Operational Calculus for Sigma-Time Transforms
Year: 2026
Type: preprint
Abstract: This paper develops, positions, and records the reproducibility boundary for the operational-transform layer of Sigma Transform Calculus. A bounded-variation clock σ determines a clock measure µσ and a canonical mass-coordinate selector ισ. The sigma transform of a signal is defined by selecting the signal into mass time and applying the ordinary Laplace kernel there. This converts clock-relative transform questions into mass-coordinate Laplace questions while keeping atoms, flats, endpoint conventions, and convergence domains explicit. The resulting theorem spine proves the transform-domain definition, the mass-coordinate reduction, linearity and boundedness, the sigma-derivative operational rule, the mass-convolution product theorem, a pure-atomic specialization, a bounded-generator evolution/resolvent interface, and a uniqueness boundary. Contribution sentence. The paper packages the sigma transform as a clock-measure operational calculus by reducing it to mass-coordinate Laplace calculus and transporting the resulting identities back to sigma time.
Author: Tibola, Ben F.T.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162117649
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