$\mathcal Z_g=\left\{y\in\mathbb R:143y^6-143y^4+33y^2-1=0\right\}$
$y\in\mathcal Z_g\iff g_{yy}(y)=0$
On this locus, $g^{yy}$ is undefined and $\Gamma^y{}_{yy}$ is singular unless simultaneous numerator cancellation occurs.
E0 exact algebraic locus; E1 event-detection interface in the numerical solver.
Boundary citizen partitioning the admissible intervals of the polynomial metric-geodesic system.
Geometric Computation Borough → Correction Borough → Singularity Watch → Observatory.
For the unforced sector,
$\ddot y+\Gamma^y{}{yy}\dot y^2=0\quad\Longrightarrow\quad g{yy}(y)\dot y^2=\mathrm{constant}$
This conservation law is attached to C-41/C-43 and is not enrolled as a duplicate citizen.
The locus marks degeneracy of this coordinate metric model. It is not automatically a curvature singularity or physical boundary.