core_status
plain-language theorem explainer
The definition core_status assembles a fixed verification string that reports completion of the foundational types in recognition geometry. A researcher tracing how space emerges from recognition maps would reference it to confirm that the basic axioms hold before proceeding to derived structures. The construction proceeds by direct concatenation of preset messages listing each established component.
Claim. The core status is the string formed by concatenating the messages confirming that a configuration space exists (RG0), an event space is nontrivial, and a recognition triple bundles the two.
background
Recognition geometry treats space as emergent from recognition maps rather than primitive. The module introduces three core notions: ConfigSpace as a nonempty type of possible world states (with witness extraction), EventSpace as a type of observable outcomes required to contain at least two distinct events, and RecognitionTriple as the structure pairing one ConfigSpace with one EventSpace. Upstream, ConfigSpace is equipped with an empty element, commutative join, consistency predicate, and independence relation from the CostFromDistinction module; a separate ConfigSpace definition in Modal.Possibility restricts to positive-value configurations.
proof idea
The definition is a direct string concatenation of six fixed verification lines followed by a completion banner. No lemmas or tactics are applied; the body simply assembles the literal messages for each sibling definition.
why it matters
This definition records that the RG0 nonempty-configuration axiom and the nontrivial-event requirement are in place, closing the initial layer of recognition geometry. It sits at the base of the Recognition Science chain before any forcing steps or phi-ladder constructions are invoked. No downstream theorems currently cite it, leaving open whether later modules will import the status string for documentation or testing.
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