Python 3.13.5
SymPy 1.14.0

Running sympy_verify_lifts.py ...
det J = -2
F (0, 0, -1/4) = [-1/4, 0, 0]
F (1, -3/2, 13/2) = [-1/4, 0, 0]
F (-1, 3/2, 13/2) = [-1/4, 0, 0]

A = J^{-1} entries are polynomials, max total degree per entry:
  A[0,0] degree 8, 5 terms
  A[0,1] degree 9, 7 terms
  A[0,2] degree 11, 11 terms
  A[1,0] degree 6, 5 terms
  A[1,1] degree 7, 6 terms
  A[1,2] degree 9, 9 terms
  A[2,0] degree 8, 9 terms
  A[2,1] degree 9, 11 terms
  A[2,2] degree 11, 14 terms

Weyl relations verified:
  [phi(d_i), phi(x_j)] = delta_ij
  [phi(d_i), phi(d_j)] = 0

Poisson relations verified from the same identities:
  {Phi(xi_i), Phi(x_j)} = delta_ij
  {Phi(xi_i), Phi(xi_j)} = 0

=== Explicit endomorphism phi of A_3 ===
phi(x1) = (x*y + 1)*(x**2*y**2*z + 3*x*y**3 + 2*x*y*z + 4*y**2 + z)
phi(x2) = 3*x**3*y**2*z + 9*x**2*y**3 + 6*x**2*y*z + 12*x*y**2 + 3*x*z + y
phi(x3) = -x*(x**2*z + 3*x*y - 2)

phi(d1) =
    + (x**3*(3*x**3*y*z + 9*x**2*y**2 + 3*x**2*z + 3*x*y - 4)) * d1
    + (3*x*(x**3*y*z + 3*x**2*y**2 + x**2*z + x*y - 1)) * d2
    + (-9*x**5*y*z**2 - 45*x**4*y**2*z - 9*x**4*z**2 - 54*x**3*y**3 - 30*x**3*y*z - 27*x**2*y**2 + 9*x**2*z + 21*x*y + 1) * d3

phi(d2) =
    + (-x**2*(3*x**4*y**2*z + 9*x**3*y**3 + 6*x**3*y*z + 12*x**2*y**2 + 3*x**2*z - x*y - 3)/2) * d1
    + (-(3*x**4*y**2*z + 9*x**3*y**3 + 6*x**3*y*z + 12*x**2*y**2 + 3*x**2*z - 2)/2) * d2
    + ((9*x**5*y**2*z**2 + 45*x**4*y**3*z + 18*x**4*y*z**2 + 54*x**3*y**4 + 75*x**3*y**2*z + 9*x**3*z**2 + 81*x**2*y**3 + 21*x**2*y*z + 6*x*y**2 - 6*x*z - 16*y)/2) * d3

phi(d3) =
    + (-(x*y + 1)**2*(3*x**4*y**2*z + 9*x**3*y**3 + 6*x**3*y*z + 12*x**2*y**2 + 3*x**2*z - x*y - 1)/2) * d1
    + (-3*(x*y + 1)**2*(x**2*y**2*z + 3*x*y**3 + 2*x*y*z + 4*y**2 + z)/2) * d2
    + ((9*x**5*y**4*z**2 + 45*x**4*y**5*z + 36*x**4*y**3*z**2 + 54*x**3*y**6 + 165*x**3*y**4*z + 54*x**3*y**2*z**2 + 189*x**2*y**5 + 216*x**2*y**3*z + 36*x**2*y*z**2 + 222*x*y**4 + 117*x*y**2*z + 9*x*z**2 + 89*y**3 + 21*y*z)/2) * d3
PASSED: sympy_verify_lifts.py

Running independent_verify_lifts.py ...
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).
PASSED: independent_verify_lifts.py

Running generate_operators.py --check --check-source weyl-poisson-lifts.tex ...
PASSED: operators.tex matches generated formulas
PASSED: inline formulas in weyl-poisson-lifts.tex match generated formulas
PASSED: generate_operators.py --check --check-source weyl-poisson-lifts.tex

ALL EXACT VERIFICATION CHECKS PASSED
Verified: det(JF), the three-point collision, JA=AJ=I, all nine commuting-vector-field coefficients, the Weyl and Poisson lift relations, operators.tex, and the inline manuscript formulas.
