Unification of Dimensional Depth and Scanning Parameter Via DDP&DUP

Abstract

<p>This thesis is the first thesis of the trilogy thesis project "Spectrum of Dimension". I addressed classical dimension as continuous entity, and devised two operators DDP, and DUP to deal with the continuity. Handling singularity problem through distribution theory, I managed to prove these operators are isomorphic to integral-differential operators. Following problem was the justification of the synthesis of dimension, which is also expressed as 'Conservation of Geometric Measure'. Via Fubni's Theorem, it is possible to treat dimension not only as discrete, but continuum. This unique theory is proved by the duality theorem by Edward Witten, concluding that reducing dimension via Scanning Parameter does not destroy information but merely <br>transforms its state of existence—from "Geometric Coexistence" to "Temporal Sequentiality.</p>