VectorField
VectorField aliases the (1,0) tensor on 4D spacetime. Lattice fluid dynamicists and relativists cite it when passing continuous tensor fields into discrete operators such as advection or covariant derivatives. The definition is a direct one-line abbreviation of Tensor 1 0.
claimA vector field on 4D spacetime is the map type $ (Fin 4 → ℝ) → (Fin 1 → Fin 4) → (Fin 0 → Fin 4) → ℝ $, i.e., a (1,0)-tensor.
background
The Tensor module is marked a scaffold outside the certificate chain. Its core definition states that a (p,q) tensor is the function type (Fin 4 → ℝ) → (Fin p → Fin 4) → (Fin q → Fin 4) → ℝ, fixing all geometry to four-dimensional spacetime. VectorField selects the contravariant vector case p=1, q=0.
proof idea
This is a one-line abbreviation that directly instantiates Tensor with indices 1 and 0.
why it matters in Recognition Science
The abbreviation supplies the vector type used by eight downstream declarations, including advection, divergence, vectorLaplacian and CoreNSOperator in the discrete Navier-Stokes module plus covariant_deriv_vector in Connection. It supplies a basic geometric primitive for the relativity scaffold, though the module carries no certificate status and touches none of the T0-T8 forcing steps or the Recognition Composition Law.
scope and limits
- Does not prove any property of vector fields or tensors.
- Does not link to the phi-ladder mass formula or J-uniqueness.
- Does not define a discrete site-based vector field.
- Does not incorporate spacetime metric or curvature.
- Does not participate in the main certificate chain.
formal statement (Lean)
15abbrev VectorField := Tensor 1 0