Three-Five Residue Collision and Dimension

Abstract

The three-five coordinate pair has its explicit collision, while the full system has statistical dimension three.

Theorem 1.1 (The three-five collision accompanies dimension three).

$$\mathrm{Merges}\left(\{q3,q5\},0,15\right)\wedge statisticalDimension=3$$

Proof. Machine-checked in Lean as D5/S3/Observer/ArithmeticTomography/ThreeFiveResidueCollisionDimension.three_five_residue_collision_and_dimension (✓ std3). ∎

Source. Repository-derived.

Commentary.

The canonical readings modulo three and modulo five identify zero with fifteen. This is the explicit collision required for the three-five coordinate pair.

On the same ZMod 30 state carrier, all three prime coordinates are complete and every two-coordinate selection is incomplete. Therefore the least complete coordinate count is three.

References

• Truth anchor: D5/S3/Observer/ArithmeticTomography/ThreeFiveResidueCollisionDimension.three_five_residue_collision_and_dimension
• Dependency: D5/S3/Observer/ArithmeticTomography/ResidueCoordinateDimension