Canonical identity

$g_{yy}(y)=\dfrac{1701}{128}\left(143y^6-143y^4+33y^2-1\right)$

$\Gamma^y{}_{yy}(y)=\dfrac{429y^5-286y^3+33y}{143y^6-143y^4+33y^2-1}$

$\Gamma^y{}_{yy}(y)=\dfrac12\,\partial_y\log\left|143y^6-143y^4+33y^2-1\right|$

Evidence class

E0 exact differential-geometric identity extracted from the Python definition.

Civic role

Defines the one-dimensional polynomial metric and its Levi-Civita connection as an independent geometric citizen.

Transit credential

Geometric Computation Borough → Differential Geometry Desk → Numerical Basin Survey.

Boundary

The identity is exact wherever $g_{yy}\neq0$. Interpretation as a physical spacetime metric is not certified.