Canonical identity

$\ddot y+\Gamma^y{}_{yy}(y)\dot y^2+f'(y)|f'(y)|=0$

where

$f'(y)=\dfrac{34749}{128}y^5-\dfrac{243243}{640}y^4+\dfrac{18711}{128}y^3-\dfrac{1701}{128}y+\dfrac{3}{40}$

Evidence class

E0 exact ODE definition; E1 adaptive SciPy trajectory implementation.

Civic role

Combines one-dimensional metric transport with a signed nonlinear forcing term.

Transit credential

Geometric Computation Borough → Dynamics Line → Basin Classification Platform → Observatory.

Boundary

This is an augmented geodesic system, not a free geodesic equation. QuTiP cross-validation in the source is implementation-level and requires independent rerun before certification.