The Sharipov Smooth Quartic-Core Metric: An Action-Based Regular Black-Hole Model and a General-Relativistic Validation Framework

We propose a smooth modification of the original Sharipov spherical ansatz and study it as a mathematical and physical model of a regular black hole. The proposed lapse is A_sc(r) = 1 - R_s r^2 / (r^4 + a^4)^(3/4), with a = gamma R_s. It is asymptotically Schwarzschild and has an even central expansion. In Cartesian coordinates the local metric coefficients are real analytic at the center. The background is generated exactly by Einstein gravity coupled to a reconstructed, purely magnetic nonlinear-electrodynamics source. The source has finite central density, p_r = -rho, and a specified Lagrangian L(F). This resolves the background-level action, source, and local smoothness questions. Rotation is not imposed through the singular Kerr geometry: it is formulated through a coupled slow-rotation Einstein--electrodynamics system for the frame-dragging function h(r) and the electromagnetic response omega(r). This supplies the governing field-equation law and the mathematical stability criteria for the rotating branch. The reconstructed one-invariant NED source has an unusual strong-field constitutive regime in the core. In particular, the combination L_F + 2F L_FF changes sign for r < (6/5)^(1/4) a. This sign change does not alter the finite density, finite curvature, or Cartesian analyticity of the SSQC background; it identifies the domain in which the effective matter description must be enlarged. A parity-even two-invariant class L(F, P^2) is therefore adopted as the appropriate framework for causal perturbative dynamics. The paper organizes the mathematical and physical checks required by general relativity, nonlinear electrodynamics, horizon geometry, perturbation theory, and observational forward modelling. The public calibrated 2017 M87 EHT data release is identified as the reference data product for the visibility-level comparison protocol. The model is presented as a proposed new approach to regular black holes, not as a claim of a complete fundamental theory.