Axioms

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 The following axioms govern the behavior of voxels and the causal structure of physical reality as described by Voxel  Theory.  Each axiom is expressed in a conditional (if/then/else) format to preserve logical rigor and causal necessity.  

Axiom 1:  IF a voxel transitions, THEN it does so based on its own saturation and causal pressure, ELSE it remains in its current state, unaffected by nonlocal events.

Axiom 2:  IF space is required for fields, particles, or motion to exist, THEN space must itself be real and structured (tessellated), ELSE space is undefined and cannot host causality, fields, or energy.  

Axiom 3:  IF causal tension propagates through voxel interactions, THEN the sequence of these transitions will appear as time, ELSE time does not exist and cannot be used as a coordinate or mechanism. 

Axiom 4:  IF the causal field is made of a fixed number of voxels with boundary topology, THEN motion, redshift, and 'expansion' are curved trajectories, not inflation, ELSE the universe would require infinite energy, space, or undefined boundary conditions.  

Axiom 5:  IF mass, energy, charge, and spin emerge from field deformation and voxel topology, THEN no hidden variables or extra dimensions are needed to explain observable reality, ELSE they must be justified as emergent structures or dismissed as abstractions.  

Axiom 6:  IF voxel behavior is deterministic and local, THEN apparent randomness is a product of complex causal overlap, ELSE we mistake epistemic limitations for ontological indeterminacy.  

Axiom 7:  IF the field updates only based on local causal saturation, THEN there is no need for a global clock, simultaneity, or preferred frame, ELSE hidden synchronization must be introduced, violating causality.  

Axiom 8:  IF the universe is composed of discrete voxels, THEN smoothness and continuity are statistical illusions at scale, ELSE mathematical convenience would be mistaken for physical structure.  

Axiom 9:  IF all energy corresponds to resistance, deformation, or resolution within the voxel field, THEN energy conservation is the preservation of causal structure, ELSE energy remains a symbolic abstraction lacking mechanical definition. 

Axiom 10:  IF the field is finite and cyclical, THEN some matter and causal patterns will persist across bounces, ELSE each cycle would require perfect reinitialization, contradicting observed anomalies.  

Meta-Axiom:  All propositions within Voxel Theory must be framed such that any dichotomy (A or B) arises from causal and ontological necessity, not arbitrary assertion.  No proposition may introduce a false dichotomy.  Any violation of causal, structural, or ontological consistency shall require reformulation of the offending axiom or  mechanism