Faster numerical derivatives: isolated prototype
Question
Can the software retain its wider-precision position and residual calculation while computing derivatives in ordinary binary64 arithmetic? Derivatives guide the optimizer; they must not feed back into the physical position calculation. The aim is lower runtime without changing the measurements, physical model, calibration bounds or stopping and accuracy rules.
Isolation
Use a separate derived-source adapter. Preserve the wide scalar path, all 26/27 derivative columns, clock dispatch, profile mapping, query fractions and native interface. Change only derivative storage and derivative coefficients. Reuse the shared loader in a private function namespace, with exact source hashes. Do not patch its globals or edit a running study's dependencies.
The metadata transformation accepts already-generated C++ text, so its tests need no numerical imports. Native compilation and comparison wait for a free core through the existing shared test queue.
First gate
Run three metadata checks and six real-native cases: all three physical candidates under both processing assumptions. Use the existing two-second known-motion fixture and one fixed nonzero parameter vector. Require bitwise identical predicted positions and residuals, unchanged boundary counts and every derivative column within the fixed numerical tolerance. Verify that the original loader and arithmetic remain untouched.
One source-bound test execution is allowed, with one numerical thread and three reserved threads. It waits at most eight hours for a completed shard of the current study to release its core. No retry, original-data read, fit or observed model comparison is authorized. The native checks make 24 short kernel calls across six cases, plus twelve per-case compiler invocations at most.
Passing these small checks does not qualify a replacement method or establish a speed improvement. A separate finite long-record benchmark, followed by training/forecast qualification, is required before any observed fitting. If bitwise value agreement fails, preserve the failure; do not weaken that requirement merely to accept the prototype.
The active noisy-data study, existing evidence and protected confirmation groups remain unchanged.