Digit-Curvature Operators on Physical Constants and Their Clifford Algebra Structure
Year: 2026
Type: preprint
Abstract: We introduce a discrete curvature operator $\Delta^2$ acting on the significant digit sequences of physical and mathematical constants, producing 8-dimensional vectors in the Clifford algebra $\mathrm{Cl}(8,0)$. The operator maps a real number to its second finite differences in base 10, yielding an 8-component vector whose algebraic products encode structural relationships between constant pairs. We show that this encoding reveals a non-trivial geometric skeleton: consecutive Riemann zeta zeros $\gamma_2$ and $\gamma_3$ are exactly orthogonal in the $\Delta^2$ inner product, the Boltzmann and Planck constants are antiparallel at $178.5°$, and nine constant pairs achieve exact or near-exact orthogonality. We extend the method to scalar fields on a three-dimensional grid, where the $\Delta^2$ grade decomposition is dominated by the trivector (grade-3) component at $69$–$73\%$ of total content, significantly above a measured null baseline of $65.6\%$. The structural excess is traced to an anomalous isotropy of the evolved field's digit-curvature gradients — $20\times$ more isotropic than any synthetic comparison field. We report an observable numerical coincidence: the CFL stability condition on a $\zeta$-structured Laplacian field produces a beat period whose reciprocal matches the angular migration rate of Earth's magnetic north pole on $S^3$ to five significant figures, with one free parameter.
Author: Hammarsten, Mattias
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7161746501
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