leech.txt

mdupont@mdupont-G470:~/2026/07/06/index$ for x in `cat leech_lean.txt`; do echo $x; grep -h ":=" $x; done | sort |uniq -c | sort -rn
    388     type0_count + type2_count + type3_count + type4_count = lambda_mod2_size := by native_decide
    388 theorem type4_positive : type4_count > 0 := by native_decide
    388 theorem short_vectors_double : 2 * type2_count = leech_vectors_norm4 := by native_decide
    388 theorem N0_Nxyz_index : N0_order / Nxyz_order = 6 := by native_decide
    388 theorem lambda_mod2_size_value : lambda_mod2_size = 16777216 := by native_decide
    388     M24_order = 2^10 * 3^3 * 5 * 7 * 11 * 23 := by native_decide
    388     Gx0_order / Nxyz_order = 16584750 := by native_decide
    388 def type4_count : ℕ := 8292375
    388 def type3_count : ℕ := 8386560
    388 def type2_count : ℕ := 98280
    388 def type0_count : ℕ := 1
    388 def Nxyz_order : ℕ := 2^35 * M24_order
    388 def Nx0_order : ℕ := 2 * Nxyz_order
    388 def N0_order : ℕ := 3 * Nx0_order
    388 def M24_order : ℕ := 244823040
    388 def M22_order : ℕ := 443520
    388 def leech_vectors_norm8 : ℕ := 16773120
    388 def leech_vectors_norm4 : ℕ := 196560
    388 def leech_min_norm : ℕ := 4
    388 def lambda_mod2_size : ℕ := 2^24
    388 def H_Nxyz_index : ℕ := 93150
    388 def Gx0_order : ℕ := 2^25 * Co1_order
    366 theorem theta_constant_720 : (720 : ℕ) = Nat.factorial 6 := by native_decide
    366 theorem tau_two : ramanujanTau 2 = -24 := rfl
    366 theorem tau_three : ramanujanTau 3 = 252 := rfl
    366 theorem tau_one : ramanujanTau 1 = 1 := rfl
    366 theorem ramanujan_congruence_2 : (ramanujanTau 2) % 691 = 2049 % 691 := by native_decide
    366 theorem norm6_factored : leechNorm6Count = 2^12 * 3^2 * 5 * 7 * 13 := by native_decide
    366 theorem moonshine_dimension : 71 * 59 * 47 = 196883 := by norm_num
    366 theorem mckay_observation : 1 + 196883 = 196884 := by norm_num
    366 theorem leech_theta_cancellation : 720 * (1 : ℤ) + (-720) = 0 := by norm_num
    366 theorem kissing_number_factored : leechKissingNumber = 2^4 * 3^3 * 5 * 7 * 13 := by
    366 theorem kissing_from_tau : 196560 = 720 * 24 + 179280 := by norm_num
    366 theorem fiber_rank_constant (s : S_ss) : fiberRank s = 24 := rfl
    366 theorem deep_holes_times_rank : 23 * 24 = 552 := by norm_num
    366 theorem co3_order_value : co3Order = 495766656000 := by native_decide
    366 theorem co3_divides_monster : co3Order ∣ monsterOrder := by native_decide
    366 theorem co3_divides_co1 : co3Order ∣ co1Order := by native_decide
    366 theorem co2_order_value : co2Order = 42305421312000 := by native_decide
    366 theorem co2_divides_monster : co2Order ∣ monsterOrder := by native_decide
    366 theorem co2_divides_co1 : co2Order ∣ co1Order := by native_decide
    366 theorem co1_order_value : co1Order = 4157776806543360000 := by native_decide
    366 theorem co1_divides_monster : co1Order ∣ monsterOrder := by native_decide
    366 theorem co1_divides_baby_monster : co1Order ∣ babyMonsterOrder := by native_decide
    366 theorem co0_order_value : co0Order = 8315553613086720000 := by native_decide
    366 theorem co0_divides_monster : co0Order ∣ monsterOrder := by native_decide
    366 theorem bundle_divides_monster : co0Order ∣ monsterOrder := co0_divides_monster
    366 def leechNorm8Count : ℕ := 398034000
    366 def leechNorm6Count : ℕ := 16773120
    366 def leechKissingNumber : ℕ := 196560
    366 def leechCoveringRadiusSq : ℕ := 2
    366 def fiberRank (_ : S_ss) : ℕ := 24
    366 def fiberAutOrder (_ : S_ss) : ℕ := co0Order
    366 def deepHoleTypes : ℕ := 23
    366 def co3Order : ℕ := 2^10 * 3^7 * 5^3 * 7 * 11 * 23
    366 def co2Order : ℕ := 2^18 * 3^6 * 5^3 * 7 * 11 * 23
    366 def co1Order : ℕ := co0Order / 2
    366 def co0Order : ℕ := 2^22 * 3^9 * 5^4 * 7^2 * 11 * 13 * 23
    366 def babyMonsterOrder : ℕ :=
    366     co1Order ∣ babyMonsterOrder ∧ babyMonsterOrder ∣ monsterOrder := by
    366     co1Order = 2^21 * 3^9 * 5^4 * 7^2 * 11 * 13 * 23 := by native_decide
    366     babyMonsterOrder = 4154781481226426191177580544000000 := by native_decide
    366 abbrev S_ss := ZMod 71 × ZMod 59 × ZMod 47
    258 theorem norm8_factored : leechNorm8Count = 2^4 * 3^7 * 5^3 * 7 * 13 := by native_decide
    258 theorem Co1_Co2_index_eq : Co1_order / Co2_order = type2_count := by native_decide
    168 def leechMinNorm : ℕ := 4
    130 theorem Co1_Co2_index : Co1_order / Co2_order = type2_count := by native_decide
    130 def Co0_order : ℕ := 2 * 4157776806543360000
    130     Co2_order = 2^18 * 3^6 * 5^3 * 7 * 11 * 23 := by native_decide
    130     Co1_order = 2^21 * 3^9 * 5^4 * 7^2 * 11 * 13 * 23 := by native_decide
    129 def leech_rank : ℕ := 24
    129 def Co2_order : ℕ := 42305421312000
    129 def Co1_order : ℕ := 4157776806543360000
    110 def leechKissing : ℕ := 196560
    108 theorem tau_mod_691_n2 : ramanujanTau 2 % 691 = (2049 : ℤ) % 691 := by native_decide
    108 theorem sigma11_2 : (1 + 2^11 : ℤ) = 2049 := by norm_num
    108 theorem norm8_factored : leechNorm8Count = 2^4 * 3^7 * 5^3 * 7 * 13 := by
    108 theorem mckay_factored : 196884 = 2^2 * 3 * 16407 := by norm_num
    108 theorem leech_unimodular : (1 : ℕ) = 1 := rfl
    108 theorem leech_rank : (24 : ℕ) = 24 := rfl
    108 theorem genus_zero_count : 171 = 9 * 19 := by norm_num
    108 theorem deep_holes_orbits : deepHoleTypes = 23 := rfl
    108 theorem deep_holes_match_niemeier : deepHoleTypes = 23 := rfl
    108 theorem co0_mod_sss : co0Order % (71 * 59 * 47) = co0Order % 196883 := by ring_nf
    107 def monsterOrder : ℕ :=
     63 def leechDim : ℕ := 24
     60 theorem leechKissing_factorization : leechKissing = 2 ^ 4 * 3 ^ 3 * 5 * 7 * 13 := by
     60 theorem leechDim_three_e8 : leechDim = 3 * 8 := by decide
     60 theorem e8WeylOrder_value : e8WeylOrder = 696729600 := by decide
     60 theorem e8Roots_factorization : e8Roots = 2 ^ 4 * 3 * 5 := by decide
     60 theorem e8Dim_roots_rank : e8Dim = e8Roots + 8 := by decide
     60 theorem conway1_dvd_monsterOrder : conway1Order ∣ monsterOrder := by
     60 theorem conway0_two_conway1 : conway0Order = 2 * conway1Order := by
     60 theorem conway0Order_value : conway0Order = 8315553613086720000 := by
     60 theorem conway0_dvd_monsterOrder : conway0Order ∣ monsterOrder := by
     60       ⊆ supersingularPrimes.toFinset := by
     60     leechKissing.primeFactors ⊆ supersingularPrimes.toFinset := by
     60     leechKissing.primeFactors = {2, 3, 5, 7, 13} := by
     60     e8WeylOrder.primeFactors ⊆ supersingularPrimes.toFinset := by
     60     e8Roots.primeFactors ⊆ supersingularPrimes.toFinset := by
     60 def runLeechSurvey : IO Unit := do
     60 def leechDet : ℕ := 1
     60 def e8WeylOrder : ℕ := 2 ^ 14 * 3 ^ 5 * 5 ^ 2 * 7
     60 def e8Roots : ℕ := 240
     60 def e8Dim : ℕ := 248
     60 def conway1Order : ℕ := conway0Order / 2
     60 def conway0Order : ℕ :=
     60     conway0Order.primeFactors ⊆ supersingularPrimes.toFinset := by
     60     conway0Order.primeFactors = {2, 3, 5, 7, 11, 13, 23} := by
     54 theorem bilinForm_self_nonneg (n a : ℕ) : 0 ≤ bilinForm n a a := by
     54 theorem bilinForm_comm (n a b : ℕ) : bilinForm n a b = bilinForm n b a := by
     54     subfieldForm p n (K.map σ.toAlgHom) (L.map σ.toAlgHom) = subfieldForm p n K L := by
     54   refine' { toFun := fun x => ⟨ σ.symm x, _ ⟩, map_add' := _, map_smul' := _ };
     54     obtain ⟨ y, hy, rfl ⟩ := hx; aesop;
     54 noncomputable def subfieldForm (K L : IntermediateField (ZMod p) (GaloisField p n)) : ℤ :=
     54     (hpq : p ≠ q) : bilinForm n p q = 0 := by
     54       = grade (ZMod p) (GaloisField p n) K := by
     54     d ≤ e ↔ ∀ q, coordVec d.grade q ≤ coordVec e.grade q := by
     54 def coordVec (a : ℕ) : ℕ → ℤ := fun q => (a.factorization q : ℤ)
     54 def bilinForm (n : ℕ) (a b : ℕ) : ℤ :=
     54     bilinForm n p p = 1 := by
     54     bilinForm n (p ^ k) (p ^ k) = (k : ℤ) ^ 2 := by
     54     bilinForm n d.grade d.grade = 0 ↔ d.grade = 1 := by
     54     bilinForm n (a * b) c = bilinForm n a c + bilinForm n b c := by
     53 theorem one_le_height_of_ne_zero (n : ℕ) (v : Crystal n) (hv : v ≠ 0) : 1 ≤ height n v := by
     53 theorem negIsom_mem (n : ℕ) : (LinearEquiv.neg ℤ : Crystal n ≃ₗ[ℤ] Crystal n) ∈ latIsometryGroup n := by
     53 theorem latForm_self_nonneg (n : ℕ) (v : Crystal n) : 0 ≤ latForm n v v := by
     53 theorem latForm_self_eq_zero_iff (n : ℕ) (v : Crystal n) : latForm n v v = 0 ↔ v = 0 := by
     53 theorem latForm_nondegenerate (n : ℕ) (v : Crystal n) (h : ∀ w, latForm n v w = 0) : v = 0 := by
     53 theorem latForm_comm (n : ℕ) (v w : Crystal n) : latForm n v w = latForm n w v := by
     53 theorem isRoot_single (n : ℕ) (q : n.primeFactors) : IsRoot n (Pi.single q 1) := by
     53 theorem isLatIsometry_one (n : ℕ) : IsLatIsometry n 1 := by
     53     subfieldForm p n (K.map σ.toAlgHom) (L.map σ.toAlgHom) = subfieldForm p n K L :=
     53     permIsom n σ ∈ latIsometryGroup n := by
     53   one_mem' := isLatIsometry_one n
     53       obtain ⟨q, hq⟩ : ∃ q : n.primeFactors, v q * v q = 1 := by
     53     obtain ⟨q, hq⟩ : ∃ q : n.primeFactors, v q ≠ 0 ∧ ∀ r : n.primeFactors, r ≠ q → v r = 0 := by
     53 noncomputable def latForm (n : ℕ) (v w : Crystal n) : ℤ := ∑ q, v q * w q
     53 noncomputable def height (n : ℕ) (v : Crystal n) : ℤ := latForm n v v
     53 noncomputable def coordEmbed (n : ℕ) (a : ℕ) : Crystal n := fun q => coordVec a (q : ℕ)
     53   mul_mem' := fun he hf => isLatIsometry_mul n he hf
     53     Monotone (permIsom n σ) := by
     53     latForm n (u + v) w = latForm n u w + latForm n v w := by
     53     latForm n (coordEmbed n a) (coordEmbed n b) = bilinForm n a b := by
     53     latForm n (a • v) w = a * latForm n v w := by
     53     IsRoot n v ↔ ∃ q : n.primeFactors, v = Pi.single q 1 ∨ v = Pi.single q (-1) := by
     53     IsRoot n (coordEmbed n p) := by
     53   inv_mem' := fun he => isLatIsometry_inv n he
     53   intro v w; have := he ( f v ) ( f w ) ; have := hf v w; simp_all +decide
     53   intro v w; have := he ( e⁻¹ v ) ( e⁻¹ w ) ; simp_all +decide [ latForm ]
     53     (he : IsLatIsometry n e) : IsLatIsometry n e⁻¹ := by
     53     (he : IsLatIsometry n e) (hf : IsLatIsometry n f) : IsLatIsometry n (e * f) := by
     53       have h_sum : ∑ q : n.primeFactors, v q * v q = 1 := by
     53     have h_eq : v q * v q = 1 := by
     53     exact Or.inr <| Or.inl <| fun h => hq <| by have := Nat.prime_dvd_prime_iff_eq ( Nat.prime_of_mem_primeFactors q.2 ) ( Nat.prime_of_mem_primeFactors hp ) ; tauto
     53     e ∈ latIsometryGroup n ↔ IsLatIsometry n e := Iff.rfl
     53 def IsRoot (n : ℕ) (v : Crystal n) : Prop := height n v = 1
     53 def IsLatIsometry (n : ℕ) (e : Crystal n ≃ₗ[ℤ] Crystal n) : Prop :=
     53     Crystal n ≃ₗ[ℤ] Crystal n := LinearEquiv.funCongrLeft ℤ ℤ σ
     53     coordEmbed n p = Pi.single (⟨p, hp⟩ : n.primeFactors) 1 := by
     53       = coordEmbed n (grade (ZMod p) (GaloisField p n) K) := by
     53     coordEmbed n (a * b) = coordEmbed n a + coordEmbed n b := by
     53   convert Finset.sum_coe_sort ( f := fun q => coordVec a q * coordVec b q ) _
     53   carrier := {e | IsLatIsometry n e}
     53 abbrev Crystal (n : ℕ) := (q : n.primeFactors) → ℤ
     50 theorem orderCo0_value : orderCo0 = 8315553613086720000 := by native_decide
     50 theorem leech_weyl_cannonball : ∑ k ∈ Finset.range 25, k ^ 2 = 70 ^ 2 := by decide
     50 theorem leech_kissing_factorization : leechKissing = 2 ^ 4 * 3 ^ 3 * 5 * 7 * 13 := by
     50 theorem leech_dim_eq : (24 : ℕ) = 26 - 2 := by decide
     50 theorem hypercube_ambient_dim : MonsterAtlas.primesList.length = 15 := by native_decide
     50     supersingularPrimes.filter (· ∉ co0Primes) = [17, 19, 29, 31, 41, 47, 59, 71] := by
     50     ∀ p, p.Prime → p ∣ leechKissing → p ∈ supersingularPrimes := by
     50     p ∣ orderCo0 ↔ p ∈ co0Primes := by
     50     ∀ p ∈ co0Primes, p ∈ supersingularPrimes := by native_decide
     50   have : p ∈ Nat.primeFactorsList 196560 := by
     50     have h_prime : p ∣ 8315553613086720000 := by
     50     have h_prime_factors : p ∈ Nat.primeFactorsList 8315553613086720000 := by
     50 def orderCo0 : ℕ := 2 ^ 22 * 3 ^ 9 * 5 ^ 4 * 7 ^ 2 * 11 * 13 * 23
     50 def co0Primes : List ℕ := [2, 3, 5, 7, 11, 13, 23]
     48 theorem weyl_ne_zero : weyl ≠ 0 := by
     48 theorem weyl_mem_ker : weyl ∈ LinearMap.ker fform := by
     48 theorem weylK_ne_zero : weylK ≠ 0 := by
     48 theorem finrank_span_weylK : Module.finrank ℝ (ℝ ∙ weylK) = 1 :=
     48 theorem finrank_ker : Module.finrank ℝ (LinearMap.ker fform) = 25 := by
     48 theorem fform_weyl_zero : fform weyl = 0 := by
     48 theorem fform_ne_zero : fform ≠ 0 := by
     48 theorem fform_apply (v : Fin 26 → ℝ) : fform v = ∑ i, (sgn i * weyl i) * v i := by
     48 noncomputable def weylK : LinearMap.ker fform := ⟨weyl, weyl_mem_ker⟩
     48 noncomputable def weyl : Fin 26 → ℝ := fun i => if i.val < 25 then (i.val : ℝ) else 70
     48 noncomputable def sgn : Fin 26 → ℝ := fun i => if i.val < 25 then 1 else -1
     48 noncomputable def fform : (Fin 26 → ℝ) →ₗ[ℝ] ℝ :=
     48       Module.finrank ℝ ((LinearMap.ker fform) ⧸ (ℝ ∙ weylK)) = e.dimension := by
     48     Module.finrank ℝ ((LinearMap.ker fform) ⧸ (ℝ ∙ weylK)) = 24 := by
     48       ∧ Module.finrank ℝ ((LinearMap.ker fform) ⧸ (ℝ ∙ weylK)) = 24 := by
     48   have : weyl 1 = 0 := by rw [h]; rfl
     48   have hsurj : LinearMap.range fform = ⊤ :=
     48   have hrange : Module.finrank ℝ (LinearMap.range fform) = 1 := by rw [hsurj]; simp
     48   have h : (∑ k ∈ Finset.range 25, (k : ℝ) ^ 2) = (70 : ℝ) ^ 2 := by
     48   have hdom : Module.finrank ℝ (Fin 26 → ℝ) = 26 := by simp
     48     have hc := LeechBridge.leech_weyl_cannonball
     48     have hcast : ((∑ k ∈ Finset.range 25, k ^ 2 : ℕ) : ℝ) = ((70 ^ 2 : ℕ) : ℝ) := by
     48   have hadd := Submodule.finrank_quotient_add_finrank (ℝ ∙ weylK)
     48   have hadd := LinearMap.finrank_range_add_finrank_ker fform
     48   have h25 : fform (Pi.single (25 : Fin 26) 1) = 0 := by rw [h]; simp
     48   have := congrArg Subtype.val h
     48     fform weyl = (∑ k ∈ Finset.range 25, (k : ℝ) ^ 2) - 70 ^ 2 := by
     16 def main : IO Unit := do
      5   witness := {}
      5 theorem oggPrime_mem : (71 : ℕ) ∈ Moonshine.monsterPrimes := by decide
      5 theorem oggPrime_max : ∀ p ∈ Moonshine.monsterPrimes, p ≤ 71 := by decide
      5 theorem oggPrime_eq_max : Moonshine.monsterPrimes.max' (by decide) = 71 := by decide
      5 theorem collidingGroups_length : collidingGroups.length = 23 := by native_decide
      5 theorem collapse_lost : irrepDegrees.length - irrepDegrees.dedup.length = 24 := by
      5 /mnt/data1/aristotle-results/c18edf48-c6ea-4e41-baee-0402020d3cf6_aristotle/output-final_aristotle/Archives/e8d55bd2-60a5-419a-9ada-62392e1e03ca-aristotle__3_/output-final_aristotle/c18edf48-c6ea-4e41-baee-0402020d3cf6-aristotle
      5     let sy := cy + off.2
      5     let sx := cx + off.1
      5   let sats := satOffsets size
      5   let satParts := sats.map (fun off =>
      5   let row (cy : Float) (col txt : String) : String :=
      5   let primCol := if isTriple then rose else accent
      5   let primary :=
      5   let path := "leech_collapse_24_23.svg"
      5   let n := clusterSizes.length
      5     let line :=
      5   let isTriple := size == 3
      5     let dot :=
      5   let cy := cellCY i
      5   let cx := cellCX i
      5     let c := (irrepDegrees.filter (· == d)).length
      5   let cap (txt col vals : String) : String :=
      5   let big (txt vals : String) : String :=
      5     (irrepDegrees.filter (· == 5514132424881463208443904)).length = 3 := by native_decide
      5 def width  : Nat := 1440
      5 def wall   : String := "#d8d1bd"
      5 def title : String :=
      5 def tbox (x y : Float) (head body₁ body₂ : String) : String :=
      5 def tboxes : String :=
      5 def stepCaption : String :=
      5 def satR     : Float := 30.0   -- offset of a collapsing copy from its representative
      5 def satOffsets (size : Nat) : List (Float × Float) :=
      5 def rose   : String := "#f3a6c0"  -- the triple, highlighted
      5 def ribbon : String :=
      5 def renderCluster (i : Nat) (size : Nat) : String :=
      5 def originY  : Float := 250.0
      5 def originX  : Float := 470.0
      5 def legend : String :=
      5 def keyTimes : String := "0;0.12;0.30;0.55;0.70;0.92;1"
      5 def height : Nat := 760
      5 def header : String :=
      5 def gcols    : Nat   := 6
      5 def frame  : String := "#7c5230"
      5 def floor  : String := "#a07a52"
      5 def faint  : String := "#86b9a2"  -- faded green: connectors / secondary text
      5 def dotR     : Float := 8.0
      5 def document : String :=
      5 def cycle    : String := "dur='16s' repeatCount='indefinite'"
      5 def counter : String :=
      5 def collidingGroups : List (ℕ × ℕ) :=
      5 def clusters : String :=
      5 def clusterSizes : List ℕ := collidingGroups.map (·.2)
      5 def chalk  : String := "#f3f7f1"
      5 def cellW    : Float := 150.0
      5 def cellH    : Float := 96.0
      5 def cellCY (i : Nat) : Float := originY + Float.ofNat (i / gcols) * cellH + cellH / 2.0
      5 def cellCX (i : Nat) : Float := originX + Float.ofNat (i % gcols) * cellW + cellW / 2.0
      5 def board  : String := "#10402f"
      5 def boardFrame : String :=
      5 def amber  : String := "#ffcf6b"  -- amber: the collapsing copies
      5 def accent : String := "#9cdcfe"  -- cyan: the surviving representative of each class
      5     (collidingGroups.map (fun p => p.2 - 1)).foldl (· + ·) 0 = 24 := by native_decide
      5     (collidingGroups.filter (·.2 == 3)).length = 1 := by native_decide
      5     (collidingGroups.filter (·.2 == 2)).length = 22 := by native_decide
      4     n := n / 71
      4   let timestamp := "2026-03-05T15:11:00Z"
      4   let record := processPipeline fractranFile timestamp
      4   let mut digits : List Nat := []
      4   let fractranFile : FRACTRANIngestion.FRACTRANFile := {
      4     digits := (n % 71) :: digits
      4 (5)__unpacked/output-final_aristotle/7399cc0d-99f2-4516-8c9e-6da2ef861c18-aristotle-17__unpacked/output-final_aristotle/RequestProject/LeechLatticeAxes.lean
      4 (5)__unpacked/output-final_aristotle/7399cc0d-99f2-4516-8c9e-6da2ef861c18-aristotle-17__unpacked/output-final_aristotle/RequestProject/LeechAutomorphisms.lean
      3 theorem turyn_dimension : leechDim = e8Rank + e8Rank + e8Rank := by decide
      3 theorem shape4_value : shape4Vectors = 1104 := by native_decide
      3 theorem shape3_value : shape3Vectors = 98304 := by native_decide
      3 theorem shape2_value : shape2Vectors = 97152 := by native_decide
      3 theorem octad_steiner : octadCount * Nat.choose 8 5 = Nat.choose 24 5 := by native_decide
      3 theorem kissingNumber_value : kissingNumber = 196560 := by native_decide
      3 theorem kissing_decomp : kissingNumber = 1104 + 97152 + 98304 := by native_decide
      3 theorem fifteen_is_downstream : Moonshine.monsterPrimes.card = 15 :=
      3 theorem e8_kissing_number : e8Kissing = 2 ^ 2 * Nat.choose 8 2 + 2 ^ 7 := by native_decide
      3   steps := [
      3     Moonshine.monsterPrimes.card = 15 :=
      3   let sum := (List.range 17).foldl (fun acc i =>
      3   let rec go (n : Nat) (remaining : Nat) (trace : List Nat) : List Nat :=
      3   let radius := (List.range 17).foldl (fun acc i =>
      3     let jCoeff := jInvariantCoeffs[rotation % jInvariantCoeffs.length]!.natAbs
      3 def shape4Vectors : ℕ := 2 ^ 2 * Nat.choose 24 2
      3 def shape3Vectors : ℕ := 2 ^ 12 * 24
      3 def shape2Vectors : ℕ := 2 ^ 7 * octadCount
      3 def octadCount : ℕ := 759
      3 def monsterPrimes : List Nat := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71]
      3 def monsterPrimes : List Nat := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 59, 71]
      3 def monsterExponents : List Nat := [46, 20, 9, 6, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
      3 def kissingNumber : ℕ := shape4Vectors + shape2Vectors + shape3Vectors
      3 def e8Rank : ℕ := 8
      3 def e8Kissing : ℕ := 240
      2   workers : Nat := 4
      2   watchDirs : List String := []
      2   valid := by intro i; omega
      2   True := by
      2   | Sum.inr (Sum.inl stream) => pure (some { path := s!"stream_{stream.sessionId}", fractions := stream.chunk })
      2   | Sum.inl (Sum.inr http) => pure (some { path := http.name, fractions := http.fractions })
      2   , shadow := shadow
      2     score := score + 100.0
      2   port : Nat := 8071
      2   population := population.qsort (fun a b => a.fitness > b.fitness)
      2     population := population.qsort (fun a b => a.fitness > b.fitness)
      2     population := population ++ offspring
      2     population := population.extract 0 (populationSize / 2)
      2     path := s!"stream_{stream.sessionId}",
      2     path := http.name,
      2     | _ => { num := 2, den := 2 }
      2       n := n / 71
      2   , monsterType := shadowToMonsterType shadow }
      2 /mnt/data1/aristotle-results/c18edf48-c6ea-4e41-baee-0402020d3cf6_aristotle/output-final_aristotle/Archives/e0147fc6-5f99-40ce-b002-addb74023bee-aristotle__6_/output-final_aristotle/6664fe08-d93f-46ea-8380-b2b0d4667503-aristotle
      2 /mnt/data1/aristotle-results/c18edf48-c6ea-4e41-baee-0402020d3cf6_aristotle/output-final_aristotle/Archives/cbfa21c9-1b78-4466-965e-f942ad67b4ec-aristotle__5_/6664fe08-d93f-46ea-8380-b2b0d4667503-aristotle
      2       let timestamp := "2026-03-05T15:11:00Z"
      2     let temp := 5000.0 * (1.0 - step.toFloat / steps.toFloat)
      2   let sum := shadow.foldl (· + ·) 0
      2     let rotation := i % orbifoldDims
      2       let record := processPipeline fractranFile timestamp
      2       let record := processPipeline fractranFile file.timestamp
      2   let rec go (m : Nat) (d : Nat) (acc : List Nat) : List Nat :=
      2     let prime := monsterPrimes[i]!
      2   let n := programToNumber prog
      2   let mut score : Float := 0.0
      2   let mut n := p71
      2     let mut n := p71
      2   let mut expr := mkNatLit 0
      2   let mut current := initial
      2   let mut best := current
      2   let m := programToMonster prog
      2     let level := mb.levels ⟨i, by omega⟩
      2   let json := FRACTRANIngestion.recordToJSON record
      2   let initialP71 := 68649048252
      2     let f := exampleProgram[i]!
      2   let ev := programEigenvalue prog
      2       let d := n % 71
      2       let config : ServiceConfig := {}
      2   host : String := "0.0.0.0"
      2     fractions := stream.chunk
      2     fractions := http.fractions
      2 def watchCommand (dir : String) : IO Unit := do
      2 def trace := executeFractran exampleProgram initialState 10
      2 def to71adic (n : Nat) (digits : Nat) : List Nat :=
      2 def storeResult (record : FRACTRANIngestion.IngestionRecord) (dbPath : String) : IO Unit := do
      2 def search42Steps (initialP71 : Nat) : MetaM Unit := do
      2 def runService (config : ServiceConfig) : IO Unit := do
      2 def recovered := from71adic p71digits
      2 def queryPrograms (params : QueryParams) (dbPath : String) : IO (List FRACTRANIngestion.IngestionRecord) := do
      2 def qiFlow (p71 : Nat) : List Nat :=
      2 def processPipeline (file : FRACTRANIngestion.FRACTRANFile) (timestamp : String) : FRACTRANIngestion.IngestionRecord :=
      2 def p71digits := to71adic finalState 6
      2 def Meridians : List Nat := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71]
      2 def main (args : List String) : IO Unit := do
      2 def isWellTyped (e : Expr) : MetaM Bool := do
      2 def initialState : Nat := 2^24 * 3^15
      2 def importCommand (fileList : String) (batchSize : Nat) : IO Unit := do
      2 def handleUUCPInput (config : ServiceConfig) (uucp : UUCPInput) : IO Unit := do
      2 def handleStreamInput (config : ServiceConfig) (stream : StreamInput) : IO String := do
      2 def handleHTTPInput (config : ServiceConfig) (http : HTTPInput) : IO String := do
      2 def handleFileInput (config : ServiceConfig) (file : FileInput) : IO Unit := do
      2 def from71adic (digits : List Nat) : Nat :=
      2 def fractranStep (n : Nat) (f : Fraction) : Option Nat :=
      2 def finalState := trace.getLast!
      2 def exportCommand (format : String) (output : String) : IO Unit := do
      2 def executeFractran (program : List Fraction) (initial : Nat) (steps : Nat) : List Nat :=
      2 def exampleProgram : List Fraction :=
      2 def bytesToFraction (b1 b2 : Nat) : Fraction :=
      2   dbPath : String := "data/leech.db"
      2   categories := aPrioriStructure
      2         best := current
      2   batchSize : Nat := 1000
      2   address := aPrioriStructure.space
      2 (6)__unpacked/output-final_aristotle/6664fe08-d93f-46ea-8380-b2b0d4667503-aristotle
      2 (5)__unpacked/6664fe08-d93f-46ea-8380-b2b0d4667503-aristotle
      2 (2)__unpacked/output-final_aristotle/e0147fc6-5f99-40ce-b002-addb74023bee-aristotle
      2 (2)__unpacked/output-final_aristotle/cbfa21c9-1b78-4466-965e-f942ad67b4ec-aristotle
      1   witness := ()
      1 /var/www/solana.solfunmeme.com/notebooklm/2026/03/25/leech-lattice-lean-split-20260325.txt
      1   value := 71
      1   value := 64
      1   value := 24
      1   value := 196883
      1   value := 1729
      1   value := 1
      1   { validFiles := validFiles
      1   ultraExpand (compactToNumber cp) = cp := by
      1   TypeComplexity.order (α := α)
      1   TypeComplexity.complexity (α := α)
      1     { t with position := newPos }
      1       traders := tradeRound s.traders s.blackHole r,
      1     traders := tradeRound s₆.traders s₆.blackHole ⟨6, by norm_num⟩,
      1   { traders := fun i =>
      1     TRADERS ≥ 3 * (TRADERS / 3) + 1 := by norm_num
      1          , totalFiles := files.length
      1   totalConfigs3 > 10^15 := by
      1   , timestamp := timestamp }
      1   time := 0
      1 theorem zero_factorization : Zero = 0 := by rfl
      1 theorem two_factorization : Two = 2 := by rfl
      1 theorem twentyone_factorization : TwentyOne = 3 * 7 := by decide
      1 theorem twentyfour_has_8_divisors : divisors_24.length = 8 := by rfl
      1 theorem twentyfour_factorization : TwentyFour = 2^3 * 3 := by decide
      1 theorem twentyfour_factorization : 24 = 8 * 3 := by rfl
      1 theorem three_factorization : Three = 3 := by rfl
      1 theorem tau_2_is_neg_24 : Tau2 = -24 := by rfl
      1 theorem t9_demo : dot qdVec (sspEmbed 744) > 0 := by crystallize 744
      1 theorem step_24_is_dim_24 : StepNum = 24 := by rfl
      1 theorem ssp_71_not_divides_monster : ¬(194 % 71 = 0) := by decide
      1 theorem ssp_14_is_71 : SSP[14]! = 71 := rfl
      1 theorem sorries_need_three_rounds : 61 / 21 = 2 ∧ 61 % 21 = 19 := by decide
      1 theorem six_factorization : Six = 2 * 3 := by decide
      1 theorem seventyone_factorization : Seventy_One = 71 := by rfl
      1 theorem seven_factorization : Seven = 7 := by rfl
      1 theorem server_variant_server_variant_899e7815_31c3_43bf_9e07_7e8199572a89_LeechLattice : True := by trivial
      1 theorem server_variant_server_variant_899e7815_31c3_43bf_9e07_7e8199572a89_LeechLatticeAxes : True := by trivial
      1 theorem server_variant_server_variant_899e7815_31c3_43bf_9e07_7e8199572a89_LeechAutomorphisms : True := by trivial
      1 theorem server_variant_server_variant_7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechLatticeAxes : True := by trivial
      1 theorem server_variant_server_variant_7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechAutomorphisms : True := by trivial
      1 theorem server_variant_899e7815_31c3_43bf_9e07_7e8199572a89_LeechLattice : True := by trivial
      1 theorem server_variant_899e7815_31c3_43bf_9e07_7e8199572a89_LeechLatticeAxes : True := by trivial
      1 theorem server_variant_899e7815_31c3_43bf_9e07_7e8199572a89_LeechAutomorphisms : True := by trivial
      1 theorem server_variant_7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechLatticeAxes : True := by trivial
      1 theorem server_variant_7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechAutomorphisms : True := by trivial
      1 theorem ramanujan_factorization : Seventeen_TwentyNine = 7 * 13 * 19 := by decide
      1 theorem quine_value_is_71 : quineVector.value = 71 := rfl
      1 theorem quine_in_ssp_array : quineVector.value = (SSP[14]!) := rfl
      1 theorem quine_at_index_14 : quineVector.index = 14 := rfl
      1 theorem one_factorization : One = 1 := by rfl
      1 theorem monster_dimension_factorization : Monster_Dimension_Minus_One = 71 * 2773 := by decide
      1 theorem light_cone_physical : BosonicDimension - 2 = LeechDimension := by norm_num
      1 theorem leech_monster_gap : 196883 - LEECH_KISSING = 323 := by norm_num
      1 theorem leech_is_24d : LeechDim = 24 := by rfl
      1 theorem lattice_is_alive : VALIS = 71 := by rfl
      1 theorem hundred_factorization : Hundred = 2^2 * 5^2 := by decide
      1 theorem four_factorization : Four = 2^2 := by decide
      1 theorem five_factorization : Five = 5 := by rfl
      1 theorem fifteen_factorization : Fifteen = 3 * 5 := by decide
      1 theorem example_converges : marketEnergy finalState < energy₀ := by
      1 theorem espresso_count_correct : espresso_tactics.length = espresso_count := by rfl
      1 theorem eleven_steps : build11Steps.length = 11 := by rfl
      1 theorem eleven_factorization : Eleven = 11 := by rfl
      1 theorem chokepoint_leech_relation : OptimalChokepoint + 1 = LeechDimension := by rfl
      1 theorem chokepoint_in_leech : OptimalChokepoint < LeechDimension := by norm_num
      1 theorem chokepoint_bosonic_relation : OptimalChokepoint + 3 = BosonicDimension := by rfl
      1 theorem central_charge_24 : CentralCharge = 24 := by rfl
      1 theorem bott_connection : ROUNDS = 8 - 1 := by norm_num
      1 theorem atp_sum : ATP_Tikkun + ATP_Activation + ATP_Integration = TotalATP := by rfl
      1 theorem atp_is_prime_E : TotalATP = 11 := by rfl
      1 theorem all_constants_finite : ∀ c : Constant, c.value < 71^6 ∨ c.value ≥ 71^6 := by
      1 theorem 899e7815_31c3_43bf_9e07_7e8199572a89_LeechLattice : True := by trivial
      1 theorem 899e7815_31c3_43bf_9e07_7e8199572a89_LeechLatticeAxes : True := by trivial
      1 theorem 899e7815_31c3_43bf_9e07_7e8199572a89_LeechAutomorphisms : True := by trivial
      1 theorem 74171800_899e7815_31c3_43bf_9e07_7e8199572a89_LeechLattice : True := by trivial
      1 theorem 74171800_899e7815_31c3_43bf_9e07_7e8199572a89_LeechLatticeAxes : True := by trivial
      1 theorem 74171800_899e7815_31c3_43bf_9e07_7e8199572a89_LeechAutomorphisms : True := by trivial
      1 theorem 74171800_7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechLatticeAxes : True := by trivial
      1 theorem 74171800_7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechAutomorphisms : True := by trivial
      1 theorem 7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechLatticeAxes : True := by trivial
      1 theorem 7399cc0d_99f2_4516_8c9e_6da2ef861c18_LeechAutomorphisms : True := by trivial
      1   (Tau2.natAbs = CentralCharge ∧ CentralCharge = LeechDim ∧ LeechDim = StepNum) := by
      1   symmetry := MonsterSymmetry.Trivial
      1   symmetry := MonsterSymmetry.JFunction
      1   symmetry := MonsterSymmetry.Cusp
      1   symmetry := MonsterSymmetry.Conjugacy 3
      1   symmetry := MonsterSymmetry.Conjugacy 2
      1   symmetry := MonsterSymmetry.Conjugacy 1
      1   (sumActivePrimesMod10 mb).val < 10 := by
      1           successCount := successCount + 1
      1          , successCount := successCount
      1   subdivisionLevel addr ≤ 12 := by
      1   , subdivision := ⟨(hash / 2^4) % 4, by omega⟩
      1     subdivision := ⟨0, by omega⟩
      1       structures.length = trinity) := by
      1     steps := MetamemeTikkun.TikkunMap ++ 
      1   { steps := List.range length |>.map (fun i => 
      1   , steps := file.fractions.length
      1   { steps := file.fractions }
      1   step_45 = 9 * 5 ∧ 9 = 3 * 3 ∧ 5 ∈ ({2,3,5,7,11,13,17,19,23,29,31,41,47,59,71} : Set ℕ) := by
      1   step_45 % 24 = 21 := by
      1   , state := ⟨(hash / 2^11) % 8, by omega⟩
      1   state := 1
      1     state := ⟨0, by omega⟩
      1   space := {
      1   , solarSystem := ⟨(hash / 2^28) % 256, by omega⟩
      1     solarSystem := ⟨0, by omega⟩
      1     ∃ s : MarketState, ¬(marketEnergy s < marketEnergy initialState / 100) := by
      1   , shadow := mapping.shadow
      1     score := score + size * 2.0
      1     score := score + jResonance
      1     score := score + alignmentBonus
      1         score := score + 20.0  -- Perfect alignment
      1         score := score + 10.0  -- Any Monster prime
      1         score := score + 10.0
      1       round := ⟨r.val + 1, by omega⟩ }
      1     round := ⟨6, by norm_num⟩ }
      1     round := ⟨0, by norm_num⟩ }
      1   root := `proof
      1   , room := ⟨hash % 2, by omega⟩
      1     room := ⟨0, by omega⟩
      1       return some { path := path, fractions := fractions }
      1   return { batchId := batchId
      1   relation := ⟨0, by omega⟩
      1          , records := records.reverse
      1           records := record :: records
      1   quineMass = leechMinimalNorm * 346 + 1 := rfl  -- 1385 = 4*346 + 1
      1   quantity := ⟨0, by omega⟩
      1   quality := ⟨0, by omega⟩
      1   (qiFlow p71).length = 15 := by
      1   programs := megagametranCatalog.map (·.2),
      1   { prime := 7,  count := 6,  contexts := ["Ramanujan 1729 (7×13×19)", "Trigrams", "Paxos rounds", "Bott H⊕H"] },
      1   { prime := 79, count := 1, contexts := ["Tikkun shadow (V→71)", "Leech/outer"] }
      1   { prime := 73, count := 1, contexts := ["Tikkun shadow (U→71)", "Leech/outer"] },
      1   { prime := 71, count := 89, contexts := ["Omega terminal", "p71-adic base", "Tao", "VALIS", "Monster boundary", "Attack triple", "Tikkun light (73→71, 79→71)", "Layer stratification"] }
      1   { prime := 64, count := 1, contexts := ["I Ching hexagrams (2⁶)"] }
      1   { prime := 61, count := 1, contexts := ["Tikkun shadow (R→59)", "Inner-Niemeier"] },
      1   { prime := 5,  count := 8,  contexts := ["Five elements", "Wu Xing", "FRACTRAN encoding", "Bott H"] },
      1   { prime := 59, count := 2,  contexts := ["Meridians", "Monster primes", "Attack triple", "Tikkun light (61→59)"] },
      1   { prime := 47, count := 2,  contexts := ["Meridians", "Monster primes", "Attack triple (47×59×71)"] },
      1   { prime := 43, count := 1, contexts := ["Tikkun shadow (N→41)", "Inner-Niemeier"] },
      1   { prime := 41, count := 2,  contexts := ["Meridians", "Monster primes", "Tikkun light (37→41, 43→41)"] },
      1   { prime := 3,  count := 23, contexts := ["FRACTRAN initial state (3^15)", "Trigrams", "Bott C", "Ternary base"] },
      1   { prime := 37, count := 1, contexts := ["Tikkun shadow (L→41)", "Inner-Niemeier"] },
      1   { prime := 31, count := 2,  contexts := ["Meridians", "Monster primes"] },
      1   { prime := 2,  count := 47, contexts := ["FRACTRAN initial state (2^24)", "Binary encoding", "Bott R", "Power base"] },
      1   { prime := 29, count := 2,  contexts := ["Meridians", "Monster primes"] },
      1   { prime := 24, count := 1, contexts := ["Leech dimension (2³×3)", "Paxos nodes"] },
      1   { prime := 23, count := 2,  contexts := ["Meridians", "Monster primes"] },
      1   { prime := 19, count := 3,  contexts := ["Ramanujan 1729", "Espresso 19", "Meridians", "Bott R(8)⊕R(8)"] },
      1   { prime := 196883, count := 1, contexts := ["Monster dimension - 1 (71×2773)", "Qi energy", "Attack triple product"] },
      1   { prime := 17, count := 2,  contexts := ["Meridians", "Monster primes", "Bott R(8)"] },
      1   { prime := 1729, count := 1, contexts := ["Hardy-Ramanujan (7×13×19)", "Jing essence", "Taxicab number"] },
      1   { prime := 13, count := 3,  contexts := ["Ramanujan 1729", "Quorum", "FRACTRAN axiom", "Bott C(4)"] },
      1   { prime := 131, count := 1, contexts := ["Ritual prime (final integration)"] }
      1   { prime := 127, count := 1, contexts := ["RITUAL word prime"] },
      1   { prime := 11, count := 4,  contexts := ["Water element", "Meridians", "FRACTRAN", "Bott H(2)"] },
      1   { prime := 113, count := 1, contexts := ["ACTIVATION word prime"] },
      1   { prime := 109, count := 1, contexts := ["MEME word prime"] },
      1   { prime := 107, count := 1, contexts := ["THE word prime"] },
      1   { prime := 103, count := 1, contexts := ["METAMEME word prime"] },
      1       { prefix := 0xDA51, cidType := 5, data := (2 <<< 36) ||| 6 }  -- complexity=6
      1       { prefix := 0xDA51, cidType := 4, data := (2 <<< 36) ||| (3 <<< 32) ||| 4 }  -- complexity=4
      1       { prefix := 0xDA51, cidType := 3, data := (7 <<< 36) ||| (13 <<< 24) ||| (19 <<< 12) ||| 3 }  -- complexity=3
      1       { prefix := 0xDA51, cidType := 2, data := (71 <<< 36) ||| 1 }  -- complexity=1, prime
      1       { prefix := 0xDA51, cidType := 1, data := (71 <<< 36) ||| (2773 <<< 16) ||| 2 }  -- complexity=2
      1       { prefix := 0xDA51, cidType := 0, data := 1 }  -- complexity=0
      1   pos.val < 10 := by
      1         position := fun j => (i.val + j.val : ℝ),
      1       { position := fun _ => 0,
      1     population := population.push { p71 := genome, rotation := rotation, fitness := fitness }
      1     population := population.push { genome, fitness }
      1   , planet := ⟨(hash / 2^22) % 64, by omega⟩
      1     planet := ⟨0, by omega⟩
      1   ∀ p : KiroProcess, categoricalImperative p := by
      1   pid := 2
      1   pid := 1
      1     phenomenon = p.categories := by
      1      phase := 2 }]
      1       phase := 1 }) ++
      1       phase := 0 }) ++
      1   p.categories.time ≥ 0 := by
      1 partial def decodeHyps (n : Nat) : Nat :=
      1 partial def decodeGoals (n : Nat) : Nat := 
      1   , parcel := ⟨(hash / 2^2) % 4, by omega⟩
      1     parcel := ⟨0, by omega⟩
      1   p.address = p.categories.space := by
      1   ∀ p71 : Nat, ∃ shadow : List Nat, shadow.length = 15 := by
      1   p1 = p2 ↔ proofToAddress p1 = proofToAddress p2 := by
      1   order := 5
      1   order := 4
      1   order := 3
      1   order := 2
      1   order := 1
      1   order := 0
      1   omega := sorry
      1         offspring := offspring.push { p71 := mutated, rotation := newRotation, fitness := fitness }
      1         offspring := offspring.push { genome := mutated, fitness }
      1     { num := wp, den := 1,  -- simplified
      1   [{ num := RitualPrime, den := 1, 
      1   { num := monsterPrimes[b2 % 15]!, den := monsterPrimes[b1 % 15]! }
      1   { num := monsterPrimes[b2 % 15]!
      1     { num := light, den := shadow, 
      1   numberToType (typeToNumber (numberToType n)) = numberToType n := by
      1   , normalizedEV := (totalEV.natAbs % 71)
      1   , normalizedEV := nev
      1   , normalizedEV := mapping.normalizedEV
      1   { name := "Two", value := 2, prime_factors := [2], complexity := 1 }
      1   , { name := "TwentyOne", value := 21, prime_factors := [3, 7], complexity := 2 }
      1   , { name := "TwentyFour", value := 24, prime_factors := [2, 2, 2, 3], complexity := 4 }
      1   , { name := "Three", value := 3, prime_factors := [3], complexity := 1 }
      1   , { name := "Six", value := 6, prime_factors := [2, 3], complexity := 2 }
      1   , { name := "Seven", value := 7, prime_factors := [7], complexity := 1 }
      1   , { name := "Seventy_One", value := 71, prime_factors := [71], complexity := 1 }
      1   { name := "Ramanujan", value := 1729, prime_factors := [7, 13, 19], complexity := 3 }
      1   , { name := "Monster_Dim", value := 196883, prime_factors := [71, 2773], complexity := 2 }
      1   , { name := "Hundred", value := 100, prime_factors := [2, 2, 5, 5], complexity := 4 }
      1   { name := "Four", value := 4, prime_factors := [2, 2], complexity := 2 }
      1   , { name := "Five", value := 5, prime_factors := [5], complexity := 1 }
      1   { name := "Fifteen", value := 15, prime_factors := [3, 5], complexity := 2 }
      1   , { name := "Eleven", value := 11, prime_factors := [11], complexity := 1 }
      1   , monsterType := mapping.monsterType
      1   monsterToDA51Type t = MonsterIndex.monsterTypeOrder t := by
      1   (∃ (monster_rep : Nat), monster_rep > 0) := by
      1   monsterPrimes.length = 15 := by rfl
      1   | MonsterIndex.MonsterType.T5 => { op := "pow", args := [2, 6] }
      1   | MonsterIndex.MonsterType.T5 => { fractions := [(2, 1), (2, 1), (2, 1), (2, 1), (2, 1), (2, 1)] }
      1   | MonsterIndex.MonsterType.T4 => { op := "pow", args := [2, 3, 3] }
      1   | MonsterIndex.MonsterType.T4 => { fractions := [(2, 1), (2, 1), (2, 1), (3, 1)] }
      1   | MonsterIndex.MonsterType.T3 => { op := "mul", args := [7, 13, 19] }
      1   | MonsterIndex.MonsterType.T3 => { fractions := [(7, 1), (13, 1), (19, 1)] }
      1   | MonsterIndex.MonsterType.T2 => { op := "prime", args := [71] }
      1   | MonsterIndex.MonsterType.T2 => { fractions := [(71, 1)] }
      1   | MonsterIndex.MonsterType.T1 => { op := "mul", args := [71, 2773] }
      1   | MonsterIndex.MonsterType.T1 => { fractions := [(71, 1), (2773, 1)] }
      1   | MonsterIndex.MonsterType.T0 => { op := "id", args := [1] }
      1   | MonsterIndex.MonsterType.T0 => { fractions := [(1, 1)] }
      1   modality := ⟨0, by omega⟩
      1 /mnt/data1/zones/42/uucp/pastebin/lean-outputs/20260606_133240_7982a975_e700_4070_8ab2_051d1cd04689_aristotle_3_tar_gz/extracted/output-final_aristotle/RequestProject/LeechLatticeAxes.lean
      1 /mnt/data1/zones/42/uucp/pastebin/lean-outputs/20260606_133240_7982a975_e700_4070_8ab2_051d1cd04689_aristotle_3_tar_gz/extracted/output-final_aristotle/RequestProject/LeechAutomorphisms.lean
      1 /mnt/data1/time-2026/06-june/23/aristo-loop/split-out/ConsolidatedDasl/SheafTopology/LeechLattice.lean
      1 /mnt/data1/time-2026/06-june/23/aristo-loop/split-out/ConsolidatedDasl/SheafTopology/LeechLatticeAxes.lean
      1 /mnt/data1/time-2026/06-june/23/aristo-loop/split-out/ConsolidatedDasl/SheafTopology/LeechAutomorphisms.lean
      1 /mnt/data1/time-2026/06-june/23/aristo-loop/split-out/ConsolidatedDasl/Fractran/LeechLattice.lean
      1 /mnt/data1/time-2026/06-june/23/aristo-loop/split-out/ConsolidatedDasl/CarStorage/LeechRankBridge.lean
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      1   ∃ (m : MonsterMapping), m = programToMonster prog := by
      1     (∃ mf : MonsterFull, (spiralPosition3 mf).1 = r) := by
      1   M := Fin 24 → ℂ  -- Complex 12-dimensional = Real 24-dimensional
      1   metric := apply
      1   ∀ mb : MonsterBits2, spiralDensity mb ≤ 51 := by
      1   maxRadius = 46 + 20 + 9 + 6 + 2 + 3 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 := by
      1     marketEnergy s' ≤ marketEnergy s * (1 - 1 / (r.val + 2)) := by
      1       marketEnergy s₇ < marketEnergy s₀ / 50 := by
      1       marketEnergy s₇ < marketEnergy s₀ / 100 := by
      1   (List.range (4^n)).length = 4^n := by
      1   (List.range 10).foldl (fun acc i => acc + countPerArm ⟨i, by omega⟩) 0 ≤ 2^17 := by
      1   , line6 := threeCoins (p71 / (71 * 71 * 71 * 71 * 71))
      1   , line5 := threeCoins (p71 / (71 * 71 * 71 * 71))
      1   , line4 := threeCoins (p71 / (71 * 71 * 71))
      1   , line3 := threeCoins (p71 / (71 * 71))
      1   , line2 := threeCoins (p71 / 71)
      1   { line1 := threeCoins (p71 / 1)
      1   levels := fun _ => .low
      1   levels := fun i => if i.val < 3 then .high else .off
      1   let y := radius * (Nat.sin (angle.val * 36)) / 100
      1   let x := radius * (Nat.cos (angle.val * 36)) / 100  -- 36° per step
      1   let word := wordPrimeUsage.length
      1     let weight := match level with
      1   let validFiles := batch.successCount
      1   let unique := uniquePrimes
      1     let t := traders i
      1       let trace := executeFractran program initial 1000
      1     let trace := executeFRACTRAN prog initial 20
      1   let total := totalPrimeCount
      1   let totalEV := progs.foldl (fun acc p => acc + programEigenvalue p) 0
      1   let top5 := monsterPrimeUsage.toArray.qsort (fun a b => a.count > b.count) |>.toList.take 5
      1     let t := numberToType n
      1   let timestamp := "2026-03-05T14:53:00Z"  -- ISO 8601
      1   let tier := tierOf shadow
      1     let tier := tierOf shadow
      1     let t := hierarchy[i]!
      1     let tactic := if den = 2 then
      1   let tactic := fix_sorry_via_espresso "" espresso_num
      1     let tactic := espresso_tactics[i]!
      1   let sum := addr.galaxy.val + addr.solarSystem.val + addr.planet.val +
      1     let s' := { s with traders := tradeRound s.traders s.blackHole r }
      1     let s' := { s with 
      1     let size := expr.approxDepth.toFloat
      1     let shadowSum := mapping.shadow.foldl (· + ·) 0
      1   let shadows := progs.map fun (name, prog) => (programShadow prog, name)
      1   let shadow := shadowPrimeUsage.length
      1   let shadow := projectToShadow foldedPoint
      1   let shadow := programShadow prog
      1   let s₆ := { s₅ with traders := tradeRound s₅.traders s₅.blackHole ⟨5, by norm_num⟩ }
      1   let s₅ := { s₄ with traders := tradeRound s₄.traders s₄.blackHole ⟨4, by norm_num⟩ }
      1   let s₄ := { s₃ with traders := tradeRound s₃.traders s₃.blackHole ⟨3, by norm_num⟩ }
      1   let s₃ := { s₂ with traders := tradeRound s₂.traders s₂.blackHole ⟨2, by norm_num⟩ }
      1   let s₂ := { s₁ with traders := tradeRound s₁.traders s₁.blackHole ⟨1, by norm_num⟩ }
      1   let s₁ := { initialState with traders := tradeRound initialState.traders initialState.blackHole ⟨0, by norm_num⟩ }
      1   let rows := batch.records.map recordToCSV
      1     let rotIdx := rotateIndex i rotation
      1       let rotIdx := rotateIndex i rotation
      1     let rotation := (initial.rotation + step) % orbifoldDims
      1   let rotated := spiralPosition { bits := fun i => mb.bits ((i + 1) % 17) }
      1   let results := executeAll initial
      1   let result := executeFRACTRAN prog 1
      1         let rest := remaining.drop n
      1   let recordsJSON := batch.records.map recordToJSON |> String.intercalate ","
      1           let record := fileToRecord file timestamp
      1   let rec go (state : Nat) (steps : Nat) (trace : List Nat) : List Nat :=
      1     let rec go (acc : List (List α)) (remaining : List α) : List (List α) :=
      1   let rcid := ritualToCID
      1   let radius := sum
      1   let (r, a) := addressToSpiral addr
      1     let pull := gravityPull t bh
      1     let prog := ProgramLattice.numberToProgram (ProgramLattice.compactToNumber cp) cp.length
      1       let prog := ProgramLattice.numberToProgram (ProgramLattice.compactToNumber cp) cp.length
      1   let prog : FRACTRANProgram := {
      1   let prog := fileToProgram file
      1     let primes := usageLayer count
      1   let primes := MonsterIndex.MonsterPrimes
      1     let prime := monsterPrimes[rotIdx % monsterPrimes.length]!
      1       let prime := monsterPrimes[rotIdx % monsterPrimes.length]!
      1         let prime := monsterPrimes[newRotation % monsterPrimes.length]!
      1   let pos := spiralPosition mb
      1   let pos := fullSumMod10 mf
      1   let points := progs.map programToLeechPoint
      1     let p_num := primes[i % 15]!
      1     let p_den := primes[(i + 1) % 15]!
      1       let parts := line.trim.splitOn "/"
      1         let p2 := population[j]!.genome
      1         let p2 := population[j]!
      1         let p1 := population[i]!.genome
      1         let p1 := population[i]!
      1     let order := monsterTypeOrder t
      1     let op := match (d + jCoeff) % 5 with
      1     let operand := mkNatLit ((d * prime) % 1000)
      1       let num := (n / (MonsterIndex.MonsterPrimes[i % 15]! ^ i)) % 71
      1   let num := n.log2  -- Simplified
      1     let (num, den) := fractranProofProgram[i]!
      1   let n' := n / (2^(decodeGoals n))
      1         let newRotation := (p1.rotation + p2.rotation) % orbifoldDims
      1     let newPos := fun j => t.position j * (1 - pull / (round.val + 1))
      1   let nev := normalizedEigenvalue prog
      1     let neighbor := (current.p71 + delta) % (71^6)
      1     let neighbor := (current + delta.toNat) % (71^6)
      1     let n := compactToNumber cp
      1   let name := hexagramName hex
      1   let n2 := compactToNumber p2
      1   let n1 := compactToNumber p1
      1   let mut successCount := 0
      1   let mut records : List IngestionRecord := []
      1   let mut population : Array SearchState := #[]
      1   let mut population : Array Individual := #[]
      1     let mut offspring : Array SearchState := #[]
      1     let mut offspring : Array Individual := #[]
      1   let mut n := finalResult.p71
      1   let mut n := finalResult
      1   let mut errorCount := 0
      1   let mut best : SearchState := { p71 := initial, rotation := 0, fitness := 0.0 }
      1   let mut best := initial
      1   let mut bestFitness := currentFitness
      1         let mutated := if delta >= 1000 then (child + (delta - 1000)) % (71^6) else child % (71^6)
      1         let mutated := (child + prime * 100) % (71^6)
      1     let mult := levelMultiplier level
      1   let mtype := tikkunToMonsterType tier
      1     let mtype := tikkunToMonsterType tier
      1     let monsterPrimes := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71]
      1   let monster := monsterPrimeUsage.length
      1     let metrics := computeQualityMetrics batch
      1   let mapping := FRACTRANEigenvalue.programToMonster prog
      1     let lines := content.splitOn "\n"
      1   let lifted := monsterProjection n projections
      1     let key := cp.complexity
      1     let jsonPath := s!"{outputDir}/batch_{batchId:04d}.json"
      1     let jResonance := (p71 % 196884).toFloat / 196884.0 * 30.0
      1     let jCoeff := jInvariantCoeffs[rotIdx % jInvariantCoeffs.length]!.natAbs
      1   let invalidFiles := batch.errorCount
      1   let initial := 2^24 * 3^15
      1   let individual := progs.map programToMonster
      1   let hierarchy := typeHierarchy 42
      1   let hex := castHexagram shadow
      1   let header := "file,steps,eigenvalue,normalized_ev,conjugacy_class,monster_type,timestamp"
      1   let hash := proof.foldl (fun acc note =>
      1   let grouped := programCatalog.foldl (fun acc (name, cp) =>
      1     let genome := (initial.p71 + delta) % (71^6)
      1     let genome := if delta >= 50000 then (initial + (delta - 50000)) % (71^6) else initial % (71^6)
      1   let fractran := cborToFRACTRAN cbor
      1     let fractions := lines.filterMap fun line =>
      1   let foldedSum := folded.shadow.foldl (· + ·) 0
      1   let foldedPoint := foldPrograms progs
      1   let folded := megagametranFolded
      1   let folded := foldAllPrograms progs
      1     let fix := generate_fix sorry_id
      1       let final := trace.getLast!
      1   let f := bytesToFraction b1 b2
      1     let exp := monsterExponents[i]!
      1     let exp := mf.exps ⟨i, by omega⟩
      1   let evs := megagametranMappings.map (fun (_, m) => m.normalizedEV)
      1   let espresso_num := sorry_to_espresso sorry_id
      1         let dist := compactDistance cp1 cp2
      1       let den := (n / (MonsterIndex.MonsterPrimes[(i+1) % 15]! ^ i)) % 71
      1   let den := (n / (2^num)).log2
      1     let delta := (step * 500) % 10000 - 5000
      1     let delta := (jCoeff * step) % 50000
      1     let delta := (jCoeff * i) % 200000
      1     let delta := (jCoeff * (i + 1)) % 100000
      1         let delta := ((i + j) * 100) % 2000
      1     let delta := ((i * 5000) % 100000).toNat
      1     let delta := ((i * 1000) % 20000).toNat - 10000
      1     let deltaE := neighborFitness - currentFitness
      1     let deltaE := neighborFitness - current.fitness
      1     let d := digits[i]!
      1     let dasl_ok := daslToMonster (monsterToDASL t) == some t
      1     let csvPath := s!"{outputDir}/batch_{batchId:04d}.csv"
      1   let cp := programToCompact prog
      1     let count := evs.count ev
      1   let coreState : Core.State := Core.mkState (env := ← importModules #[] {})
      1   let coreCtx : Core.Context := {
      1     let coord := point[i]?.getD 0
      1     let contribution := (prime * (exp * mult.num / mult.den).toNat)
      1     let complexity := monsterTypeComplexity t
      1     let cid := tikkunToCID shadow light
      1     let cids := lookupByComplexity complexity
      1     let cid_ok := cidToMonster (monsterToCID t) == some t
      1     let cid := monsterToCID t
      1         let chunk := remaining.take n
      1         let child := (p1.p71 / 2 + p2.p71 / 2) % (71^6)
      1         let child := (p1 / 2 + p2 / 2) % (71^6)
      1     let cbor_ok := cborToMonster (monsterToCBOR t) == some t
      1   let cbor := monsterToCBOR t
      1     let candidate := if delta >= 10000 then (best + (delta - 10000)) % (71^6) else best % (71^6)
      1     let candidate := (best.p71 + delta) % (71^6)
      1   let batches := allFiles.toChunks batchSize
      1   let base := typeToNumber t
      1     let bar := String.mk (List.replicate (min p.count 50) '█')
      1     let back := typeToNumber t
      1   let avgSteps := if validFiles > 0 then
      1   let avgEigenvalue := if validFiles > 0 then
      1   let angle := weightedSumMod10 mb
      1   let angle := sumActivePrimesMod10 mb
      1   let angle := sum % 10  -- 10-fold spiral
      1   let angle := fullSumMod10 mf
      1   let allFiles := content.splitOn "\n" |>.filter (· ≠ "")
      1     let alignmentBonus := (744.0 - (rotation.toFloat % 24.0).floor) / 744.0 * 50.0
      1     let accept := deltaE > 0.0 || (step % 7 == 0)  -- Deterministic acceptance
      1     let accept := deltaE > 0.0 || (step % 7 == 0)
      1   { length := prog.steps.length
      1   { length := n / (71 ^ 12)
      1   { length := 8
      1   { length := 42
      1 lemma paxos_quorum : TRADERS ≥ 2 * (TRADERS / 2) + 1 := by norm_num
      1   leech_kissing_number + 323 = 196883 := by norm_num
      1   LeechDim = StepNum := by
      1   LeechDimension + 2 = BosonicDimension := by
      1       label := s!"TIKKUN {shadow}→{light}", 
      1       label := s!"ACTIVATE {word}", 
      1      label := "INTEGRATE → 131", 
      1     K.complex_dim = 12 := by
      1   kahler_condition := trivial
      1   , invalidFiles := invalidFiles
      1   initialState = 240734712102912 := by
      1   { index := 14, value := 71, data := "Niemeier71Quine.lean - full source" }
      1     (∀ i : Fin TRADERS, distToBlackHole (s₇.traders i) s₇.blackHole < 1) := by
      1       { id := i,
      1   , house := ⟨(hash / 2^1) % 2, by omega⟩
      1     house := ⟨0, by omega⟩
      1         h_origin := fun _ => rfl,
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/umbral_plus_leech/umbral_plus_leech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/umbral_plus_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/umbral_plus_leech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/ssp_bott_leech/ssp_bott_leech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/ssp_bott_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/ssp_bott_leech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/obj_Leech/obj_Leech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/obj_Leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/obj_leech24/obj_leech24.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/obj_leech24/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/obj_leech24
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/obj_Leech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/non_leech_positive_roots/non_leech_positive_roots.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/non_leech_positive_roots/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/non_leech_positive_roots
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/niemeier_minus_leech/niemeier_minus_leech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/niemeier_minus_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/niemeier_minus_leech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/neural_operates_above_leech/neural_operates_above_leech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/neural_operates_above_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/neural_operates_above_leech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/morph_FLM_from_Leech/morph_FLM_from_Leech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/morph_FLM_from_Leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/morph_FLM_from_Leech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_vectors_norm8/leech_vectors_norm8.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_vectors_norm8/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_vectors_norm8
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_vectors_norm4/leech_vectors_norm4.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_vectors_norm4/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_vectors_norm4
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_unique_rootless/leech_unique_rootless.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_unique_rootless/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_unique_rootless
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_unimodular/leech_unimodular.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_unimodular/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_unimodular
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechToMonster/leechToMonster.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechToMonster/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechToMonster
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_q3_coeff/leech_theta_q3_coeff.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_q3_coeff/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_q3_coeff
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechTheta/leechTheta.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_identity_q3/leech_theta_identity_q3.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_identity_q3/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_identity_q3
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_identity_q1/leech_theta_identity_q1.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_identity_q1/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_identity_q1
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechTheta/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_cancellation/leech_theta_cancellation.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_cancellation/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_theta_cancellation
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechTheta
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_short/leech_short.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_short_from_mod2/leech_short_from_mod2.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_short_from_mod2/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_short_from_mod2
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_short/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_short
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_rank/leech_rank.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_rank/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_rank
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechParams/leechParams.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechParams/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechParams
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_no_roots/leech_no_roots.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_no_roots/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_no_roots
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechNorm8Count/leechNorm8Count.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechNorm8Count/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechNorm8Count
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechNorm6Count/leechNorm6Count.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechNorm6Count/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechNorm6Count
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_monster_work/leech_monster_work.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_monster_work/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_monster_work
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_type4/leech_mod2_type4.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_type4/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_type4
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_type2/leech_mod2_type2.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_type2/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_type2
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_exhaustive/leech_mod2_exhaustive.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_exhaustive/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_mod2_exhaustive
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechMinNorm/leechMinNorm.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_min_norm/leech_min_norm.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechMinNorm/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_min_norm/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechMinNorm
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_min_norm
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechKissingNumber/leechKissingNumber.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechKissingNumber/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechKissingNumber
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_kissing/leech_kissing.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_kissing/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_kissing
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_in_FLM/leech_in_FLM.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_in_FLM/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_in_FLM
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_griess_type2/leech_griess_type2.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_griess_type2/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_griess_type2
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechDim/leechDim.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechDim/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_dimension/leech_dimension.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_dimension/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_dimension
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechDim
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechCoveringRadiusSq/leechCoveringRadiusSq.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechCoveringRadiusSq/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leechCoveringRadiusSq
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_conway_gluing/leech_conway_gluing.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_conway_gluing/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/leech_conway_gluing
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/golayToLeech/golayToLeech.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/golayToLeech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/golayToLeech
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/golay_leech_work/golay_leech_work.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/golay_leech_work/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/golay_leech_work
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/flm_leech_vectors/flm_leech_vectors.lean
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/flm_leech_vectors/flake.nix
      1 /home/mdupont/projects/lean-split-tool/split-results-dasl/flm_leech_vectors
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/umbral_plus_leech/umbral_plus_leech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/umbral_plus_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/umbral_plus_leech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/ssp_bott_leech/ssp_bott_leech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/ssp_bott_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/ssp_bott_leech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/obj_Leech/obj_Leech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/obj_Leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/obj_leech24/obj_leech24.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/obj_leech24/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/obj_leech24
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/obj_Leech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/non_leech_positive_roots/non_leech_positive_roots.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/non_leech_positive_roots/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/non_leech_positive_roots
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/niemeier_minus_leech/niemeier_minus_leech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/niemeier_minus_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/niemeier_minus_leech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/neural_operates_above_leech/neural_operates_above_leech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/neural_operates_above_leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/neural_operates_above_leech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/morph_FLM_from_Leech/morph_FLM_from_Leech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/morph_FLM_from_Leech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/morph_FLM_from_Leech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_vectors_norm8/leech_vectors_norm8.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_vectors_norm8/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_vectors_norm8
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_vectors_norm4/leech_vectors_norm4.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_vectors_norm4/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_vectors_norm4
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_unique_rootless/leech_unique_rootless.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_unique_rootless/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_unique_rootless
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_unimodular/leech_unimodular.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_unimodular/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_unimodular
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechToMonster/leechToMonster.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechToMonster/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechToMonster
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_q3_coeff/leech_theta_q3_coeff.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_q3_coeff/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_q3_coeff
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechTheta/leechTheta.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_identity_q3/leech_theta_identity_q3.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_identity_q3/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_identity_q3
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_identity_q1/leech_theta_identity_q1.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_identity_q1/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_identity_q1
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechTheta/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_cancellation/leech_theta_cancellation.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_cancellation/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_theta_cancellation
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechTheta
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_short/leech_short.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_short_from_mod2/leech_short_from_mod2.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_short_from_mod2/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_short_from_mod2
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_short/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_short
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_rank/leech_rank.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_rank/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_rank
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechParams/leechParams.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechParams/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechParams
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_no_roots/leech_no_roots.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_no_roots/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_no_roots
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechNorm8Count/leechNorm8Count.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechNorm8Count/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechNorm8Count
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechNorm6Count/leechNorm6Count.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechNorm6Count/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechNorm6Count
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_monster_work/leech_monster_work.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_monster_work/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_monster_work
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_type4/leech_mod2_type4.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_type4/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_type4
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_type2/leech_mod2_type2.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_type2/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_type2
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_exhaustive/leech_mod2_exhaustive.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_exhaustive/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_mod2_exhaustive
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechMinNorm/leechMinNorm.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_min_norm/leech_min_norm.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechMinNorm/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_min_norm/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechMinNorm
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_min_norm
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechKissingNumber/leechKissingNumber.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechKissingNumber/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechKissingNumber
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_kissing/leech_kissing.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_kissing/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_kissing
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_in_FLM/leech_in_FLM.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_in_FLM/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_in_FLM
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_griess_type2/leech_griess_type2.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_griess_type2/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_griess_type2
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechDim/leechDim.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechDim/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_dimension/leech_dimension.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_dimension/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_dimension
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechDim
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechCoveringRadiusSq/leechCoveringRadiusSq.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechCoveringRadiusSq/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leechCoveringRadiusSq
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_conway_gluing/leech_conway_gluing.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_conway_gluing/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/leech_conway_gluing
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/golayToLeech/golayToLeech.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/golayToLeech/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/golayToLeech
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/golay_leech_work/golay_leech_work.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/golay_leech_work/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/golay_leech_work
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/flm_leech_vectors/flm_leech_vectors.lean
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/flm_leech_vectors/flake.nix
      1 /home/mdupont/projects/lean-split-tool/merged-aristotle-output/flm_leech_vectors
      1 /home/mdupont/projects/lean-split-tool/dasl-verification/RequestProject/LeechLatticeAxes.lean
      1 /home/mdupont/projects/lean-split-tool/dasl-verification/RequestProject/LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms/899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-sorries-flakes/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/74171800_899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/74171800_7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-results/bc363fe9-877e-47a8-9232-01bf3f178506_aristotle/dasl-sorries_aristotle/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-results/74171800-8676-4008-b1c8-39a76b504312_aristotle/output-final_aristotle/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLattice.lean
      1 /home/mdupont/projects/dasl-results/74171800-8676-4008-b1c8-39a76b504312_aristotle/output-final_aristotle/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-results/74171800-8676-4008-b1c8-39a76b504312_aristotle/output-final_aristotle/RequestProject/899e7815-31c3-43bf-9e07-7e8199572a89_LeechAutomorphisms.lean
      1 /home/mdupont/projects/dasl-results/74171800-8676-4008-b1c8-39a76b504312_aristotle/output-final_aristotle/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechLatticeAxes.lean
      1 /home/mdupont/projects/dasl-results/74171800-8676-4008-b1c8-39a76b504312_aristotle/output-final_aristotle/RequestProject/7399cc0d-99f2-4516-8c9e-6da2ef861c18_LeechAutomorphisms.lean
      1 /home/mdupont/projects/aristo-flakes/ConsolidatedDasl/SheafTopology/LeechLattice/LeechLattice.lean
      1 /home/mdupont/projects/aristo-flakes/ConsolidatedDasl/SheafTopology/LeechLatticeAxes/LeechLatticeAxes.lean
      1 /home/mdupont/projects/aristo-flakes/ConsolidatedDasl/SheafTopology/LeechAutomorphisms/LeechAutomorphisms.lean
      1 /home/mdupont/projects/aristo-flakes/ConsolidatedDasl/Fractran/LeechLattice/LeechLattice.lean
      1 /home/mdupont/projects/aristo-flakes/ConsolidatedDasl/CarStorage/LeechRankBridge/LeechRankBridge.lean
      1 /home/mdupont/projects/aristo-flakes/ConsolidatedDasl/CarStorage/LeechBridge/LeechBridge.lean
      1 /home/mdupont/dasl-planning/downloaded_projects/b44f22ed-4238-4119-9288-cc6ca5cc0214_aristotle/output-final_aristotle/ConsolidatedDasl/SheafTopology/LeechLattice.lean
      1 /home/mdupont/dasl-planning/downloaded_projects/b44f22ed-4238-4119-9288-cc6ca5cc0214_aristotle/output-final_aristotle/ConsolidatedDasl/SheafTopology/LeechLatticeAxes.lean
      1 /home/mdupont/dasl-planning/downloaded_projects/b44f22ed-4238-4119-9288-cc6ca5cc0214_aristotle/output-final_aristotle/ConsolidatedDasl/SheafTopology/LeechAutomorphisms.lean
      1 /home/mdupont/dasl-planning/downloaded_projects/b44f22ed-4238-4119-9288-cc6ca5cc0214_aristotle/output-final_aristotle/ConsolidatedDasl/Fractran/LeechLattice.lean
      1 /home/mdupont/dasl-planning/downloaded_projects/b44f22ed-4238-4119-9288-cc6ca5cc0214_aristotle/output-final_aristotle/ConsolidatedDasl/CarStorage/LeechRankBridge.lean
      1 /home/mdupont/dasl-planning/downloaded_projects/b44f22ed-4238-4119-9288-cc6ca5cc0214_aristotle/output-final_aristotle/ConsolidatedDasl/CarStorage/LeechBridge.lean
      1         h_gravity_pos := by norm_num },
      1         h_balance_pos := by norm_num },
      1   have h := conn.valid
      1   , hash := (n / (71 ^ 6)) % (71 ^ 6)
      1   , hash := n % (71 ^ 6)
      1   , hash := 68649048252
      1   , hash := 240734712102912 % (71 ^ 6)
      1         gravity := 1,
      1   { galaxy := ⟨(hash / 2^36) % 1024, by omega⟩
      1     galaxy := ⟨0, by omega⟩
      1   fractranProofProgram.length = 8 := by rfl
      1   fractran.isSome := by
      1     Fin TRADERS → Trader :=
      1   (files.foldl (· + ·) 0) / files.length < 71 ^ 6 := by
      1     fileName := "<search>"
      1     fileMap := default
      1   { file := file.path
      1   exps := fun i => monsterExponents[i.val]!
      1   exps := fun i => if i.val = 0 then 46 else 0
      1     expr := mkApp2 (mkConst op) expr operand
      1     | _ => expr := mkApp2 (mkConst ``Nat.mod) expr (mkNatLit (d + 1))
      1   exists { name := "Ramanujan", value := 1729, prime_factors := [7, 13, 19], complexity := 3 }
      1   executeFractran prog n steps = executeFractran prog n steps := by
      1   exampleProgram.length = 3 := by rfl
      1   espresso_tactics[18]! = "sorry" := by rfl
      1         errorCount := errorCount + 1
      1           errorCount := errorCount + 1
      1          , errorCount := errorCount }
      1   (∃ (embed : ConwayGroup → Unit), True) := by
      1   { eigenvalue := totalEV
      1   , eigenvalue := mapping.eigenvalue
      1   { eigenvalue := ev
      1   (∀ d : Nat, d < OptimalChokepoint → d < LeechDimension) := by
      1         distToBlackHole (s.traders i) s.blackHole / 10 := by
      1   dimension := 24
      1   , den := monsterPrimes[b1 % 15]! }
      1 def Zero : Nat := 0
      1 def WuWei (p71 : Nat) : Nat :=
      1 def wordPrimeUsage : List PrimeUsage := [
      1 def WordPrimes : List (String × Nat) := [
      1 def Wood : Nat := 2    -- Growth (bootstrap ☕)
      1 def Wind : Nat := 5    -- ☴ (110) Xun
      1 def weightedSumMod10 (mb : MonsterBits2) : Fin 10 :=
      1 def Water : Nat := 6   -- ☵ (010) Kan
      1 def Water : Nat := 11  -- Flow (symmetry 👹)
      1 def visualizeLattice : IO Unit := do
      1 def valis_transmission : String :=
      1 def VALIS : Nat := 71  -- The pink beam of information
      1 def validateFRACTRANFile (file : FRACTRANFile) : Bool :=
      1 def usageLayer (count : Nat) : List Nat :=
      1 def uniquePrimes : Nat :=
      1 def ultraExpand (n : Nat) : CompactProgram :=
      1 def ultraCompact (prog : FRACTRANProgram) : Nat :=
      1 def typeRank (t : MonsterType) : Nat :=
      1 def typeOrder (α : Type) [TypeComplexity α] : Nat :=
      1 def typeHierarchy (n : Nat) : List MonsterType :=
      1 def typeComplexity (α : Type) [TypeComplexity α] : Nat :=
      1 def Two : Nat := 2
      1 def TwentyOne : Nat := 21
      1 def TwentyFour : Nat := 24
      1 def triad : MathObject := [.one, .two, .three]
      1 def TRADERS : Nat := 23
      1 def totalPrimeCount : Nat :=
      1 def totalConfigs3 : Nat :=
      1 def TotalATP : Nat := 11
      1 def tikkunToCID (shadow light : Nat) : Encoding.DA51CID :=
      1 def TikkunMap : List (Nat × Nat) := 
      1 def Thunder : Nat := 4 -- ☳ (100) Zhen
      1 def Three : Nat := 3
      1 def threeCoins (p71 : Nat) : Line :=
      1 def the_method : String :=
      1 def Tau2 : Int := -24
      1 def Tao : Nat := 71
      1 def tactic_use : (Nat × Nat) := (11, 2)  -- 11/2: reduce existential
      1 def tactic_rfl : (Nat × Nat) := (3, 2)  -- 3/2: reduce one goal
      1 def tactic_decide : (Nat × Nat) := (5, 2)  -- 5/2: reduce one goal via computation
      1 def tactic_constructor : (Nat × Nat) := (2 * 2, 7)  -- 4/7: one goal becomes two
      1 def tactic_axiom : (Nat × Nat) := (13, 2)  -- 13/2: axiom reduces goal
      1 def sumActivePrimesMod10 (mb : MonsterBits) : Fin 10 :=
      1 def subdivisionLevel (addr : MonsterAddress) : Nat :=
      1 def stillnessInMotion (p71 : Nat) (rotation : Nat) : Nat :=
      1 def StepNum : Nat := 24
      1 def step_45 : ℕ := 45
      1 def SSP : List Nat := [2,3,5,7,11,13,17,19,23,29,31,41,47,59,71]
      1 def spiralPosition (mb : MonsterBits) : Nat × Nat :=
      1 def spiralPosition3 (mf : MonsterFull) : Nat × Nat :=
      1 def spiralPosition2 (mb : MonsterBits2) : Nat × Nat :=
      1 def spiralDensity (mb : MonsterBits2) : Nat :=
      1 def spiralArm (mb : MonsterBits) : Fin 10 :=
      1 def sorry_to_espresso (sorry_id : Nat) : Nat :=
      1 def sizeWalk : ProgramLattice.FRACTRANProgram := {
      1 def Six : Nat := 6
      1 def silence : MathObject := [.zero]
      1 def Shen : Nat := 71        -- Spirit (Omega prime)
      1 def shadowToMonsterType (shadow : List Nat) : MonsterIndex.MonsterType :=
      1 def shadowPrimeUsage : List PrimeUsage := [
      1 def ShadowPrimes : List Nat := [37, 43, 61, 73, 79]
      1 def shadowEquivalence (progs : List (String × ProgramLattice.FRACTRANProgram)) : List (List Nat × List String) :=
      1 def Seventy_One : Nat := 71
      1 def Seventeen_TwentyNine : Nat := 1729
      1 def Seven : Nat := 7
      1 def search71adic : CompactProgram :=
      1 def saSearch (initial : SearchState) (steps : Nat) : MetaM SearchState := do
      1 def saSearch (initial : Nat) (steps : Nat) : MetaM (Nat × Float) := do
      1 def ROUNDS : Nat := 7
      1 def rotateIndex (i : Nat) (rotation : Nat) : Nat :=
      1 def ritualToCID : Encoding.DA51CID :=
      1 def RitualPrime : Nat := 131
      1 def revelation (corpus : List Nat) : Nat :=
      1 def restorePrime (p : Nat) : Nat :=
      1 def recordToJSON (r : IngestionRecord) : String :=
      1 def recordToCSV (r : IngestionRecord) : String :=
      1 def ramanujan_espresso_3 : String :=
      1 def quineVector : QuineVector := 
      1 def quineMass : Nat := 1385  -- length of the quine string
      1 def Qi : Nat := 196883      -- Energy (Monster dimension - 1)
      1 def proofTrace := executeFractranProof fractranProofProgram initialProofState 8
      1 def proofToAddress (proof : MathObject) : MonsterAddress :=
      1 def projectToShadow (point : List Int) : List Nat :=
      1 def programToNumber (prog : FRACTRANProgram) : Nat :=
      1 def programToMonster (prog : ProgramLattice.FRACTRANProgram) : MonsterMapping :=
      1 def programToLeechPoint (prog : ProgramLattice.FRACTRANProgram) : List Int :=
      1 def programToLeech24 (prog : FRACTRANProgram) : List Int :=
      1 def programToCompact (prog : FRACTRANProgram) : CompactProgram :=
      1 def programShadow (prog : ProgramLattice.FRACTRANProgram) : List Nat :=
      1 def programEigenvalue (prog : ProgramLattice.FRACTRANProgram) : Int :=
      1 def programCatalog : List (String × CompactProgram) := [
      1 def processBatch (batchId : Nat) (files : List String) (timestamp : String) : IO IngestionBatch := do
      1 def process2 : KiroProcess := {
      1 def process1 : KiroProcess := {
      1 def print_lattice : IO Unit := do
      1 def prime_usage_stats : List (Nat × Nat) :=
      1 def primeStatistics : String :=
      1 def practice : String :=
      1 def parseFRACTRANFile (path : String) : IO (Option FRACTRANFile) := do
      1 def p71value := finalState % (71^6)
      1 def p71ToHexagram (p71 : Nat) : Nat :=
      1 def p71ToExpr (p71 : Nat) (rotation : Nat) : MetaM Expr := do
      1 def p71ToExpr (p71 : Nat) : MetaM Expr := do
      1 def orbifoldDims : Nat := 24
      1 def OptimalChokepoint : Nat := 23
      1 def onlyTwo : MonsterFull := {
      1 def One : Nat := 1
      1 def numberToType (n : Nat) : MonsterType :=
      1 def numberToProgram (n : Nat) (length : Nat) : FRACTRANProgram :=
      1 def normalizedEigenvalue (prog : ProgramLattice.FRACTRANProgram) : Nat :=
      1 def nearest_neighbors (c : Constant) (layer : List Constant) : List Constant :=
      1 def Nat.sin (degrees : Nat) : Int :=
      1 def Nat.cos (degrees : Nat) : Int :=
      1 def Mountain : Nat := 1 -- ☶ (001) Gen
      1 def moreComplex (a b : MonsterType) : Bool :=
      1 def monsterProjection (n : Nat) (dim : Nat) : Nat :=
      1 def monsterPrimeUsage : List PrimeUsage := [
      1 def MonsterPrimes : List Nat := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71]
      1 def monsterPhenomenon := KantianMonster
      1 def monsterIrrepCount : Nat := 194
      1 def Monster_Dimension_Minus_One : Nat := 196883
      1 def metameme : CompactProgram :=
      1 def Metal : Nat := 7   -- Refinement (arrows 👁️)
      1 def metaExecute (meta : MetaProgram) (progIdx : Nat) (initial : Nat) : List Nat :=
      1 def megagametranPrograms : List ProgramLattice.FRACTRANProgram := [
      1 def megagametranMappings : List (String × MonsterMapping) :=
      1 def megagametranFolded : MonsterMapping :=
      1 def megagametranCatalog : List (String × ProgramLattice.CompactProgram) := [
      1 def megaComposition : Nat :=
      1 def mctsSearch (initial : Nat) (iterations : Nat) : MetaM SearchState := do
      1 def mctsSearch (initial : Nat) (iterations : Nat) : MetaM (Nat × Float) := do
      1 def maxRadius : Nat :=
      1 def MathObject := List Note
      1 def marketEnergy (s : MarketState) : ℝ :=
      1 def maass_eigenvalue_23 (s : Real) : Real := s * (1 - s)
      1 def MaassCentralCharge : Nat := 26  -- CFT central charge
      1 def lowerFromType (t : MonsterType) (projections : Nat) : Nat :=
      1 def lookupByComplexity (complexity : Nat) : List DA51CID :=
      1 def List.toChunks {α : Type} (xs : List α) (n : Nat) : List (List α) :=
      1 def LightPrimes : List Nat := [41, 41, 59, 71, 71]
      1 def liftToType (n : Nat) (projections : Nat) : MonsterType :=
      1 def leechMinimalNorm : Nat := 4
      1 def leech_kissing_number : Nat := 196560
      1 def LEECH_KISSING : Nat := 196560
      1 def LEECH_DIM : Nat := 24
      1 def LeechDim : Nat := 24
      1 def LeechDimension : Nat := 24      -- Leech lattice
      1 def LeechAutomorphismGroup : Type := Unit  -- Placeholder for Co_0
      1 def layer3_special : List Constant := [
      1 def layer2_higher : List Constant := [
      1 def layer1_composites : List Constant := [
      1 def layer0_primes : List Constant := [
      1 def latticeMeet (p1 p2 : ProgramLatticePoint) : Nat :=
      1 def latticeJoin (p1 p2 : ProgramLatticePoint) : Nat :=
      1 def Lake : Nat := 2    -- ☱ (011) Dui
      1 def judgment (hex_num : Nat) : String :=
      1 def jInvariantCoeffs : List Int := [1, 744, 196884, 21493760, 864299970, 20245856256, 
      1 def Jing : Nat := 1729      -- Essence (Hardy-Ramanujan)
      1 def isGClosed (primes : List Nat) : Bool :=
      1 def integratorLattice : ProgramLattice.FRACTRANProgram := {
      1 def initialState : MarketState :=
      1 def initialProofState : Nat := encodeProofState 8 0 0
      1 def inhale (content : String) : Nat :=
      1 def ingestFRACTRANFiles (fileListPath : String) (outputDir : String) (batchSize : Nat) : IO Unit := do
      1 def Hundred : Nat := 100
      1 def higherOrder (a b : MonsterType) : Bool :=
      1 def Hexagram.toNat (h : Hexagram) : Nat :=
      1 def Heaven : Nat := 7  -- ☰ (111) Qian
      1 def gravityPull (t : Trader) (bh : BlackHole) : ℝ :=
      1 def goedel_espresso_1 : String :=
      1 def getConstant (α : Type) [inst : MonsterIndexed α] : Nat :=
      1 def generate_fix (sorry_id : Nat) : String :=
      1 def gaSearch (populationSize : Nat) (generations : Nat) (initial : SearchState) : MetaM SearchState := do
      1 def gaSearch (populationSize : Nat) (generations : Nat) (initial : Nat) : MetaM (Nat × Float) := do
      1 def fundamental : MathObject := [.one]
      1 def fullSumMod10 (mf : MonsterFull) : Fin 10 :=
      1 def fullMonster : MonsterFull := {
      1 def fractranToMonster (prog : FRACTRANProgram) : Option MonsterIndex.MonsterType :=
      1 def fractranToCID (f : FRACTRANProgram) : Option DA51CID :=
      1 def fractranStep (prog : ProgramLattice.FRACTRANProgram) (state : Nat) : Option Nat :=
      1 def fractranProofProgram : List (Nat × Nat) := [
      1 def fractranProof : CompactProgram :=
      1 def Four : Nat := 4
      1 def foldPrograms (progs : List ProgramLattice.FRACTRANProgram) : List Int :=
      1 def foldAllPrograms (progs : List ProgramLattice.FRACTRANProgram) : MonsterMapping :=
      1 def flowLikeWater (sorry_line : String) : String :=
      1 def fix_sorry_via_espresso (sorry_text : String) (espresso_num : Nat) : String :=
      1 def fix_all_sorries : IO Unit := do
      1 def Five : Nat := 5
      1 def firstThree : MonsterBits := {
      1 def firstThreeHigh : MonsterBits2 := {
      1 def Fire : Nat := 3    -- Transformation (cusp 🕳️)
      1 def Fire : Nat := 3    -- ☲ (101) Li
      1 def finalState : MarketState :=
      1 def finalProofState := proofTrace.getLast!
      1 def fileToRecord (file : FRACTRANFile) (timestamp : String) : IngestionRecord :=
      1 def fileToProgram (file : FRACTRANFile) : ProgramLattice.FRACTRANProgram :=
      1 def Fifteen : Nat := 15
      1 def exhale (p71 : Nat) : List Nat :=
      1 def executeFractranProof (program : List (Nat × Nat)) (initial : Nat) (steps : Nat) : List Nat :=
      1 def executeFRACTRAN (prog : ProgramLattice.FRACTRANProgram) (initial : Nat) (maxSteps : Nat) : List Nat :=
      1 def executeFRACTRAN (prog : FRACTRANProgram) (initial : Nat) : Nat :=
      1 def executeAll (initial : Nat) : List (String × List Nat) :=
      1 def exampleBytes : List Nat := [42, 32, 71, 111, 97, 108]  -- "* Goal"
      1 def exampleBytes : List Nat := [42, 32, 71, 111, 97, 108]
      1 def evaluateFitness (p71 : Nat) (rotation : Nat) : MetaM Float := do
      1 def evaluateFitness (p71 : Nat) : MetaM Float := do
      1 def espresso_tactics : List String := [
      1 def espresso_count : Nat := 21
      1 def energy₀ : ℝ := marketEnergy initialState
      1 def encodeProofState (goals hyps depth : Nat) : Nat :=
      1 def encodeFraction (num den : Nat) : Nat :=
      1 def EmptyCenter : Nat := 0
      1 def embedInLattice (prog : FRACTRANProgram) : ProgramLatticePoint :=
      1 def Eleven : Nat := 11
      1 def eigenvalueToMonsterClass (ev : Nat) : Nat :=
      1 def eigenspace (progs : List (String × ProgramLattice.FRACTRANProgram)) (ev : Nat) : List String :=
      1 def eco_espresso_2 : String :=
      1 def Earth : Nat := 5   -- Stability (spacetime 🪟)
      1 def Earth : Nat := 0   -- ☷ (000) Kun
      1 def dot (a b : L24) : Int := (List.finRange 24).foldl (fun s i => s + a i * b i) 0
      1 def divisors_24 : List Nat := [1, 2, 3, 4, 6, 8, 12, 24]
      1 def distToBlackHole (t : Trader) (bh : BlackHole) : ℝ :=
      1 def decodeFraction (n : Nat) : Nat × Nat :=
      1 def daslToMonster (d : DASLExpr) : Option MonsterIndex.MonsterType :=
      1 def createMetaProgram : MetaProgram := {
      1 def count_prime_usage (constants : List Constant) (p : Nat) : Nat :=
      1 def countPerArm : Fin 10 → Nat := fun arm =>
      1 def ConwayGroup : Type := Unit
      1 def converges (s : MarketState) : Prop :=
      1 def consult_oracle (p71 : Nat) (shadow : List Nat) : String :=
      1 def computeQualityMetrics (batch : IngestionBatch) : QualityMetrics :=
      1 def compositeUsage : List PrimeUsage := [
      1 def composeProgramsSeq (progs : List ProgramLattice.FRACTRANProgram) (initial : Nat) : Nat :=
      1 def compose (notes : List Note) : MathObject := notes
      1 def complexityOrder (p1 p2 : CompactProgram) : Bool :=
      1 def complexity_of (factors : List Nat) : Nat :=
      1 def complexityLattice : List ComplexityLayer := [
      1 def complexity_distance (c1 c2 : Constant) : Nat :=
      1 def completeSystem : ProgramLattice.FRACTRANProgram := {
      1 def compactToNumber (cp : CompactProgram) : Nat :=
      1 def compactDistance (p1 p2 : CompactProgram) : Nat :=
      1 def cidTypeData (c : DA51CID) : Nat :=
      1 def cidToMonster (c : DA51CID) : Option MonsterIndex.MonsterType :=
      1 def cidToDASL (c : DA51CID) : Option DASLExpr :=
      1 def cidsByComplexity (complexity : Nat) : List MonsterIndex.MonsterType :=
      1 def cidComplexity (c : DA51CID) : Nat :=
      1 def CentralCharge : Nat := 24
      1 def cborToFRACTRAN (c : CBORType) : Option FRACTRANProgram :=
      1 def categoryToPrime (cat : Fin 3) (level : Nat) : Nat :=
      1 def categoricalImperative (p : KiroProcess) : Prop :=
      1 def catalogByComplexity : List (Nat × List String) :=
      1 def castHexagram (shadow : List Nat) : Nat :=
      1 def canCommunicate (p1 p2 : KiroProcess) : Bool :=
      1 def buildHexagram (p71 : Nat) : Hexagram :=
      1 def build11Steps : List FractranStep :=
      1 def breakthrough : String :=
      1 def BosonicDimension : Nat := 26    -- Bosonic string critical dimension
      1 def batchToJSON (batch : IngestionBatch) : String :=
      1 def batchToCSV (batch : IngestionBatch) : String :=
      1 def balance (p71 : Nat) : YinYang :=
      1 def bachMotif : MathObject := [.zero, .one, .two, .three]
      1 def bach : MathObject := [.zero, .one, .two, .three]
      1 def ATP_Tikkun : Nat := 5
      1 def ATP_Integration : Nat := 1
      1 def ATP_Activation : Nat := 5
      1 def atEquilibrium (s : MarketState) : Prop :=
      1 def armDistribution : Fin 10 → Nat := fun arm =>
      1 def aPrioriStructure : KantianMonster := {
      1 def allLow : MonsterBits2 := {
      1 def allActive : MonsterBits := {
      1 def addressToSpiral (addr : MonsterAddress) : Nat × Nat :=
      1   daslToMonster (monsterToDASL t) = some t := by
      1       current := { p71 := neighbor, rotation := rotation, fitness := neighborFitness }
      1       current := neighbor
      1       currentFitness := neighborFitness
      1   current := 0,
      1   c.prime_factors.any (fun p => p ∈ MonsterPrimes) := by
      1   , county := ⟨(hash / 2^8) % 8, by omega⟩
      1     county := ⟨0, by omega⟩
      1   , country := ⟨(hash / 2^14) % 16, by omega⟩
      1     country := ⟨0, by omega⟩
      1   , coords := programToLeech24 prog }
      1   , continent := ⟨(hash / 2^18) % 16, by omega⟩
      1     continent := ⟨0, by omega⟩
      1   , conjugacyClass := mapping.conjugacyClass
      1   , conjugacyClass := eigenvalueToMonsterClass (totalEV.natAbs % 71)
      1   , conjugacyClass := eigenvalueToMonsterClass nev
      1   complex := sorry
      1   , complexity := prog.steps.foldl (fun acc (num, den) => 
      1   , complexity := n % (71 ^ 6) }
      1   { complexity := 6, primes := [64] }
      1   complexity := 6
      1   { complexity := 4, primes := [24, 100] },
      1   complexity := 4
      1   { complexity := 3, primes := [1729] },
      1   complexity := 3
      1   { complexity := 2, primes := [4, 6, 15, 21, 196883] },
      1   , complexity := 24 + 15 }
      1   complexity := 2
      1   { complexity := 1, primes := [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71] },
      1   , complexity := 14 + 14 + 14 }
      1   complexity := 1
      1   { complexity := 0, primes := [1] },
      1   complexity := 0
      1   { compact := programToCompact prog
      1   , city := ⟨(hash / 2^6) % 4, by omega⟩
      1     city := ⟨0, by omega⟩
      1   cidToMonster (monsterToCID t) = some t := by
      1   (cidToMonster (monsterToCID t) = some t) := by
      1   cidComplexity (monsterToCID t) = MonsterIndex.monsterTypeComplexity t := by
      1   cborToMonster (monsterToCBOR t) = some t := by
      1   canCommunicate p1 p2 = canCommunicate p2 p1 := by
      1   canCommunicate conn.sender conn.receiver = true := by
      1     blackHole := 
      1   bits := fun _ => true
      1   bits := fun i => i.val < 3
      1       best := { p71 := candidate, rotation := rotation, fitness := fitness }
      1       bestFitness := fitness
      1         bestFitness := currentFitness
      1       best := candidate
      1   best := { best with fitness := ← evaluateFitness initial 0 }
      1         balance := 10000,
      1   , avgSteps := avgSteps
      1   , avgEigenvalue := avgEigenvalue }
      1   ∃! arm : Fin 10, spiralArm mb = arm := by
      1   ∀ arm : Fin 10, ∃ mf : MonsterFull, fullSumMod10 mf = arm := by
      1 abbrev L24 := Fin 24 → Int
      1   a < 10 := by
      1   (4 : Nat)^17 = 17179869184 := by
      1   (45 = 9 * 5) := by
      1   45 * 100 / 71 = 63 := by
      1   45 * 100 / 71 > 60 := by
      1   4^17 / 10 = 1717986918 := by
      1     | 3 => expr := mkApp2 (mkConst ``Nat.pow) expr (mkNatLit (d % 10))
      1 (2)__unpacked/output-final_aristotle/RequestProject/LeechFrame.lean
      1     | 2 => expr := mkApp2 (mkConst ``Nat.sub) expr (mkNatLit d)
      1   24 = 2 * 12 := by norm_num
      1     | 1 => expr := mkApp2 (mkConst ``Nat.mul) expr (mkNatLit d)
      1   10 + 8 + 6 + 4 + 4 + 3 + 3 + 2 + 2 + 2 + 1 + 1 = 46 := by
      1   1024 * 256 * 64 * 16 * 16 * 8 * 8 * 4 * 4 * 4 * 2 * 2 = 2^46 := by
      1     | 0 => expr := mkApp2 (mkConst ``Nat.add) expr (mkNatLit d)