A narrow source class.
A continuous-band bound.
The unchanged measured-window kernel satisfies a proposed ±50 Hz source and uncertainty budget using exact rational interval enclosures and an analytic remainder.
The source premise is explicit.
The complex envelope has spectral support within ±50 Hz relative to the fixed carrier and complex spectral-measure total variation at most 1 V. True amplitude must be at least 1/2 V wherever phase is reported. Combined input error must be at most 1/2000 V; constant baseline magnitude is at most 3 V.
These are proposed design restrictions. They are stronger than observing a spectral peak or a finite-record RMS bandwidth. The earlier faster-envelope and pulse cases are not silently readmitted.
| Quantity | Conditional bound | Target |
|---|---|---|
| Total complex error | <0.005788 V | 1/100 V |
| Phase error | <0.011693 rad | 1/50 rad |
| Availability delay | 524.288 microseconds | 600 microseconds |
Every frequency in the declared band is covered.
The proof bounds main-response distortion and conjugate-image leakage with center moments, first derivatives and a global second-derivative remainder. Saved binary64 kernel coefficients are interpreted as exact dyadics; no coefficient refit occurs.
Integer-directed 160-bit intervals enclose trigonometric moments using Machin’s pi formula and explicit Taylor remainders. Exact fractions carry the comparisons; displayed decimals are explanatory. The separate rounding allowance applies to a declared serial binary64 dot product, not arbitrary libraries or all platforms.
Exact certificate fractions →Standard-Python certificate replay ↓A concrete failure stays visible.
A 600 Hz unit tone has a certified complex-error lower bound above 0.2305 for this kernel, so it fails 1% recovery. This is not a no-go against other kernels. A larger input-error allowance fails the sufficient budget, while a 500 microsecond delay cap rejects the unchanged window.
Next derive a leakage-tolerant source contract and allocate the remaining margin to spectral tails and instrument uncertainty. Source bandwidth, noise, gain/skew, full energy, absolute native support and action normalization remain open.
Requirements and limits →Preserved local estimator →