# Verification of planar normalized area rigidity

The completed scope is Theorem 1.1 and Corollary 1.2: arbitrary positive
Newtonian masses, noncollinear planar rigidity on any open collision-free
interval, and the full collision-free exactly periodic planar classification.
No general spatial classification is claimed.

The analytic self-audit checks the area normalization, coefficient-line
distinctness, unrestricted normal variation, all divisions, and continuation
on a connected finite algebraic cover. At the isolated binary branch the
linear momentum equation has a regular coefficient and a finite nonzero
solution. The two remaining cases give nonzero energy coefficients 9/4 times
w_0 squared R squared, and -24 times ell squared R squared. Complex squares
are not replaced by absolute squares. Endpoint shapes, collinear motion,
zero angular momentum and exact inertial periodicity are treated separately.

The reproducibility program makes 26 exact symbolic checks, including a
six-component real Cartesian kinetic calculation, angular momenta, planar
and spatial normal equations, the body Euler equations and their Casimir,
the distinct binary coefficient lines, and both complex leading coefficients.
Normal and optimized runs with SymPy 1.14.0 have identical outputs. Explicit
exceptions enforce failures; disabling Python assertions does not disable
the tests. These checks are not formal verification of the analytic proof.

Both the built-in LaTeX compiler and Tectonic compiled the final source.
All five final PDF pages were visually inspected. Escaped-spacing defects
found in the first render were corrected, and every final page was checked
again. The title, author footnote, formulas, references and pagination are
readable; there are no unresolved references or overfull boxes.

AI-assisted, self-audited and unrefereed. Neither independent review nor
absolute novelty is certified. The handwritten spatial attempt is retained
in the research dossier and is not presented as a completed theorem.