← Session 31 — ii′-5f: tight R-bound 10.5/48 (piece 3 + pinch)
thinking (4468 chars)
`Summable.add` is NOT the constructor-style lemma I assumed — it's `Summable.add (hf : Summable f) (hg : Summable g) : Summable (f + g)` — so `apply Summable.add` treats it as a two-arg function producing Summable (f+g): the apply leaves TWO goals (f's summable and g's). My `apply Summable.add (fun i => ...)` passed the FUNCTION as the first arg — wrong: Summable.add's first arg is hf : Summable f (a PROOF), with f implicit. So: `apply Summable.add` leaves two goals f and g's summability with f,g as metavars unified by the goal — but the goal's function (A+B+C-lambda) vs (f+g) — the SAME Pi.add unification issue.
The right pattern: `exact ((hA).add hB).add hC` where each .add is at the PROOF level: (tail14_inv_add_sq_summable.mul_left _).add (tail14_log_div_add_sq_summable.mul_left _) : Summable ((fun c0·A) + (fun c1·B)) — then .add (tail14_loglog...mul_left _) : Summable ((c0A+c1B)+c2C) — the TYPE is Summable (Pi.add (Pi.add A B) C) — vs the goal Summable (fun i => (A i + B i) + C i) — Pi.add applied twice: ((A+B)+C) i = (A i + B i) + C i ✓ DEFEQ — should unify when given as `exact`. The earlier failure was from `apply Summable.add` + `exact` splitting — the `exact` alone should work if the unification succeeds. The timeout at 3217 (isDefEq) is at farGLeftMaj_summable presumably — meaning even the EXACT approach hits isDefEq timeouts elsewhere.
WAIT — hold on. Let me reconsider the whole area: the timeouts at 3217/3241/3179 with isDefEq/whnf — and earlier at 3156/3157 — ALL in the farGLeftMaj region. Something about farGLeftMaj itself. farGLeftMaj's body: `if 14 ≤ ℓ then 4.5 * C0hat ((ℓ : ℝ) + 1) / (10 + (ℓ : ℝ)) ^ 2 else 0` — contains `C0hat` (a def) — and `((ℓ : ℝ) + 1)`... When Lean elaborates `farGLeftMaj (ℓ + 14)` in the types of the shift lemmas, and does whnf/isDefEq on them, it unfolds C0hat (which has Real.log terms) — fine.
Hmm — could the REAL culprit be `two_le_C0hat`/`farGLeftMaj_nonneg`'s positivity call?? farGLeftMaj_nonneg uses `positivity` after two_le_C0hat — maybe positivity chokes?
Let me BISECT: temporarily comment out the farGLeftMaj section (from `def farGLeftMaj` to `farGLeftMaj_series_le`) and the farGLeft_le, and see if the rest compiles + how long. Actually — faster: check the timeout locations precisely: 3157 (combo_summable), 3179 (farGLeftMaj_summable), 3217 (series_le's hsplit area), 3241 (series_le's hdecomp area).
New idea: the `summable_nat_add_iff` in farGLeftMaj_summable and in tail14_inv_add_sq_summable/tail11 bricks — those worked before. The difference: farGLeftMaj has the IF. When `.mp farGLeftMaj_shift_summable` unifies `Summable (fun n => farGLeftMaj (n + 14))` with `Summable farGLeftMaj` — isDefEq between fun n => farGLeftMaj (n+14) and fun n => farGLeftMaj (n+14)... trivial. whnf timeout at 3179 (farGLeftMaj_summable) — maybe `.mp` vs `.mpr` direction?! summable_nat_add_iff (k) : Summable (fun n => f (n + k)) ↔ Summable f — `.mp : Summable (fun n => f (n+k)) → Summable f` ✓ that's what I want. whnf timeout — the unification of farGLeftMaj_shift_summable's TYPE (Summable fun ℓ => farGLeftMaj (ℓ+14)) against .mp's domain — unfolding farGLeftMaj (ℓ+14) vs f (n+14) with f := farGLeftMaj — needs farGLeftMaj (ℓ+14) ≡ farGLeftMaj (n+14) — whnf on the IF with metavariable ℓ vs n... should be instant.
I'm clearly missing something environmental. Let me look at 3217:8 and 3241:4 content directly, and also check whether farGLeftMaj_nonneg's positivity is the issue by testing a minimal snippet. Actually — let me check the TIME: each `lake env lean` run on this 3300-line file takes ~2-4 min. I've done ~15 runs. The bisection will take several more. Let me be smart: extract the problematic region into a scratch file with the same imports and iterate there — NO, the file dependencies (farGLeftMaj needs farGLeft_fiber_le etc.) — but for the SUMMABILITY section only the bricks + C0hat + farGLeftMaj are needed... still need the whole file context.
Alternative theory — the `Summable.tsum_le_tsum farGLeftMaj_shift_le farGLeftMaj_shift_summable farGLeftMaj_combo_summable` call (hle at series_le): Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) (hf : Summable f) (hg : Summable g) — with f = farGLeftMaj(·+14) and g = combo-lambda — and farGLeftMaj_shift_le's type: ∀ ℓ, farGLeftMaj (ℓ+14) ≤ combo-lambda ℓ ✓. If farGLeftMaj_combo_summable is broken/missing (kernel unknown), the hle call would error not timeout...
Let me look at the exact current error locations.
Let me look at the exact timeout locations to bisect the pathology.
tool: Read ok
input
{
"file_path": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiTightR.lean",
"offset": 3166,
"limit": 100
}
result 2026-08-24 20:01:01Z → 2026-08-25 05:01:01Z
{
"type": "text",
"file": {
"filePath": "D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiSkeleton.lean",
"content": "theorem marginTilde_convex (F : \u211d \u2192 \u211d) (hF : ContDiffOn \u211d 2 F (Set.Ioi 1))\n (h\u03c8 : \u2200 T : \u211d, Real.sqrt 20 + 1 \u2264 T \u2192\n deriv (deriv F) T - deriv F T / (T - 1) < 0) :\n ConvexOn \u211d (Set.Ici 20) (marginTilde F) := by\n have hCDfull : ContDiffOn \u211d 2 (marginTilde F) (Set.Ioi 20) := by\n rw [marginTilde_eq_expanded F]\n exact contDiffOn_marginExpanded F hF\n apply convexOn_of_deriv2_nonneg (convex_Ici 20)\n \u00b7 rw [marginTilde_eq_expanded F]\n exact continuousOn_marginExpanded F hF\n \u00b7 rw [interior_Ici]\n exact hCDfull.differentiableOn (by norm_num)\n \u00b7 rw [interior_Ici]\n exact ((hCDfull.deriv_of_isOpen (m := 1) isOpen_Ioi (by norm_num))).differentiableOn\n one_ne_zero\n \u00b7 intro n hn\n rw [interior_Ici] at hn\n have hn20 : 20 < n := hn\n have hn0 : (0 : \u211d) < n := by linarith\n have hn4 : (0 : \u211d) < 4 * n := by linarith\n have hTn : Real.sqrt 20 + 1 \u2264 Real.sqrt n + 1 := by\n have h := Real.sqrt_le_sqrt (show (20 : \u211d) \u2264 n by linarith)\n linarith\n -- diff-fact helpers\n have hdd : \u2200 {P : \u211d \u2192 \u211d}, ContDiffOn \u211d 2 P (Set.Ioi 20) \u2192\n DifferentiableAt \u211d (deriv P) n := fun hCD =>\n ((hCD.deriv_of_isOpen (m := 1) isOpen_Ioi (by norm_num)).differentiableOn\n one_ne_zero).differentiableAt (Ioi_mem_nhds hn20)\n have hev : \u2200 {P : \u211d \u2192 \u211d}, ContDiffOn \u211d 2 P (Set.Ioi 20) \u2192\n (\u2200\u1da0 m in \ud835\udcdd n, DifferentiableAt \u211d P m) := fun hCD => by\n filter_upwards [Ioi_mem_nhds hn20] with m hm\n exact (hCD.differentiableOn (by norm_num)).differentiableAt (Ioi_mem_nhds hm)\n -- unweighted composition bundles\n have hCDFc : ContDiffOn \u211d 2 (fun m => F (Real.sqrt m + 1)) (Set.Ioi 20) :=\n hF.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift_Ioi1\n have hCDTL1c : ContDiffOn \u211d 2\n (fun m => (fun t => t * Real.log (t + 2)) (Real.sqrt m + 1)) (Set.Ioi 20) :=\n contDiffOn_TL1.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDTL2c : ContDiffOn \u211d 2\n (fun m => (fun t => t * Real.log (Real.log (t + 2))) (Real.sqrt m + 1))\n (Set.Ioi 20) :=\n contDiffOn_TL2.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDL1sqc : ContDiffOn \u211d 2\n (fun m => (fun t => Real.log (t + 2) ^ 2) (Real.sqrt m + 1)) (Set.Ioi 20) :=\n contDiffOn_L1sq.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDL1L2c : ContDiffOn \u211d 2\n (fun m => (fun t => Real.log (t + 2) * Real.log (Real.log (t + 2)))\n (Real.sqrt m + 1)) (Set.Ioi 20) :=\n contDiffOn_L1L2.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDL2sqc : ContDiffOn \u211d 2\n (fun m => (fun t => Real.log (Real.log (t + 2)) ^ 2) (Real.sqrt m + 1))\n (Set.Ioi 20) :=\n contDiffOn_L2sq.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDL1c : ContDiffOn \u211d 2\n (fun m => (fun t => Real.log (t + 2)) (Real.sqrt m + 1)) (Set.Ioi 20) :=\n contDiffOn_L1.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDL2c : ContDiffOn \u211d 2\n (fun m => (fun t => Real.log (Real.log (t + 2))) (Real.sqrt m + 1))\n (Set.Ioi 20) :=\n contDiffOn_L2.comp contDiffOn_sqrt_shift mapsTo_sqrt_shift\n have hCDIIM : ContDiffOn \u211d 2 IIMaj (Set.Ioi 20) := by\n have hId : IIMaj = fun m => psiTilde (Real.sqrt m) :=\n funext fun m => IIMaj_eq_psiTilde_sqrt m\n rw [hId]\n exact (psiTilde_contDiff.contDiffOn).comp\n (contDiffOn_id.sqrt (fun x hx => by\n have h : 20 < x := hx\n exact ne_of_gt (by linarith : (0 : \u211d) < x))) (Set.mapsTo_univ _ _)\n -- piece values\n have vS : deriv (deriv fun m => (1/2)*m*Real.log m +\n (lagariasC1 - Real.eulerMascheroniConstant/2)*m - 4) n = 1/(2*n) :=\n marginS_deriv2 _ hn0\n have vF : deriv (deriv (mFblock F)) n =\n (-2) * (psiOf F (Real.sqrt n + 1) / (4 * n)) := by\n unfold mFblock\n rw [deriv2_const_mul (-2) (hdd hCDFc) (hev hCDFc),\n chain_rule_sqrt_shift_on F (le_refl 1) hF n hn0, \u2190 psiOf_sqrt_rel]\n have vTL1 : deriv (deriv mTL1b) n = (-((8/3)*0.433 + 42)) *\n (psiOf (fun t => t * Real.log (t + 2)) (Real.sqrt n + 1) / (4 * n)) := by\n unfold mTL1b\n rw [deriv2_const_mul _ (hdd hCDTL1c) (hev hCDTL1c),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_TL1 n hn0, \u2190 psiOf_sqrt_rel]\n have vTL2 : deriv (deriv mTL2b) n = (-((8/3)*0.886)) *\n (psiOf (fun t => t * Real.log (Real.log (t + 2))) (Real.sqrt n + 1) / (4 * n)) := by\n unfold mTL2b\n rw [deriv2_const_mul _ (hdd hCDTL2c) (hev hCDTL2c),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_TL2 n hn0, \u2190 psiOf_sqrt_rel]\n have vId : deriv (deriv mIdb) n = (-((8/3)*2.9 + 192)) *\n (psiOf id (Real.sqrt n + 1) / (4 * n)) := by\n unfold mIdb\n have hCDidc : ContDiffOn \u211d 2 (fun m => id (Real.sqrt m + 1)) (Set.Ioi 20) :=\n contDiffOn_id.comp contDiffOn_sqrt_shift (Set.mapsTo_univ _ _)\n rw [show (fun m => -(8/3*2.9 + 192) * (Real.sqrt m + 1)) =\n (fun m => -(8/3*2.9 + 192) * id (Real.sqrt m + 1)) from rfl,\n deriv2_const_mul _ (hdd hCDidc) (hev hCDidc),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_id n hn0, \u2190 psiOf_sqrt_rel]\n have vL1sq : deriv (deriv mL1sqb) n = (-(42*0.433^2*(Real.exp 4 + 1))) *\n (psiOf (fun t => Real.log (t + 2) ^ 2) (Real.sqrt n + 1) / (4 * n)) := by\n unfold mL1sqb\n rw [deriv2_const_mul _ (hdd hCDL1sqc) (hev hCDL1sqc),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_L1sq n hn0, \u2190 psiOf_sqrt_rel]\n have vL1L2 : deriv (deriv mL1L2b) n = (-(42*(2*0.433*0.886)*(Real.exp 4 + 1))) *\n (psiOf (fun t => Real.log (t + 2) * Real.log (Real.log (t + 2)))\n (Real.sqrt n + 1) / (4 * n)) := by\n unfold mL1L2b\n rw [deriv2_const_mul _ (hdd hCDL1L2c) (hev hCDL1L2c),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_L1L2 n hn0, \u2190 psiOf_sqrt_rel]\n have vL2sq : deriv (deriv mL2sqb) n = (-(42*0.886^2*(Real.exp 4 + 1))) *\n (psiOf (fun t => Real.log (Real.log (t + 2)) ^ 2) (Real.sqrt n + 1) / (4 * n)) := by\n unfold mL2sqb\n rw [deriv2_const_mul _ (hdd hCDL2sqc) (hev hCDL2sqc),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_L2sq n hn0, \u2190 psiOf_sqrt_rel]\n have vL1 : deriv (deriv mL1b) n = (-((42*(2*0.433*2.9) + 147)*(Real.exp 4 + 1))) *\n (psiOf (fun t => Real.log (t + 2)) (Real.sqrt n + 1) / (4 * n)) := by\n unfold mL1b\n rw [deriv2_const_mul _ (hdd hCDL1c) (hev hCDL1c),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_L1 n hn0, \u2190 psiOf_sqrt_rel]\n have vL2 : deriv (deriv mL2b) n = (-(42*(2*0.886*2.9)*(Real.exp 4 + 1))) *\n (psiOf (fun t => Real.log (Real.log (t + 2))) (Real.sqrt n + 1) / (4 * n)) := by\n unfold mL2b\n rw [deriv2_const_mul _ (hdd hCDL2c) (hev hCDL2c),\n chain_rule_sqrt_shift_on _ (by norm_num : (-1 : \u211d) \u2264 1) contDiffOn_L2 n hn0, \u2190 psiOf_sqrt_rel]\n have vIIM : deriv (deriv mIIM) n = (-1) * deriv (deriv IIMaj) n := by\n unfold mIIM\n rw [deriv2_const_mul (-1) (hdd hCDIIM) (hev hCDIIM)]\n -- prefix ContDiffOn chain\n have hCD1 := (contDiffOn_mS (lagariasC1 - Real.eulerMascheroniConstant/2)).add\n (contDiffOn_mFblock F hF)\n have hCD2 := hCD1.add contDiffOn_mTL1b\n have hCD3 := hCD2.add contDiffOn_mTL2b\n have hCD4 := hCD3.add contDiffOn_mIdb\n have hCD5 := hCD4.add contDiffOn_mL1sqb\n have hCD6 := hCD5.add contDiffOn_mL1L2b\n have hCD7 := hCD6.add contDiffOn_mL2sqb\n have hCD8 := hCD7.add contDiffOn_mL1b\n have hCD9 := hCD8.add contDiffOn_mL2b\n have hCD10 := hCD9.add contDiffOn_mIIM\n -- split the sum\n rw [marginTilde_eq_expanded F]\n show (0 : \u211d) \u2264 deriv (deriv (marginExpanded F)) n\n unfold marginExpanded\n dsimp only\n rw [deriv2_add (hdd hCD10) (hdd contDiffOn_const) (hev hCD10) (hev contDiffOn_const),\n deriv2_const_val,\n deriv2_add (hdd hCD9) (hdd contDiffOn_mIIM) (hev hCD9) (hev contDiffOn_mIIM), vIIM,\n deriv2_add (hdd hCD8) (hdd contDiffOn_mL2b) (hev hCD8) (hev contDiffOn_mL2b), vL2,\n deriv2_add (hdd hCD7) (hdd contDiffOn_mL1b) (hev hCD7) (hev contDiffOn_mL1b), vL1,\n deriv2_add (hdd hCD6) (hdd contDiffOn_mL2sqb) (hev hCD6) (hev contDiffOn_mL2sqb),\n vL2sq,\n deriv2_add (hdd hCD5) (hdd contDiffOn_mL1L2b) (hev hCD5) (hev contDiffOn_mL1L2b),\n vL1L2,\n deriv2_add (hdd hCD4) (hdd contDiffOn_mL1sqb) (hev hCD4) (hev contDiffOn_mL1sqb),\n vL1sq,\n deriv2_add (hdd hCD3) (hdd contDiffOn_mIdb) (hev hCD3) (hev contDiffOn_mIdb), vId,\n deriv2_add (hdd hCD2) (hdd contDiffOn_mTL2b) (hev hCD2) (hev contDiffOn_mTL2b), vTL2,\n deriv2_add (hdd hCD1) (hdd contDiffOn_mTL1b) (hev hCD1) (hev contDiffOn_mTL1b), vTL1,\n deriv2_add (hdd (contDiffOn_mS _)) (hdd (contDiffOn_mFblock F hF))\n (hev (contDiffOn_mS _)) (hev (contDiffOn_mFblock F hF)), vS, vF]\n -- sign assembly: every \u03c8-term is nonneg\n have h\u03c8n : psiOf F (Real.sqrt n + 1) < 0 := h\u03c8 _ hTn\n have hnn1 : (0 : \u211d) \u2264 -2 * (psiOf F (Real.sqrt n + 1) / (4 * n)) :=\n mul_nonneg_of_nonpos_of_nonpos (by norm_num)\n (div_neg_of_neg_of_pos h\u03c8n hn4).le\n have hnn2 : (0 : \u211d) \u2264 (-((8/3)*0.433 + 42)) *\n (psiOf (fun t => t * Real.log (t + 2)) (Real.sqrt n + 1) / (4 * n)) :=\n mul_nonneg_of_nonpos_of_nonpos (by norm_num)\n (div_neg_of_neg_of_pos (psiOf_T_mul_log_shift_neg hTn) hn4).le\n have hnn3 : (0 : \u211d) \u2264 (-((8/3)*0.886)) *\n (psiOf (fun t => t * Real.log (Real.log (t + 2))) (Real.sqrt n + 1) / (4 * n)) :=\n mul_nonneg_of_nonpos_of_nonpos (by norm_num)\n (div_neg_of_neg_of_pos (psiOf_T_mul_log_log_shift_neg hTn) hn4).le\n have hnn4 : (0 : \u211d) \u2264 (-((8/3)*2.9 + 192)) *\n (psiOf id (Real.sqrt n + 1) / (4 * n)) := by\n have hp : psiOf id (Real.sqrt n + 1) < 0 :=\n (psiOf_id (Real.sqrt n + 1) (by\n have h := Real.sqrt_pos.mpr hn0\n linarith)).2\n exact mul_nonneg_of_nonpos_of_nonpos (by norm_num)\n (div_neg_of_neg_of_pos hp hn4).le\n have hnn5 : (0 : \u211d) \u2264 (-(42*0.433^2*(Real.exp 4 + 1))) *",
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raw content_json (database row)
[{"type":"thinking","thinking":"`Summable.add` is NOT the constructor-style lemma I assumed — it's `Summable.add (hf : Summable f) (hg : Summable g) : Summable (f + g)` — so `apply Summable.add` treats it as a two-arg function producing Summable (f+g): the apply leaves TWO goals (f's summable and g's). My `apply Summable.add (fun i => ...)` passed the FUNCTION as the first arg — wrong: Summable.add's first arg is hf : Summable f (a PROOF), with f implicit. So: `apply Summable.add` leaves two goals f and g's summability with f,g as metavars unified by the goal — but the goal's function (A+B+C-lambda) vs (f+g) — the SAME Pi.add unification issue.\n\nThe right pattern: `exact ((hA).add hB).add hC` where each .add is at the PROOF level: (tail14_inv_add_sq_summable.mul_left _).add (tail14_log_div_add_sq_summable.mul_left _) : Summable ((fun c0·A) + (fun c1·B)) — then .add (tail14_loglog...mul_left _) : Summable ((c0A+c1B)+c2C) — the TYPE is Summable (Pi.add (Pi.add A B) C) — vs the goal Summable (fun i => (A i + B i) + C i) — Pi.add applied twice: ((A+B)+C) i = (A i + B i) + C i ✓ DEFEQ — should unify when given as `exact`. The earlier failure was from `apply Summable.add` + `exact` splitting — the `exact` alone should work if the unification succeeds. The timeout at 3217 (isDefEq) is at farGLeftMaj_summable presumably — meaning even the EXACT approach hits isDefEq timeouts elsewhere.\n\nWAIT — hold on. Let me reconsider the whole area: the timeouts at 3217/3241/3179 with isDefEq/whnf — and earlier at 3156/3157 — ALL in the farGLeftMaj region. Something about farGLeftMaj itself. farGLeftMaj's body: `if 14 ≤ ℓ then 4.5 * C0hat ((ℓ : ℝ) + 1) / (10 + (ℓ : ℝ)) ^ 2 else 0` — contains `C0hat` (a def) — and `((ℓ : ℝ) + 1)`... When Lean elaborates `farGLeftMaj (ℓ + 14)` in the types of the shift lemmas, and does whnf/isDefEq on them, it unfolds C0hat (which has Real.log terms) — fine.\n\nHmm — could the REAL culprit be `two_le_C0hat`/`farGLeftMaj_nonneg`'s positivity call?? farGLeftMaj_nonneg uses `positivity` after two_le_C0hat — maybe positivity chokes?\n\nLet me BISECT: temporarily comment out the farGLeftMaj section (from `def farGLeftMaj` to `farGLeftMaj_series_le`) and the farGLeft_le, and see if the rest compiles + how long. Actually — faster: check the timeout locations precisely: 3157 (combo_summable), 3179 (farGLeftMaj_summable), 3217 (series_le's hsplit area), 3241 (series_le's hdecomp area). \n\nNew idea: the `summable_nat_add_iff` in farGLeftMaj_summable and in tail14_inv_add_sq_summable/tail11 bricks — those worked before. The difference: farGLeftMaj has the IF. When `.mp farGLeftMaj_shift_summable` unifies `Summable (fun n => farGLeftMaj (n + 14))` with `Summable farGLeftMaj` — isDefEq between fun n => farGLeftMaj (n+14) and fun n => farGLeftMaj (n+14)... trivial. whnf timeout at 3179 (farGLeftMaj_summable) — maybe `.mp` vs `.mpr` direction?! summable_nat_add_iff (k) : Summable (fun n => f (n + k)) ↔ Summable f — `.mp : Summable (fun n => f (n+k)) → Summable f` ✓ that's what I want. whnf timeout — the unification of farGLeftMaj_shift_summable's TYPE (Summable fun ℓ => farGLeftMaj (ℓ+14)) against .mp's domain — unfolding farGLeftMaj (ℓ+14) vs f (n+14) with f := farGLeftMaj — needs farGLeftMaj (ℓ+14) ≡ farGLeftMaj (n+14) — whnf on the IF with metavariable ℓ vs n... should be instant.\n\nI'm clearly missing something environmental. Let me look at 3217:8 and 3241:4 content directly, and also check whether farGLeftMaj_nonneg's positivity is the issue by testing a minimal snippet. Actually — let me check the TIME: each `lake env lean` run on this 3300-line file takes ~2-4 min. I've done ~15 runs. The bisection will take several more. Let me be smart: extract the problematic region into a scratch file with the same imports and iterate there — NO, the file dependencies (farGLeftMaj needs farGLeft_fiber_le etc.) — but for the SUMMABILITY section only the bricks + C0hat + farGLeftMaj are needed... still need the whole file context.\n\nAlternative theory — the `Summable.tsum_le_tsum farGLeftMaj_shift_le farGLeftMaj_shift_summable farGLeftMaj_combo_summable` call (hle at series_le): Summable.tsum_le_tsum (h : ∀ i, f i ≤ g i) (hf : Summable f) (hg : Summable g) — with f = farGLeftMaj(·+14) and g = combo-lambda — and farGLeftMaj_shift_le's type: ∀ ℓ, farGLeftMaj (ℓ+14) ≤ combo-lambda ℓ ✓. If farGLeftMaj_combo_summable is broken/missing (kernel unknown), the hle call would error not timeout...\n\nLet me look at the exact current error locations.","signature":""},{"type":"text","text":"Let me look at the exact timeout locations to bisect the pathology."},{"type":"tool_use","id":"Read_200","name":"Read","input":{"file_path":"D:\\Python\\Quantum\\research\\lean\\NguyenRH1\\NguyenRH1\\LiTightR.lean","offset":3166,"limit":100},"extra_content":null}]