Estimator Robustness and Measurement Invariance in Continuity Science: Reliable Estimation of Coherence Curvature Under Admissibility Constraints

This work examines estimator robustness and measurement invariance in Continuity Science, focusing on the estimation of coherence curvature (κ) as a latent structural quantity governed by Canonical Laws. Rather than proposing new dynamics or redefining κ, the paper analyzes the conditions under which κ-estimators are admissible and the structural consequences of estimator variation. The central contribution is a formal characterization of admissible κ-estimators, defined not by statistical optimality or identifiability, but by compliance with Canonical constraints such as continuity, boundedness, irreversibility, regime stability, and dimensional consistency. Within this admissible class, the paper proves that although estimators may disagree pointwise, they induce identical regime and failure classifications almost everywhere in time. Estimator disagreement is shown to strengthen falsifiability rather than weaken it: any admissible estimator detecting failure renders that failure canonical, while estimators permitting reversibility or boundary denial are structurally disqualified. Measurement uncertainty is thus confined to the estimator interface and does not undermine the authority of the Canon. The paper introduces no preferred estimator, no new laws, and no optimization criteria. Estimation is treated as a jurisprudential interface between observables and Canonical structure, emphasizing that the Canon constrains estimators—never the reverse. This contribution is relevant to researchers working with latent structural variables, regime classification, irreversible dynamics, and theory–measurement interfaces where identifiability is limited but structural invariance is critical. If you’d like, I can also provide: a one-paragraph short description (for Zenodo preview cards), recommended keywords, or a citation-friendly abstract variant.