Fixed-reference shared-scale qualification
Qualify the separate noncentral-dominance scale bound in Mathematics, using generated inputs only. The existing bounded-mean method and all archived results remain unchanged.
Eight frozen families, 1,024 realizations each: central residuals; large means inside the reference space; small noncentral residuals; large incorrect means; zero reference rank; dependent and absent reference columns; correlated observations whitened by a supplied independent covariance; and a smooth mean not represented by the fixed reference. Preserve all 27 columns where present.
Each realization has a fixed true scale and a 0.01 lower-tail allowance. Report coverage, upper-bound width, unsupported frequency and the exact one-sided 99% coverage lower limit. The finite qualification gate is a lower limit at least 0.97 in every family, with no unsupported realizations. This is a Monte Carlo software gate around nominal 0.99 model coverage, not a 0.99 empirical coverage claim or an assessment of the airborne error law.
Separately verify the noncentral/central lower-tail ordering at fixed thresholds, the known scalar formula, numerical allowances, rank-zero/rank-deficient designs, and rejection of adaptive references, unknown noise laws, unknown arithmetic allowances and saturated reference rank. No candidate fit, future observation or receiver archive enters the calculation.
Finite ceiling: eight identities, 8,192 generated realizations, 8,192 scale assessments, 120 cooperative seconds, one worker/four numerical threads. Zero archive reads, optimizer starts, native integrations or retries. Reserve each identity's full allowance before executing it. Preserve all failures and charges; no signals. Freeze sources, deterministic seeds and numerical environment.
Successful software qualification would still leave covariance-shape adequacy, selection, non-Gaussian errors and the native global-envelope limitations open. This does not authorize a significance claim or make any protected ESA outcome available for development.