Full joint-coordinate projection

The saved certificate audit verifies all 48 longer generated cases, but simple row contraction leaves 24 physical and all 15 auxiliary ranges unchanged. Project the same necessary training set onto all 42 coordinates before deciding whether another nonlinear refinement is required.

Use the unchanged qualified exact dual-plus-box support method. Each linear program supplies only a proposal; the mathematical bound comes from its exact nonnegative-dual certificate, with the full box residual retained. A solver's infeasibility status alone excludes nothing. Preserve all sectors, joint correlations, physical limits and known-control checks. No new future data, integrations or fits are introduced. Report every projected interval and whether it materially improves on row contraction (one part per million).

Freeze 48 identities, 84 proposals per identity, 4,032 proposals total and at most 8,064 exact support certificates. Reserve each proposal before execution. Use four workers with one numerical thread each; each LP has a one-second cooperative allowance and the study has 300 cooperative seconds. No retries, signals, native calls or original-file reads. Preserve interruptions and failures. Exact interval checks must retain the generated known control when it belongs to the sector.

This is a saved generated-data diagnosis, not physical calibration, a new aircraft result or observational uncertainty qualification. A narrower range would still require a separately frozen native-bound comparison before use.