PASS: nonnegative integer reaction data; no catalysts; correct derivative support.
PASS: all equilibrium reaction rates are positive; S*(2,3,2,2,2) = (0,0,0,0).
PASS: the constant inflow supplies balance and contributes zero to the Jacobian.
PASS: exact differentiation of the generalized power-law rates gives G = S*R.
PASS: G*v - (1/500 + 51*i/500)*v = (0,0,0,0), exactly.
PASS: all four polynomial coefficients are positive, but the third Hurwitz determinant is negative.
PASS: 24 selections: 6 of size 1, 11 of size 2, 6 of size 3, 1 of size 4.
PASS: exactly four maximal selections; every selection belongs to at least one.
PASS: all five weighted certificates have nonnegative principal minors.
PASS: exceptional polynomial = z*(z+4*d0)*(z+4*d1+2*d2) for symbolic positive d0,d1,d2.
PASS: the exceptional child has no positive diagonal weight certificate; its exact polynomial is needed.
PASS: all 24 selections covered for EVERY positive column scaling: 22 strictly negative; 2 with a zero eigenvalue.
PARAMETER MAP: at F=0.6 the boundary is E approximately 81.580594872.
SCOPE: exact counterexample checked in SymPy; figures are numerical; Lean was not run.
FIGURES: 49750 parameter points; polynomial/eigenvalue sign check passed.
LINEAR MODE: period 61.599856; amplitude doubling time 346.573590.
NUMERICAL EIGENVALUES: [[-226.3647207388466, 0.0], [0.002000000000006535, 0.10200000000000857], [0.002000000000006535, -0.10200000000000857], [-0.11194350464291586, 0.0]]