check 1: det JF == -2 identically  OK
check 2: three-point collision at (-1/4,0,0)  OK
check 3: J A == A J == I with polynomial A  OK
check 4: all nine commuting-vector-field coefficients vanish  OK
check 5: the same identities verify the Weyl and Poisson relations  OK

All Weyl and Poisson lift identities independently verified with exact arithmetic (no CAS).
