File size: 2,306 Bytes
631ca3b | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | import hashlib, math, numpy as np
from collections import defaultdict
from t112_triangle import *
def wl_bits(lut):
adj=defaultdict(set)
for v in range(N):
for u in lut[v]:
if u!=SENTINEL: adj[v].add(int(u)); adj[int(u)].add(v)
col={v:0 for v in range(N)}
for _ in range(40):
new={v:(col[v],tuple(sorted(col[u] for u in adj[v]))) for v in range(N)}
m={s:i for i,s in enumerate(sorted(set(new.values()),key=lambda x:hashlib.md5(str(x).encode()).hexdigest()))}
nc={v:m[new[v]] for v in range(N)}
if len(set(nc.values()))==len(set(col.values())): col=nc; break
col=nc
sz=defaultdict(int)
for v in col: sz[col[v]]+=1
return len(sz), -sum((c/N)*math.log2(c/N) for c in sz.values())
def connected(lut):
seen=np.zeros(N,bool); st=[0]; seen[0]=True; c=1
while st:
v=st.pop()
for u in lut[v]:
if u!=SENTINEL and not seen[u]: seen[u]=True; c+=1; st.append(int(u))
return c
lut,idx=build_triangle_lut()
print("[+] layout ", LUT_BYTES, "B uint16, <=256 KiB:", LUT_BYTES<=262144)
print("[+] cells ", N, "= T112")
print("[+] degrees ", degree_hist(lut), " (NOT uniform - this is the point)")
print("[+] connected ", f"{connected(lut)}/{N}", connected(lut)==N)
print("[+] symmetric ", all(v in [int(x) for x in lut[int(u)] if x!=SENTINEL]
for v in range(N) for u in lut[v] if u!=SENTINEL))
k,H = wl_bits(lut)
print(f"[+] WL classes {k} node identity = {H:.2f} bits (ring baseline: 1 class, 0.00 bits)")
node,acc = hop_loop(lut, 50_000, 7)
golden = hashlib.sha256(f"{node}:{acc}".encode()).hexdigest()
print(f"[+] golden node={node} acc={acc}")
print(f"[+] sha256 {golden}")
# determinism across repeats & a second construction
lut2,_ = build_triangle_lut()
n2,a2 = hop_loop(lut2, 50_000, 7)
print("[+] reproducible ", (n2,a2)==(node,acc))
# fail-closed: structural halt vs range halt
hops,err = hop_loop_failclosed(lut, 10_000, 7)
print(f"[+] structural halt at hop {hops} err={err} (2 = fell off the triangle edge)")
for p in (6328, 65535, 99999):
h,e = hop_loop_failclosed(lut, 10_000, 7, poison_at=3, poison_val=p)
assert e==1, p
print("[+] range halt 6328/65535/99999 -> err=1 at hop 3")
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