Wolfram Lagrangian Test Results
Run Summary
- Total tests: 10
- Passed: 10
- Failed: 0
Key Derived Output
EULER_LAG_02 = 2*(chi'(t) x'(t) coupling form)equivalent output confirmed by Wolfram symbolic derivative form.SOLVE_LAG_02returned a closed form forx''(t)in terms ofchi'(t),x'(t), andchi(t).
Exact solve output:
SOLVE_LAG_02={{Derivative[2][x][t] -> -((Derivative[1][chi][t]*Derivative[1][x][t])/chi[t])}}Pass/Fail Detail
TOTAL_PASS=10
TOTAL_FAIL=0
EULER_LAG_02=2*(Derivative[1][chi][t]*Derivative[1][x][t] + chi[t]*Derivative[2][x][t])
SOLVE_LAG_02={{Derivative[2][x][t] -> -((Derivative[1][chi][t]*Derivative[1][x][t])/chi[t])}}
LAG-01 identity=PASS
LAG-02 Euler-Lagrange form=PASS
LAG-02 solvable for x''(t)=PASS
LAG-03 sign inversion=PASS
LAG-04 includes chi coupling=PASS
LAG-04 includes psi coupling=PASS
LAG-04 decouples at chi=0=PASS
LAG-05 composition identity=PASS
LAG-05 interaction off at chi=0=PASS
LAG-05 includes kappa=PASSInterpretation Boundary
- These checks validate symbolic internal consistency of the current formulations and decomposition logic.
- These checks do not establish empirical confirmation; data-facing protocols remain required.
Canonical Hub: CANONICAL_INDEX