10.4 Base, tangent, and transverse reasoning

At every state, CoLT retains two diagnostic layers:

The base obstruction asks whether the current commitments compose. The tangent obstruction asks whether that composition is stable under a declared family of nearby changes. A claim can therefore be coherent at the present state but fragile under paraphrase, evidence removal, population shift, mechanism perturbation, or reordering of interacting operations.

Infinitesimal diagnosis does not confine reasoning to infinitesimal change. When \(O_k^1\) cannot be repaired inside the current realization, the repair language may propose a transverse change: a new object, path, axiom, cover, observer, or intervention vocabulary. The successor then has a changed declaration \(\mathbb S_{k+1}\). Old evidence must be transported to the new sketch, and the expanded theory must pass a new admission contract.

This is how CoLT accommodates an abductive jump without treating the jump as magic. Infinitesimal probes diagnose the boundary of the current theory; a transverse proposal changes that theory; transport and admission determine whether the proposal becomes part of the maintained model.