Wolfram Validation (LAG-02 and LAG-03)
Inputs Checked
L_spirit = chi(t)*(d/dt x)^2 - sEnt(t)*chi(t)L_anti = -L_spirit- Expanded anti form:
sEnt(t)*chi(t) - chi(t)*(d/dt x)^2
Raw Wolfram Output
IdentityCheck (L_anti - expanded form):
0
EulerLagrange[L_spirit]:
2*(chi'(t)*x'(t) + chi(t)*x''(t))
Solve EulerLagrange == 0 for x''(t):
{{x''(t) -> -((chi'(t)*x'(t))/chi(t))}}
Constant-chi case (chi'(t)=0):
2*chi(t)*x''(t)Summary
- Sign inversion check passed (
0exactly). - Euler-Lagrange form derived successfully for the Spirit Lagrangian.
- Equation of motion solved symbolically for
x''(t). - Constant-chi limit reduces to
x''(t)=0(forchi(t) != 0).
Scope Note
- This validates internal symbolic consistency.
- It does not by itself prove empirical truth; that needs data-facing tests.
Canonical Hub: CANONICAL_INDEX