A sampled controller with an actuator budget.

The control chain has an explicit model.

Calibrated flux–charge samples feed a digital command calculation, held voltage/current commands and an identified first-order actuator. The normalized plant obeys z′=F₀(z)+a+r; the actuator obeys a′=ω(c−a)+ξ. The target command U=Fₛ−F₀ includes cancellation of the physical plant.

The theorem bounds tracking by the larger of initial mismatch and K(Md+ν)+q+εₐ+KM/ω. Here K bounds command sensitivity, d is actual sample age, ν is input error, q is total command error, εₐ bounds actuator distortion, and M bounds actual history speed. Actual dynamics must support this model.

One exact design allocation fits the prior tolerance.

The total remains below 1/100 and preserves the earlier conditional nominal/fault gaps near model time 1/100. This control budget replaces the earlier ideal-delay allocation. It is counted once.

Startup and saturation are part of the test.

A proposed ten-time-constant preload starts the actuator at zero while the state and every relevant sample history stay within a radius of 1/1000000 around one fixed center. Under the identified model, release tracking error is below 4391/8000000, which is less than 1/1000.

Hold radius does not establish prehistory speed. Record both, along with release disturbances and holding work. A cold start without a tracking certificate returns HOLD.

The conservative invariant actuator magnitude is at most 9.0635. The proposed bidirectional normalized range is 10. Unbudgeted clipping, slew limits, ringing or crosstalk returns HOLD.

Physical component requirements follow the calibrated clock.

For physical time scale t₀, sampling period, extra latency and actuator time constant must each be no greater than t₀/400000 seconds. In the example, preload lasts at least t₀/40000 seconds. No numerical hertz is assigned before t₀ calibration; uncertain t₀ requires worst-case normalized bounds.

Voltage ports require range at least ±10Φ₀/t₀ and current ports at least ±10Q₀/t₀. These are per-channel requirements with the actual canonical scales and loading. The common action S₀ here is distinct from the similarly named structural coefficient in the provenance ledger.

An ideal 22-bit quantizer leaves room in the proposed input and output error budgets. Nominal bit count alone establishes neither effective resolution nor attainable rate. Additional gain, offset, noise, drift and numerical command errors must fit the remaining allowance.

The next gate is apparatus evidence.

The machine-readable contract lists actual component and port equations, first-order model identification, range and slew tests, timing records, input/command error decompositions, startup records, finite-calibration regularity and independent coupling/work readout. Every empirical field remains OPEN.

The result covers a short Gauss-discrimination prefix. It does not certify the full CD-1 campaign or SDW endpoint admission. Non-constructor adversarial review and experimental execution remain pending.