Phenomenology of Finite Resolution Physics: Physical Realizations of Non-Hamiltonian Dynamical Regimes

Finite Resolution Physics (FRP) predicts that the familiar dynamical frameworks ofphysics arise as particular realizations of a broader landscape of stabilized regimes. Inthis framework Hamiltonian dynamics appears only when the representational continuationparameter admits a continuous real component. Other continuation geometries lead to distinctdynamical structures in which no infinitesimal generator exists.The present work explores the phenomenology of these regimes. We analyze how differentcontinuation carriers produce characteristic dynamical signatures and identify classes ofphysical systems whose behavior may naturally correspond to such regimes. Examplesinclude discrete iterative dynamics, phase–wrapped systems with compact continuation, finitedynamical state spaces, and hierarchical structures associated with ultrametric geometries.We develop diagnostic criteria for identifying the effective continuation carrier of a systembased on spectral structure, recurrence behavior, existence of generators, and stabilizationproperties under refinement. The framework also predicts the possibility of regime transitionsin which changes in probing architecture or measurement resolution activate differentrepresentational realizations of the dynamics.Taken together, these results suggest that the dynamical laws observed in physics maycorrespond to particular regions within a broader space of possible regimes. The FRPframework provides a systematic approach for exploring this landscape and for identifyingphysical realizations of dynamical structures beyond the traditional Hamiltonian paradigm.