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

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