Finite joint-affine support qualification

Qualify exact support certificates before connecting them to native prediction bounds. The mathematical inequality and next dependency are described in the joint calibration plan.

Freeze 24 generated identities: twelve two-dimensional polygons checked by independent exact enumeration of all feasible vertices, eight 27-coordinate systems with two equal correlated coordinates and twenty-five wholly unidentified coordinates, and four weak-constraint/full-box fallbacks. Check both objective signs and deliberately poor nonnegative multiplier proposals.

Keep every nuisance column. Every returned bound must contain the exact known optimum; every declared feasible vertex remains represented. In the correlated systems, the difference of the first two coordinates must vanish while all unidentified contributions remain. LP failure or nonfinite multiplier proposals must fall back to a verified full-box certificate, never an empty region. Unit controls cover those failure statuses and outward overflow separately.

Limits: at most 144 certificates, 48 LP proposals, 60 cooperative seconds, four reserved numerical threads in one worker, and one thread/one cooperative second for each LP proposal. Reserve six certificates and two proposals per identity before calculation. There are zero native evaluations, optimizer starts on aircraft measurements, original-file reads or ESA evaluations. No retries, extensions or process signals. Freeze sources and environment before launch.

A pass qualifies only the mathematical support calculation. Training inequalities, nonlinear remainder bounds and measurement assumptions remain separate requirements. No observational fit follows. The next stage needs a new finite generated freeze covering the full original orientation range; this study does not narrow that range or spend any previous allowance.