Observable vs Latent Dimension

[Matesax]

Motivation

Current batteries support:

Observable Lorentzian rank 4 does not imply latent dimension 4.

The strongest theorem would identify exactly when latent dimension is recoverable.

Question

For what model classes is the observation functor faithful?

Deliverables

• Competitor-category definition.
• Faithfulness theorem or counterexample.
• Hidden-extension examples.
• Non-manifold examples.
• Reconstruction criteria.

Definition of done

A sharp theorem stating when latent dimension can and cannot be inferred.

Contributor profile

Category theory, inverse problems, geometric reconstruction.