Hyper Morphic Field Theory: Recoverable Invariant Transport Through State-Dependent Representation Geometry

Paste this into Zenodo → Description: HyperMorphic Field Theory: Recoverable Invariant Transport Through State-Dependent Representation Geometry introduces a mathematical and computational framework for systems whose representation geometry is not a fixed background substrate, but a causal, auditable, state-dependent field over histories, observations, memory contexts, moduli, charts, fibers, routing distributions, and transport paths. The central thesis is that coordinates are disposable, while recoverable invariants are primary. A representation may change chart, modulus, shard, memory corridor, or transport geometry, but the transformation is trusted only when the relevant invariant can be recovered, synchronized, or audited under stated admissibility conditions. The manuscript formalizes HyperMorphic fields, admissible transports, recoverable invariant transport, metadata-free geometry regeneration, SafeGear invertible arithmetic, HoloRAID recovery under damage, SafeMemory causal geometry synchronization, HMAR routing through representation worlds, and computational holonomy. It distinguishes formal theorem, implemented mechanism, synthetic benchmark evidence, and real-data exploratory evidence. A synthetic dark-residual benchmark demonstrates a mechanism-level case where holonomy-aware features recover a residual that visible/product summaries miss. A real SPARC galaxy rotation-curve benchmark is included as exploratory physical evidence under stronger controls, where HyperMorphic holonomy features achieve the lowest aggregate held-out RMSE in the tested suite. These results are presented as evidence for representation-geometry modelling, not as claims to solve dark matter, dark energy, cosmology, or fundamental physics. This work should be read as a computational field theory of representation: a framework for recoverable invariant transport through changing representational substrates, with applications to adaptive computation, coding, distributed recovery, continual memory, routing, residual modelling, and state-dependent geometry.