IndisputableMonolith.RecogGeom.Core
The Core module introduces the basic objects of Recognition Geometry: configuration spaces as the underlying states of the world and event spaces as the observables available to recognizers. It states RG0 as the existence of a nonempty configuration space and packages these into RecognitionTriple. All later Recognition Geometry modules cite this foundation for their definitions and axioms. The module consists of type declarations and basic existence statements with no derived theorems.
claimLet $C$ be a nonempty type (configuration space). Let $E$ be an event space. A recognition triple is a triple $(C, E, R)$ where $R : C → E$ is a function from configurations to events. RG0 asserts that such a nonempty $C$ exists.
background
Recognition Geometry separates the actual states of the world (configurations) from the data that any recognizer can access (events). The module defines ConfigSpace as the type of possible configurations and EventSpace as the type of observable events, with DecEventSpace providing a decidable variant. It introduces RecognitionTriple to bundle a configuration space, an event space, and a recognition map. The setting is axiomatic: RG0 requires only that the configuration space be nonempty, leaving all further structure to later modules.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
Core supplies the starting objects that every Recognition Geometry development requires. It directly feeds Dimension (which links recognizer structure to geometric dimension), Locality (RG1 on neighborhoods), Recognizer (RG2 on recognition maps), Foundations (the three fundamental theorems), Examples, and Integration. The module realizes the initial RG0 step before any locality or recognition axioms are imposed.
scope and limits
- Does not equip configuration spaces with metrics or topologies.
- Does not define recognition maps beyond their existence as functions.
- Does not introduce dimension, locality neighborhoods, or integration.
- Does not connect to physical constants, phi-ladders, or forcing chains.