HyperMorphic Field Theory Invariant-Constrained Lawspace Dynamics, Recoverable Representation Transport, and Computational Holonomy

This preprint introduces HyperMorphic Field Theory (HMFT), a mathematical and computational framework for systems in which the active computational law, representation space, and admissible geometry may change through time. Rather than treating representation as fixed background structure, HMFT models computation as a coupled evolution through both state space and lawspace, with explicit encoder–decoder transports required to preserve designated invariants up to controlled error. The paper develops a constructive theory of recoverable representation transport across finite and continuous lawspaces. Its main results include: a representation-bundle theorem with explicit recovery and commutation bounds; a global autonomous stability theorem under contraction and selector-margin conditions; invariant-constrained switching-regret guarantees against the best admissible changing-law path; an exact safety-compression dividend showing how compatibility constraints reduce law-path description complexity; a continuous-law covering theorem; and a chain-consistent hierarchical learning theorem with diameter-weighted regret. The continuous formulation is instantiated on the sphere S^2, where tangent fibers and Levi-Civita transport provide an operational notion of computational holonomy: two systems may return to the same law after traversing different lawspace paths while retaining different internal orientations. The manuscript also records failed constructions and counterexamples, including selector bifurcation under local recovery alone and inconsistency in independently learned refinement increments, together with the assumptions and algorithms required to repair them. A reproducibility suite accompanies the theory, including finite-law, long-horizon stability, switching-regret, continuous-law, holonomy, multiscale, and hierarchical consistency certificates. The strongest interpretation of HMFT is as a mathematical theory of computation over evolving representational laws. It does not claim experimental validation of a new physical theory, replacement of established physics, or peer review. Physical specialization would require an action principle, spacetime fields, observables, stability analysis, correspondence limits, and falsifiable predictions