lin-0213
17.4 What is exact
Define the transition between foundry frames by
For every triple overlap,
Triple consistency therefore requires no separate cycle loss.
\((H_k^{-1}H_j)(H_j^{-1}H_i)=H_k^{-1}H_i\).
This exact transition cocycle does not imply small incidence obstruction. Frame consistency and agreement of the local sections are distinct obligations.
If each candidate is accepted only after exact nonlinear auditing, every accepted iterate remains feasible to the fixed tolerance and strictly lowers incidence RMS. Moreover, if an apex linear probe has margin \(\gamma \) and the aligned repair displaces every point by less than \(\gamma /\lVert w\rVert \), its predicted labels are unchanged.
Feasibility follows inductively from the acceptance predicate. The margin claim is Cauchy–Schwarz: no signed score can move by \(\gamma \).
RADAR does not ask a scalar loss to trade incidence against private geometry. The diagram defines a vector obstruction and a feasible set; the solver chooses a direction, and the exact declarations decide whether it may enter.