Qualify bounded steps within timing intervals
The completed timing diagnostic finds correct local derivatives but an unreliable compensating step across an integration boundary. The next component should keep a proposed linear step inside the interval whose derivatives describe it, while considering both adjacent intervals and retaining every calibration coordinate.
Software component first
Add a shared bounded linear-step component. Its inputs are a complete residual,
Jacobian, anchor point and physical box for each feasible timing interval.
Its output is a proposed step and predicted residual cost, not convergence,
uncertainty or a scientific decision. Charge each linear solve before execution;
use the existing bvls tolerance 1e-10 and 100-iteration ceiling.
Qualify smooth interior minima, internal-boundary minima, physical-bound minima, coupled coordinates, redundant/zero columns, invalid boxes and exhausted charges. Use independent closed-form minima or explicit low-dimensional face enumeration as references. Preserve all 27 columns in the rank-deficient controls; agreement in predicted observations does not require unique nuisance parameters.
Implement the shared algebra in lll.timing_cells, with a small
lll.timing_cell_study definition/evaluator and a saved-only
lll.timing_cell_report. Use one lifecycle task containing all 18 solves and an
append-only charge journal. The study has zero native-call allowance.
Bounded saved-matrix review
After those checks pass, use all 18 feasible branch matrices already saved by the four-point timing diagnostic: three distances on each feasible side. Do not select only a favorable spacing. Each box retains the original physical bounds and limits timing to its adjacent integration interval, clipped at the physical offset limits. Verify the parent manifest, source-fit hashes and column order.
Allow exactly one solve per saved matrix: 18 charged linear solves, one thread, 100 iterations per solve and a ten-minute cooperative ceiling. Preserve failed or interrupted solves; no retries. Generate no measurements, noise, native calculations, forecasts or nonlinear fits. The prior diagnostic and calibration allowances remain closed.
Compare proposals across sides and spacings, reporting predicted costs and parameter-bound activity. These are linear predictions, not independently evaluated physical costs. They cannot relabel the original failed fits.
Next gate
Only after the component qualifies should a separate finite native diagnostic evaluate its proposals. A complete boundary-aware optimizer still needs known optima, repeatability and physical prediction checks before fresh calibration. Keep the original cost, stationarity and position-change limits throughout.