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

This work introduces SPSP-SSC, a framework where the observable universe is a local projection of a boundaryless quantum sphere. A projection kernel unifies observation, interaction, and resolution. Gravity appears as the propagation of the resolution state through the vacuum, while a non-propagating constraint field (Phi) enforces balance on each slice without radiating. From these assumptions we recover general relativity with the correct action and boundary term, two tensor polarizations, and the standard weak-field tests: first post-Newtonian corrections, Shapiro delay, and quadrupole gravitational waves with no dipole. On the particle side the construction yields the Standard Model gauge group, anomaly-fixed hypercharges, the full renormalizable Lagrangian, kernel-generated Yukawa structures, and a neutrino sector that allows both Dirac and Type-I seesaw masses. A central result is the Phi–topology feedback mechanism, which cancels net topological charge slice by slice and removes the strong-CP problem without an axion. The physical strong-CP parameter vanishes while CKM CP violation remains. Integrating out Phi gives a CP-even nonlocal screening term, confined to screened regions so that long-range CP-odd observables remain unaffected. We also derive the full two-loop renormalization group equations for the Standard Model in compact form, and show how they are consistently deformed by projector multipliers that change the weights of Yukawa traces and U(1) gauge contributions. This allows controlled scans of vacuum stability up to the Planck scale. Quantization is performed with background-field and BRST methods, with Phi acting only as a constraint. A small homogeneous residual of the resolution field acts as an effective cosmological constant scaling with the Hubble rate. Finally, two projection rules are proposed: ANG-POS, which ties the Higgs to a global angular mode and suppresses its quadratic sensitivity, and ZETA-POS, which connects to a critical-line symmetry explaining global theta alignment, local Phi enforcement, and antiparticle pairing.