# About the three inquiry studies

Shape, Evidence and Boundary are modern teaching studies accompanying this
working paper. Their purpose is to make an example, a comparison and a limit
inspectable. They do not add a general finite closed-form solution.

The shape study uses exact classical circular families. The comparison fixes
the symmetric Euler family at masses (1,2,1), G=a=1 and angular speed 1.5. Both
position/a and velocity/(aω) gaps are 0 at zero shift, √2 at 90°, and 2 at 180°.
The energy and angular momentum agree even when the labeled initial states do
not. This is a constructed analytical control, not an original Poincaré plate.

The target chooser evaluates the paper's stated local-series upper bound. At
half the conservative local radius, degree 13 is the least displayed degree
meeting bound/δ≤0.0001. This is a sufficient analytical bound under the paper's
assumptions, not a measured numerical error or a floating-point guarantee.
The displayed search ends at degree 24; failure there is not an impossibility
theorem. No finite bound is assigned at η=1.

Compiled Swift executed the actual production model with 221 checks. A separately
written compiled C++ reference matched 197 exported values and exercised invalid
and misleading controls. These checks support the stated examples. They do not
replace independent mathematical certification of the paper.

Three requested model roles contributed proposals, implementation and review.
Shared files and collaborative synthesis prevent an independent capability
comparison. No measured educational, accessibility or resource-saving outcome
is claimed. Original artwork, historical source tiers and research limitations
remain part of the exhibition.

[Return to the inquiry](index.html#guide) · [Read the paper](paper.md)