Hidden States as Bounded Objects?

This is an application preprint in the Atacton Working Paper Series (ATACTON-WP-HMM-001, Version 1.0). It is not peer reviewed. It is an application freeze on representation architecture, not a fitted-model preprint. No EM results, no reader results, and no forecast results are claimed. The proposition is computational unity ≠ semantic unity: one latent path can be well-defined as a statistical co-representation of unlike series and still fail as one bounded historical object. Strategy A is a mixed-state representation; Strategy B is an object-separated representation. The paper also freezes the hierarchy observed variable ≠ semantic object ≠ latent state (X ≠ R ≠ Z): data-source multiplicity does not imply object multiplicity. Frozen Kₖ v1.0 (Wong, 2026c) is called, not rewritten. The same unplayed Premier League fixture as Application 1 (Ipswich Town v Liverpool, 4 September 2026) is bound on a different evidence layer: league result path plus dated pre-kick-off quotes, not the H2H page. The framework constrains the semantic interpretation of model components; it does not determine the statistically optimal factorisation. Correspondence: joe@atacton.com