RecognitionAtlas
plain-language theorem explainer
RecognitionAtlas packages a set of recognition charts that are pairwise compatible on overlaps and whose domains cover the full configuration space C. Researchers constructing manifold structures from recognizer data in Recognition Geometry cite this when lifting local charts to global quotients. The declaration is the direct structure definition assembling the charts set, the ChartCompatible predicate, and the universal covering condition.
Claim. A recognition atlas for local configuration space $L$, recognizer $r: C→ E$, and dimension $n$ consists of a set of recognition charts such that any two charts agree on the coordinates of every shared configuration point and the union of their domains equals all of $C$.
background
The module RecogGeom.Charts connects Recognition Geometry to classical manifold theory. A RecognitionChart is a local coordinate map φ from a neighborhood U in the local structure to ℝ^n that is injective on indistinguishable configurations and continuous in the recognizer sense. ChartCompatible requires that two such charts return identical coordinate values on every point in their overlap. The module setting asks when a recognition geometry admits local coordinates that respect indistinguishability, noting that finite-resolution constraints (RG4) block continuous injections while quotients by equivalence may still be smooth.
proof idea
The declaration is the structure definition itself. It introduces the three fields charts, compatible, and covers with no further proof obligations or lemmas applied.
why it matters
RecognitionAtlas supplies the atlas object used by atlas_covers_quotient to show coverage of the recognition quotient and by IsSmoothRecognitionGeometry to define smoothness. It fills the step from local charts to global structure in the Recognition Geometry development, supporting the claim that spacetime dimensions count independent recognition distinctions rather than pre-existing geometry. The construction aligns with the framework's derivation of D=3 from the eight-tick octave and the recognition dimension hypothesis.
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