A finite calibration contract for CD-1.
Explicit plant equations and an error allocation now make the short-window Gauss fault test numerically reviewable.
Physical ports make the target explicit.
For each flux–charge pair, the ideal plant is dΦ/dt=Q/C+V and dQ/dt=−Φ/L+I. Common action products S₀=Φ₀Q₀ and energy E₀ set the physical clock t₀=S₀/E₀. Active voltage and current commands cancel the normalized plant and add the selected CD-1 field.
The manuscript gives the commands and complete Hamiltonian. These are functional port requirements; component selection, loading, bandwidth, gains and controller work still need actual records.
Finite records require a regularity certificate.
A convex-domain calibration cover of radius d, node residual bound ε and separately justified derivative bound Λ certifies a uniform residual at most ε+Λd. A rowwise modular bound can reduce the calibration dimension if hardware decomposition and crosstalk bounds are validated.
Finite samples alone cannot bound an unseen smooth residual between nodes. The manuscript proves this obstruction. A grid with no defensible derivative or structural bound returns HOLD.
Two fault gaps survive an explicit uncertainty budget.
| Design input or certified margin | Value in model units |
|---|---|
| Initial state error; endpoint reconstruction error | Each at most 1/10000 |
| Continuous field residual | At most 1/100 |
| Decision time; clock radius | 1/100; 1/100000 |
| Nominal passage slack | 0.00551444195 |
| Wrong species sign detection slack | 0.00449467027 |
| Frozen electric response detection slack | 0.00529178327 |
The calculator uses exact fractions, including preparation, two endpoint reconstruction errors, the certified decision interval and clock uncertainty. Exact symbolic checks verify the Hamiltonian identities and conservative norm bounds. Seven arithmetic controls pass; excessive measurement error and controller age return HOLD.
Controller age and readout spacing have different roles.
For target Lipschitz bound L=97/4, normalized plant bound λ≤1 and history speed M≤81/10, controller-age residual is at most (L+λ)Md. A delay allocation of 1/400 requires maximum input age d≤1/81810, or t₀/81810 seconds.
The example age 1/100000 gives total allocated residual 0.00954525. CD-1’s proposed readout spacing 1/1000 does not certify this age bound. Using 1/1000 as controller age fails the stated allocation.
The next physical return is specified.
Supply actual port and component equations; calibrated action, energy and clock scales; calibration nodes, cover radii and regularity evidence; timestamped control-age records; preparation and reconstruction bounds; independent coupling witnesses; and blinded fault-control records with joint uncertainty.
This certificate covers a short Gauss-discrimination prefix. It does not admit the full 8π campaign or the SDW endpoint theorem. A 99% per-run coverage statement also needs a joint correction before it can support 99% coverage for a whole campaign. Actual apparatus bounds and attributable non-constructor review remain open.
Read the canonical map and original CD-1 contract →