lin-0179

14.3 Anchor and closure defects

For a declared visible distribution \(\mathcal D\subseteq TM\), LASKO keeps two geometric failures separate:

\[ r_A(s,t) = [\rho (s),\rho (t)] - \rho ([s,t]_A), \]

the anchor-morphism defect, and

\[ r_{\mathrm{vis}}(s,t) = (I-P_{\mathcal D})[\rho (s),\rho (t)], \]

the visible closure residual. The first asks whether the learned section bracket predicts executable interaction. The second asks whether the realized interaction remains inside the declared visible control span.

Boundary

A large ordered-edit contrast is not sufficient evidence for a Lie algebroid. The realization must identify typed sections, an anchor, a bracket estimator, and the Leibniz or anchor compatibilities being approximated.