IndisputableMonolith.RecogGeom.Locality
The Locality module introduces RG1 of Recognition Geometry by defining local configuration spaces as configuration spaces equipped with neighborhood structures. This enables discussion of nearby configurations without metrics or full topology. Researchers building emergent geometry from recognition maps cite it as the base layer. The module supplies definitions that feed directly into foundational theorems and recognizer constructions.
claimA local configuration space is a configuration space $C$ equipped with a neighborhood structure that permits reference to nearby configurations without assuming a metric or topology.
background
Recognition Geometry treats space as emergent from the structure of recognition maps rather than primitive, per the Core module. The Locality module supplies the first axiom RG1: local configuration spaces add neighborhood structures to configuration spaces. These neighborhoods support statements about proximity while remaining metric-free.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies RG1, which Foundations uses for its three fundamental theorems of Recognition Geometry and which Recognizer extends via RG2 recognition maps. Integration imports it to assemble the full framework. It closes the initial layer before recognizers and events are introduced.
scope and limits
- Does not assume or introduce a metric on configurations.
- Does not define recognition maps or events.
- Does not prove theorems about locality properties.
- Does not specify concrete neighborhood examples beyond the type.