IndisputableMonolith.Relativity.Geometry.Manifold
The Manifold module supplies the core type for a smooth manifold equipped with explicit dimension and coordinate chart, forming the geometric base layer inside the relativity namespace. Developers building tangent spaces, covectors, and spacetime indices cite it when assembling coordinate-dependent structures. The module consists entirely of type declarations and Mathlib instances with no proof content.
claimLet $M$ be a smooth manifold of finite dimension $d$ equipped with a coordinate chart $U subset M to R^d$.
background
The module resides in Relativity.Geometry and imports Mathlib to obtain standard manifold infrastructure. It declares the central Manifold type together with supporting objects Point, TangentVector, Covector, Spacetime, SpacetimeIndex, timeIndex, spatialIndices, isSpatial, and the Kronecker delta family. These definitions establish the differentiable structure and index conventions needed for later relativity constructions.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module supplies the manifold primitives that the parent Geometry module aggregates and re-exports for convenient importing across the relativity layer. It therefore occupies the lowest geometric rung required to support coordinate-based spacetime modeling inside the Recognition framework.
scope and limits
- Does not equip the manifold with a metric tensor or connection.
- Does not treat global topological properties or compactness.
- Does not introduce differential forms or integration.
- Does not prove existence of charts or transition maps.