The Canonical Completion Object Theorem for Shadow Theory
Canonical completion as a certified initiality criterion in a public admissible completion category
Authority role
Establishes conditional canonicality: a public completion is canonical exactly when it is a certified initial object in the public admissible completion category.
Summary
Defines when a response to a certified completion need is canonical. The answer is categorical and deliberately conditional: canonical completion is certified initiality, not an automatic consequence of completion need. Formalizes the public completion context, certified category data, typed refinement morphisms, a seven-valued status classifier, and the output card handed to Paper 4.
Notes
Reading notes
Given a certified completion need from Paper 2, when is a response canonical? The answer is categorical and deliberately conditional.
A canonicality criterion, not an existence theorem.
A public completion is canonical exactly when it is a certified initial object in the public admissible completion category determined by the target, its public closure target, and certified public category data.
Key machinery: the public completion context, the certified category-data discipline, typed public refinement morphisms with explicit hom-typing, certificate-gated composition safety, and a seven-valued ordered status classifier.
Cite this paper
Rodgers, Jeremy. (2026). The Canonical Completion Object Theorem for Shadow Theory (v4). https://doi.org/10.5281/zenodo.21184607