The Bell Tower Architecture: Axiomatization, Analytical Rigor, and Formulation of the Sieve Continuum Claim
Year: 2026
Type: preprint
Abstract: his paper establishes the formal mathematical framework for the rigoroustransition from the two-dimensional discrete lattice Z2 to a continuous order field onthe complex plane C. We demonstrate that while the spectral counting function andthe convergence exponent (ρ = 1) are determined entirely within the planar domain viaDirichlet’s divisor methods, a pure two-dimensional hydrodynamic extension suffers fromunphysical local energy divergences due to pointwise Dirac delta singularities. To resolvethis boundary collapse, we establish a structural extension into the three-dimensionalspace C × R. By integrating the theory of projective operators in Hilbert spaceswith Weierstrass regularization and three-dimensional cylindrical vortex extensions, weformalize a globally stable, energy-bounded analytical architecture in alignment with themethodological criteria of Hilbert’s Sixth Problem, thereby lifting the discrete dynamicsof the sieve to a regularized stationary flow potential.
Author: Gabbianelli, Silvio
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225741166
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