Conditional remainder: fixed native controls

This software study compares the existing integration bound with a separate candidate that tightens only the initial force Taylor remainder. It uses generated inputs, not aircraft observations. Existing studies remain unchanged.

There are twelve identities: three physical models, two processing assumptions, and physical-domain versus synthetic force-constrained bounds. Each input is the first 800 packets of the qualified eight-minute generated history, retained bit for bit. Prediction is at 2.5 seconds. The original broad 27-parameter box, ±1-second clock, expansion, 24 shared error columns and normalization stay fixed. The synthetic constraint limits initial force change to ±0.2 m/s² on each axis. It is a software condition, not a measured aircraft error allowance.

Each identity reserves four native queries, two bounds and four fixed probes. Both bounds are saved before off-center outcomes are evaluated. The known probes are center, two corners and one mixed point for the physical domain; the constrained scope uses fixed small calibration changes with full clock extremes. Every probe must belong to its declared domain. No probe may be skipped or replaced.

Require unchanged shared maps, caps, bindings, physical bounds and native centers; nonwidening remainder arrays; a strictly smaller force remainder; and containment of every probe. The native center tolerance is 1 micrometre; the separate fixed probe arithmetic allowance is 10 micrometres. These are software comparison tolerances, not sensor accuracy or a whole-program rounding proof. Preserve packet-boundary counters and validate them against actual clock/query geometry.

Before each bound reserve complete 800-step source, derivative, point and direct streams. Each constrained identity reserves six LP proposals and 24 exact support checks. Each identity reserves one reference, one typed force proof, two remainder-certificate calculations, four oracle checks and one matched comparison. All auxiliary charges and artifacts are saved.

Use one worker with one numerical thread, reserving two for the current long study. The cooperative limits are 180 seconds per bound and 4,800 seconds for the study. No optimizer starts, aircraft reads, retries, process signals or allowance increases. Freeze source, generated inputs, compiler and environment before launch. Seal failures as well as successes. Publication reads saved artifacts only.

Passing qualifies this short native component only. Useful complete-history ranges, whole-period coverage and a defensible observation-error law remain separate requirements before new withheld aircraft fits.