Exact shared-error arithmetic: finite qualification
Qualify the fixed Gaussian-law calculation separately from receiver accuracy. Eight small controls compare exact state-space quadratic forms with independent rational Gaussian elimination, including missing covariance components and a perfectly correlated OU state. Eight generated prefixes test 32, 64, 128 and 292 uniformly spaced epochs under each of two predeclared discrete covariance laws. Their transition coefficients are exp(-1/10) and exp(-1/300), rounded to the nearest 24-bit dyadic number. These are explicit discrete laws, not exact continuous-time kernels.
Each identity verifies an integer-only inverse-moment lower-tail certificate and an exactly checked outward square-root endpoint. A fixed degree-seven polynomial reference uses known generated coefficients. Unit controls also test extreme scales, rank overcounting and cooperative resource failures.
Limits: 16 identities, 1,072 total innovation epochs, zero native evaluations, zero optimizer starts and zero archive reads. Each identity reserves at most 292 epochs, 131,072 numerator/denominator bits, and ten cooperative seconds; the whole study has 120 seconds. One worker reserves four numerical threads. There are no retries, budget expansions or process signals. Charge each identity and its entire epoch reservation before calculation. A failure stops the remaining sequence and remains recorded.
Acceptance requires exact dense agreement on all small controls, nonnegative quadratic forms, valid exact quantile certificates and outward endpoints, and completion of every prefix within its frozen limits. A pass permits preparation of a separate training-only recorded-source assessment. It does not validate Gaussian receiver errors, cure broad nonlinear prediction bounds, authorize observed Earth-model fits or touch protected ESA groups.