The Doctrine of Exit: Fundamental Reconfiguration of Time and Exit from the Numerical System:
The Doctrine of Exit presents a mathematical-theoretical framework for reconsidering the representation of number, time, sequence, state, and geometric structure. The starting point of this research is the question of whether structures that are commonly formulated in mathematics and physics through continuity, unrestricted extension, and conventional numerical representation can instead be represented within a discrete and cyclic state space containing a finite set of admissible states.
Within the proposed framework, a number is not treated solely as a computational quantity. It may also be defined as an operational state within a state space. Transitions between states are represented through a cyclic structure, while time is represented as the ordered evolution of states. The concept of “Exit” is consequently formulated as a structural transition from an admissible domain toward a boundary or a non-admissible domain.
The objective is to establish a unified mathematical language for examining the relationship among number, state, transition, time, geometry, and boundary. The resulting structure is proposed as a basis for investigating fundamental problems in theoretical physics, including temporal structure, gravitational boundaries, singularities, discrete space-time models, informational structures, cosmological problems, and selected questions associated with quantum structure.
A central feature of the research is the separation of mathematical construction from physical interpretation. Mathematical relations and results must follow directly from the definitions and rules of the model. Physical applications, by contrast, require independent formulation, consistency checks against established theories, numerical implementation, and ultimately experimental or observational testing.
Accordingly, The Doctrine of Exit does not claim that the introduction of an alternative numerical representation by itself constitutes a complete solution to all problems of physics. Its central proposal is more specific: some difficulties that arise within continuous formulations or conventional numerical representations may be reformulated through a different state space, transition structure, and definition of boundary.
The proposed conceptual architecture is:
Number → State → Transition → Time → Geometry → Boundary → Exit
Within this architecture, “Exit” is not merely the end of a calculation. It denotes a structural condition in which continued evolution within the defined admissible space terminates or transitions into another domain.
The framework may therefore provide a basis for developing more precise models of discrete time, finite-state dynamics, cyclic geometry, information, gravitation, and cosmology. Its ultimate physical significance must be established through explicit equations, numerical implementation, comparison with existing theories, and falsifiable predictions.
Zenodo: 10.5281/zenodo.22807548
