SPSP-SSC-XRQ: GR and SM from SSC Axioms

This work introduces SPSP–SSC, a closed axiom system in which the observable world is a local projection of a boundaryless quantum sphere. A projection kernel W(x,σ) unifies observation, interaction, and resolution. Gravity appears as propagation of an intrinsic resolution state through the vacuum; a non-propagating constraint field Phi enforces slice-wise balance and does not radiate. From these axioms we recover General Relativity with the correct Einstein–Hilbert action and Gibbons–Hawking–York boundary term, two tensor polarizations, and standard weak-field tests (1PN dynamics, Shapiro delay, quadrupole radiation with no dipole). On the particle side we obtain the Standard Model gauge group SU(3) × SU(2) × U(1), anomaly-fixed hypercharges, the full renormalizable Lagrangian, and kernel-generated Yukawa matrices (derived from W, not assumed textures). The neutrino sector accommodates Dirac or Type-I seesaw masses. A central result is a Phi–topology feedback that cancels net topological charge slice-by-slice, dynamically removing the strong-CP angle (theta-bar = 0) while preserving CKM CP violation. Integrating out Phi yields a CP-even nonlocal screening term confined to screened regions, leaving long-range CP-odd observables unaffected. We present the full two-loop Standard Model renormalization group equations in compact form and show consistent projector deformations that rescale Yukawa traces and the U(1) sector. This enables controlled vacuum-stability scans up to 10^19 GeV. In a representative projector-stable point (Mg, MY2, MY4) = (1.90, 0.10, 0.10), the Higgs quartic remains positive with lambda(10^16 GeV) ≈ 0.133 and lambda(10^19 GeV) ≈ 0.144, and no g1 Landau pole; stability persists under percent-level projector variations and standard weak-scale threshold shifts. Quantization is performed via background-field and BRST methods with Phi acting only as a constraint. A small homogeneous residual of the resolution field behaves as an effective cosmological constant scaling as Lambda = alpha H^2 / c^2 (toy alpha = 2). We also propose two projector rules — ANG-POS (Higgs linked to a global angular mode, softening quadratic sensitivity) and ZETA-POS (critical-line symmetry connecting global theta alignment, local Phi enforcement, and antiparticle pairing). All derivations are step-by-step; we provide a reproducible pipeline (two-loop integration, uncertainty scans, robustness maps) and ancillary CSVs/figures corresponding to the results reported.