What question did this study set out to answer?

This paper aims to categorize and inventory the parameters within the USSFT framework, differentiating between fundamental and derived quantities.

April 28, 2026Open Access

USSFT Paper V: The Parameter Dictionary. Fundamental Inputs, Auxiliary Quantities, and Calibration Conventions

Key Points

This paper aims to categorize and inventory the parameters within the USSFT framework, differentiating between fundamental and derived quantities.
Identified four continuous fundamental parameters in the U-field Lagrangian.
Performed dimensional analysis to check internal consistency.
Compared parameter counts in USSFT with Standard Model and General Relativity.
Four fundamental parameters established in USSFT, supporting efficient predictions.
Dimensional analysis confirms internal consistency of the parameter inventory.
Minimalist parameter set distinguishes leading-order truncation from other theories.

Abstract

This paper provides a complete inventory of the parameters appearing in the Unified Space-Time and Scale-Dependent Field Theory (USSFT) framework, distinguishing fundamental Lagrangian inputs from derived auxiliary quantities and calibration conventions. Within the leading-order EFT truncation, the U-field Lagrangian (Paper I, DOI: 10. 5281/zenodo. 19622931) contains four continuous parameters: Phi₀, LSRI, xi, lambdaU. The SRI coefficient eta = 1/12 is derived from the Taylor expansion of the hypercubic lattice stencil (Paper I) ; the coarse-graining analysis (Paper III, DOI: 10. 5281/zenodo. 19626136) provides an independent consistency check. At leading order eta enters only through the combination eta LSRI², so it is convenient to define an effective regulator length LSRIₑff = sqrt (eta) LSRI. In the minimalist count used in this paper, LSRI remains one of the four fundamental continuous inputs (Paper I), while eta is a derived O (1) coefficient fixed by lattice geometry; practical EFT predictions at this order depend primarily on LSRIₑff rather than on (eta, LSRI) separately. The dimensionless coefficients kappaₕbar and kappaG relating U-field parameters to laboratory constants are fixed by operational calibration. We perform dimensional analysis to verify internal consistency and compare the USSFT parameter count (4 fundamental) to the Standard Model (around 19 to 26) and General Relativity (2). This minimal parameter set is a defining feature of the leading-order truncation: if matching observations at the same order requires additional continuously tuned parameters, the minimalist claim fails. Status: (B) derived parameter inventory under stated EFT truncation. This is Paper V in the 18-paper USSFT technical series; for a conceptual overview, see Paper 0 (DOI: 10. 5281/zenodo. 17852167, published in Int. J. Quantum Found. 12 (2), 667-718, 2026).

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