Manifold
plain-language theorem explainer
A minimal manifold structure consisting of a single natural-number dimension field. Downstream geometry modules cite it to type points, covectors, and tangent spaces in relativity constructions. The definition is a direct structure declaration with Repr derivation and no proof obligations.
Claim. A manifold is a structure equipped solely with a dimension field taking values in the natural numbers.
background
This module supplies placeholder types for differential geometry in the Relativity section. The structure carries only a dimension parameter drawn from upstream definitions such as the spatial dimension in TauStepDerivation and the active edge count A from IntegrationGap. Related upstream results include the Actualization operator from Modal.Actualization, which supplies integer constants feeding into manifold constructions.
proof idea
The declaration is a bare structure definition introducing the field dim : ℕ with Repr derivation. No tactics or lemmas are applied; it serves as a direct type introduction.
why it matters
This definition provides the base type for manifold-dependent objects such as Point, Covector, and Spacetime used in SimplicialLedger and ModalGeometry. It fills the structural placeholder role noted in the module documentation, supporting downstream refinements like monotone separation in EffectiveManifold. It touches the open question of embedding full differential geometry into the Recognition Science certificate chain.
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