The Scretching–Planck Scale in Curved Spacetime and QCD: Covariant Dynamics, Conditional Scalar Extensions, and Quantitative Nuclear Tests

Research Description: The Scretching–Planck Framework and Proposed Scalar Extensions This research presents a systematic theoretical and computational investigation of the Scretching–Planck (SP) framework, examining its mathematical foundations, connections to established quantum field theory, and potential implications for particle physics and nuclear interactions at the characteristic SP energy scale of 256.325 MeV. The study distinguishes the original SP mass–charge reparameterization and density–phase action from two independently proposed dynamical extensions: a Higgs-mixed scalar field and a CP-even scalar coupled to gluons. The nonrelativistic SP action reproduces the Schrödinger equation, while a proposed four-dimensional curved-spacetime extension recovers the minimally coupled Klein–Gordon equation, with an independent curvature-coupling parameter. Gauge-covariant Noether currents establish probability and electric-charge conservation, while energy–momentum conservation follows from spacetime symmetries and the field equations. These results do not establish rest mass as a separate conserved U(1) charge. For the assumed minimal Higgs-portal extension, the calculated contribution to the electron anomalous magnetic moment is [\Delta a_e=2.44316\times10^{-18}\sin^2\theta.] At the benchmark mixing strength (\sin^2\theta=10^{-8}), the scalar has a calculated leptonic-only proper decay length of 57.94 meters. Comparison with published NA62 HEPData exclusion coordinates places this benchmark within the experimentally excluded region for the invisible-decay channel at 90% confidence level. An independent scalar–gluon extension produces an effective scalar–nucleon coupling of (g_{sNN}=0.24403c_G) and an attractive Yukawa interaction between nucleons. First-order calculations using three Nijmegen deuteron wavefunctions predict binding-energy shifts ranging from (-55.76c_G^2) to (-62.46c_G^2) keV. An independent Argonne V18 coupled-channel calculation yields (-57.04c_G^2) keV, demonstrating numerical consistency across the investigated nuclear models. Additional nucleon–nucleon phase-shift calculations and controlled short-range interaction refits reveal substantial degeneracy between the proposed finite-range scalar force and conventional nuclear interactions. Consequently, the available calculations do not establish a statistically calibrated constraint on the gluonic coupling (c_G). The principal contribution of this research is a clearly defined, testable separation between the established mathematical structure of the Scretching–Planck framework and hypothetical scalar interactions requiring independent experimental validation. Neither scalar coupling is derived from the original SP action. The results identify measurable theoretical consequences, demonstrate the importance of nuclear-model uncertainties, and establish a foundation for further investigations using precision particle-physics measurements, nuclear scattering experiments, and computational modeling. The work provides a framework for evaluating the efficacy, physical utility, and potential AI-assisted applications of Scretching–Planck equations while maintaining explicit distinctions between mathematical equivalence, model-dependent predictions, and experimentally validated discoveries.