IndisputableMonolith.Relativity.Geometry.Manifold
This module defines a smooth manifold equipped with dimension and coordinate charts as the base for relativistic geometry. It would be cited by any construction of spacetime points or tangent spaces. The module consists entirely of type definitions and re-exports from Mathlib with no internal proofs.
claimLet $M$ be a smooth manifold of dimension $n$ together with an atlas of coordinate charts to Euclidean space.
background
The module sits inside the Relativity domain and imports Mathlib to obtain standard manifold infrastructure. It introduces the core object Manifold along with Point, TangentVector, Covector, and index utilities such as kronecker and spatialIndices. These supply the local Euclidean structure and tangent spaces required before any metric or curvature is added.
proof idea
This is a definition module, no proofs.
why it matters in Recognition Science
The module supplies the geometric primitives re-exported by the parent Geometry aggregator. That aggregator in turn supports all downstream relativity constructions that require a manifold substrate.
scope and limits
- Does not equip the manifold with a metric tensor.
- Does not define curvature, connection, or parallel transport.
- Does not address causal structure or light cones.
- Does not specialize to Minkowski or other concrete spacetimes.