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# Argument selection and reproduction
From the defining integral, $S^{\prime}(x)=\sin(\pi x^2/2)$, so the positive extrema occur at $x=\sqrt{2n}$, $n\geq1$. These are the horizontal or vertical tangent points of Cornu's spiral CITE{NaturalArguments}.
it holds the origin and the twenty extremal heights at $x=\sqrt{2n}$, $1\leq n\leq20$; the selection is not exhaustive over the real domain
References: https://dlmf.nist.gov/7.20.ii
Install numberdb, python-flint and mpmath. Run `python generate.py` to verify the stored selection or `python checks.py T207 --live` for independent checks. The default never writes. `--fill` sends entries; `--remove-unselected` is a separate explicit choice. It does not approve or publish a table. Historical reference grids remain available in the website revision history.