A Physical Object is Defined by its Capacity for Global Causal Coherence - The Axiom of Causal Coherence

This paper introduces a single ontological axiom intended to define physical objecthood at the most fundamental level:
a physical object is defined by its capacity for global causal coherence.

Physical existence is not assumed to arise from substance, intrinsic properties, or geometric extension, but from the ability of a configuration to maintain causal unity as a whole under finite-speed information transfer. Energy and inertia are interpreted as measures of the cost required to preserve this coherence against perturbations.

The axiom is formulation-independent and compatible with discrete space, finite propagation speed, and constant-density ontologies. It provides the ontological foundation for the Volumetric Emergence Model (VEM) and clarifies the origin of squared velocity scales in physical laws without presupposing gravitation as a fundamental interaction.

Status of claims

• Ontological claim (foundational):
  The paper proposes a definition of physical objecthood. It does not introduce new empirical laws or modify existing equations.

• Conceptual claim (strong):
  Energy, inertia, and stability are interpreted as consequences of causal coherence rather than intrinsic properties of matter.

• Physical claim (conditional):
  If physical reality is discrete and information propagation is finite, then global causal coherence is a necessary condition for physical existence.

• Relation to existing models:
  The axiom is compatible with known physics but operates at a pre-dynamical level. It does not compete directly with Quantum Mechanics or General Relativity.

Falsifiable or discriminating consequences

While ontological in nature, the axiom implies several non-trivial constraints that can be confronted with physical modeling:

1. Exclusion of strictly point-like physical objects
   Any model relying on physically meaningful point entities with instantaneous internal response is ontologically inconsistent with the axiom.

2. Finite minimal update time for any physical object
   Objects with spatial extension must exhibit a minimal timescale for global state coherence.

3. Emergence of squared velocity scales
   Any consistent physical realization must naturally produce velocity-squared terms (e.g. v2v^2v2) as coherence constraints rather than as empirical constants.

4. Inertia as relational stability
   Models treating mass as an intrinsic, context-independent property are conceptually incompatible with the axiom.

Failure to reproduce these constraints within a proposed physical realization would falsify that realization, not the axiom itself.