Admit bounded tails.
Expose the instrument requirements.
The full-state quadrature theorem now budgets spectral leakage and four acquisition-error contributions. Every physical input remains a proposed requirement.
The reference includes the tail.
With in-band envelope spectral variation at most 1 V within ±50 Hz and tail variation at most 1/1000 V, the full-state tail contribution is (H+1)T. The extra T accounts for the tail in the true reference. Using HT alone would instead target the in-band component.
| Quantity | Conditional bound |
|---|---|
| Full complex error | <0.008698 V |
| Phase error at full amplitude ≥1/2 V | <0.017571 rad |
| Remaining output-error margin | >0.001202 V |
| Availability delay | 524.288 microseconds |
The exact sufficient frontier couples tail allowance and input uncertainty. Their individual ceilings cannot both be increased at once. Exact fractions, equality controls and beyond-frontier controls are retained.
Inspect the exact frontier →Four input shares, no assumed cancellation.
| Contribution | Required ceiling | Supporting condition |
|---|---|---|
| Noise and quantization | 1/10000 V | Independent acquisition bound |
| Gain | 1/20000 V | Relative error ≤1/100000 at ≤5 V |
| Timing | 1/20000 V | ≤0.2 ns with slope ≤250000 V/s |
| Baseline variation | 1/20000 V | Independent residual-baseline bound |
Total input error is at most 1/4000 V. The illustrative timing slope also assumes physical tail frequencies no higher than 200 kHz in absolute magnitude. The generic leakage theorem itself needs no such cutoff and assumes no anti-alias suppression.
A finite FFT cannot supply the missing source certificate.
Distinct tail tones can combine to vanish at every finite sample time while remaining nonzero between samples. Without independent source or norm restrictions, scaling such a combination prevents finite samples alone from bounding unrestricted tail spectral variation.
Next create an evidence checklist and fail-closed admission schema for source leakage, gain, noise, timing and baseline records. Missing or circular bounds should return HOLD. Full energy, absolute native support, primitive clock and action calibration remain open.
Frozen leakage contract →Exact budget replay ↓Inherited continuous-band certificate →