewrites afterward.\n\nLet me apply a global paren-fix across §17: replace `0.433 * Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2` → `0.433 * (Real.log ((ℓ : ℝ) + 14) / (((ℓ : ℝ) + 14) + 10) ^ 2)` and `0.886 * Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2` → `0.886 * (Real.log (Real.log ((ℓ : ℝ) + 14)) / (((ℓ : ℝ) + 14) + 10) ^ 2)` — everywhere in the farGLeftMaj region. Also the x-variant (hdecomp uses x instead of ℓ).\n\nAlso — IMPORTANT: this same precedence landmine likely affects §18 (right tail) plans — I'll use parens from the start there.\n\nLet me do a careful sed over the farGLeftMaj region.","signature":""},{"type":"text","text":"Fix confirmed. Applying the paren-grouping fix throughout the farGLeftMaj region."},{"type":"tool_use","id":"Bash_222","name":"Bash","input":{"command":"cd D:/Python/Quantum/research/lean/NguyenRH1 && python - <<'EOF'\np = 'NguyenRH1/LiTightR.lean'\nsrc = open(p, encoding='utf-8').read()\nn = 0\nfor a in [\"ℓ\", \"x\"]:\n old1 = f\"0.433 * Real.log (({a} : ℝ) + 14) / ((({a} : ℝ) + 14) + 10) ^ 2\"\n new1 = f\"0.433 * (Real.log (({a} : ℝ) + 14) / ((({a} : ℝ) + 14) + 10) ^ 2)\"\n n += src.count(old1)\n src = src.replace(old1, new1)\n old2 = f\"0.886 * Real.log (Real.log (({a} : ℝ) + 14)) / ((({a} : ℝ) + 14) + 10) ^ 2\"\n new2 = f\"0.886 * (Real.log (Real.log (({a} : ℝ) + 14)) / ((({a} : ℝ) + 14) + 10) ^ 2)\"\n n += src.count(old2)\n src = src.replace(old2, new2)\nopen(p, 'w', encoding='utf-8').write(src)\nprint(\"fixed\", n, \"occurrences\")\nEOF\nexport PATH=\"$HOME/.elan/bin:$PATH\" && lake env lean NguyenRH1/LiTightR.lean 2>&1 | head -25","description":"Apply paren fix and recompile","timeout":420000},"extra_content":null}]