IndisputableMonolith.Relativity.Calculus
The Relativity.Calculus module supplies the differential calculus layer for spacetime computations in Recognition Science. It is imported by modules on static spherical metrics, FRW cosmology, null geodesics, and post-Newtonian expansions. The module consists of one import to the Derivatives submodule that defines the standard basis vector.
claimThe module provides the standard basis vector $e_μ$ together with derivative operators for coordinate calculus on spacetime manifolds.
background
The module sits inside the Relativity domain and imports only the Derivatives submodule. That submodule's documentation states it supplies the standard basis vector $e_μ$. This notation supplies the coordinate frame used by all downstream relativity constructions. The local theoretical setting is the differential geometry required to express metrics, geodesics, and perturbations inside the Recognition Science framework.
proof idea
this is a definition module, no proofs
why it matters in Recognition Science
The module feeds IndisputableMonolith.Relativity.Compact.StaticSpherical, IndisputableMonolith.Relativity.Cosmology.FRWMetric, IndisputableMonolith.Relativity.Geodesics.NullGeodesic (null geodesics for light propagation and lensing), and IndisputableMonolith.Relativity.PostNewtonian.Metric1PN (post-Newtonian potentials). It supplies the calculus primitives required for those metric and geodesic calculations.
scope and limits
- Does not define any concrete metric tensor.
- Does not contain physical predictions or numerical results.
- Does not implement coordinate transformations or Christoffel symbols.
- Does not include any theorem statements or proofs.