Informational Requirements for Pre-Categorical Relational Models: Identifiability, Measure, Dynamic Closure, and Coarse-Graining

This technical research report studies relational models that are asked to support cardinal comparison, refinement, transition, and coarse-graining even when their primitive data contain only a relation. We study which additional informational structures are required for those operations. Order-only observations are invariant under broad monotone recalibrations and therefore do not identify latent marginal scales or densities. An additional mark q can supply relative cardinal information only when its marked law and observable coupling are not determined by the relation. Additive mass μ is required to distinguish conservative refinement from representational cloning, while locality and symmetry alone leave the transition kernel K underdetermined. For the exponential observable, the block message consisting of total mass and the effective score Q_lambda aggregates exactly. Under a centered contraction, however, the next score depends on Q evaluated at a shifted parameter. We give an exact four-point counterexample showing that equal mean and equal Q_lambda do not determine the next score on the unrestricted finite class. Thus exact static sufficiency does not imply dynamic autonomy. For Markov coarse-graining, a microscopic kernel and a partition do not generally determine a macro kernel without source occupancy π or lumpability; joint flow aggregates exactly when occupancy is supplied. These obstructions motivate the provisional informational architecture (R, q, μ, K, π). The construction is formal and does not derive physical spacetime, calibration, or a fundamental dynamics.