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mechanics of spherical harmonic spatial/temporal proportion


The encapsulated work is structured as an axiomatic extension of Euclid’s elements relevant to the geometry of proportion further-infused with notions common to Pythagorean number theory; This provides the logical foundation necessary to analyze the structure of the natural dimensional proportion of Pascal’s triangle. A novel modulus nine analysis method is deployed enabling full geometric characterization of the complementary symmetry shown to mediate the consecutive geometric transformations of such numeric proportion.

Key elements of conventional quantum theory
are placed within the context of the proposed dimensional framework: The nature of spherical harmonics, thought to control the periodic order of atomic energy states, is proven to be symmetrically governed by the complementary cuboctahedral dipole field produced by the rotational differentiation of the golden, exponential, roots of space and time. Through this lens, atomic energy is seen as the absolute measure of, electron-proton, dipole field-potential accumulated and bound-neutral via spatial/temporal differentiation. The base field symmetry is geometrically proven to culminate with the in-circle perspective of the 3-4-5 triangle, which produces an integral spectrum of electromagnetic prime-monopole proportion posited to be characteristic of photons.
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