USSFT Paper VI: Emergent Constants. The Planck Scale, Gravitational Coupling, and Quantum Action Scale from U-Field Parameters

This paper establishes the mapping between the fundamental U-field parameters {Phi_0, L_SRI, xi, lambda_U} (Paper V, DOI: 10.5281/zenodo.19626955) and the laboratory constants hbar, G, and c. In the Unified Space-Time and Scale-Dependent Field Theory (USSFT), these constants are not fundamental; they are emergent coefficients governing how the U-field resolves constraints at different scales. Working with the effective combination L_SRI_eff = sqrt(eta) L_SRI (where eta = 1/12 is derived from lattice geometry), we express all results through an effective U-field action scale hbar_eff (defined in the EFT normalization and connected to laboratory hbar by a one-time calibration). Within the EFT framework established in Papers I-V, we show that: (1) the effective U-field action scale hbar_eff scales as Phi_0^2 L_SRI_eff^2, with the numerical coefficient fixed by calibration; (2) Newton's constant G scales as 1/(xi Phi_0^2), following from the xi R Phi^2 coupling in the Lagrangian; and (3) the EFT description employs a universal limiting signal velocity c as part of its Lorentz-covariant structure (Paper IV addresses its dynamical preservation). The central result is the Planck-scale relation: combining these relations yields ell_P = L_SRI_eff sqrt(kappa_hbar kappa_G / (8 pi xi)). Interpreting this as ell_P comparable to L_SRI_eff is conditional on xi, kappa_hbar, kappa_G being O(1) within the minimal EFT setup. This same relation is independently derived in Paper XV (DOI: 10.5281/zenodo.19691421) from black hole entropy matching, providing a non-trivial consistency check. We explicitly distinguish scaling relations (which follow from dimensional analysis and Lagrangian structure) from numerical coefficients (which require calibration or future calculation). Status: (B) derived emergent-constants framework under stated EFT assumptions, with explicit O(1) calibration dependencies. This is Paper VI 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).