Research Papers

The master overview of all four geometric arrangements of the resonance matrix — Opposites, Triangles, Squares, and Odds/Evens — and the Seekins Constant relationships that unify them.

Full glossary of terms used across the research series: tHz/nm scales, the Seekins Constant, the resonance matrix, the circle code, charge classification, the Four Horsemen, and the three classes of 40.

Spectral displacement analysis of the 6 spoke-pair arrangement and the 4-triangle arrangement. Every pair and every triangle shows an identical Δ derived exactly from the Seekins Constant.

Analysis of the 3-square arrangement (40 elements each). The 19/21 shared/non-shared split, the 31/38 fractional component, and the asymmetry of Square 1 against Squares 2 and 3.

The odd and even atomic numbers form perfect spectral mirrors around 540, separated by exactly 30. The 7/16 fractional component connects directly to the first symmetry point of the circle code sequence.

1000-stage analysis of first-prime gaps within the +30 stage windows of the resonance matrix. Convergence toward 30, harmonic clustering, and the relationship between 30-unit stage width and prime arithmetic.