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

This paper develops a single coherent framework, SPSP-SSC, in which the observable world is a local projection of a boundaryless quantum sphere. Gravity is described not as a separate substance but as the phenomenon induced by the propagation of the base’s intrinsic-resolution state across the vacuum. The vacuum itself is the intrinsic resolution field updating at the universal speed of light. A non-propagating constraint field called Phi enforces balance on each slice and never radiates. Resolution is implemented by a projection kernel W, so that observation, interaction, and resolution are the same process. From these assumptions the paper derives the Einstein–Hilbert action with the correct boundary term, the Einstein field equations, exactly two tensor polarizations, and standard weak-field results including the full first post-Newtonian metric, Shapiro delay, and quadrupole gravitational-wave emission with no dipole channel. On the particle side it selects the Standard Model gauge structure SU(3) times SU(2) times U(1), fixes the hypercharges by anomaly cancellation, and presents the complete renormalizable Standard Model Lagrangian. Yukawa matrices are obtained from kernel-weighted overlaps rather than assumed textures, and the neutrino sector allows both Dirac and Majorana (Type-I seesaw) masses. A key addition is a Phi–topology feedback mechanism: the Phi constraint source is extended by the gauge-invariant topological density. Varying the action yields an elliptic equation whose neutrality sum rule (slice-wise Gauss law with screened boundary data) forces the coarse-grained net topological charge to vanish, dynamically neutralizing the strong-CP angle without introducing a propagating axion. An overall anomalous axial rephasing then removes the phase of the quark mass matrix, giving a vanishing physical strong-CP parameter while preserving the CKM source of weak CP violation. Integrating out Phi produces a CP-even nonlocal screening term that is instantaneous on each slice; varying with respect to gluons introduces sources proportional to the derivative of Phi times the Chern–Simons current, which are confined to screened regions. Thus long-range CP-odd observables such as electric dipole moments are unaffected, while local instanton and anomaly physics persists. The framework also sets up background-field and BRST quantization with the constraint implemented as a delta functional, ensuring that the scalar field does not propagate; the induced nonlocal screening term is explicitly derived and remains BRST-compatible. A worked one-loop example for the hypercharge coupling is included, while a full renormalization analysis is left to future work. Cosmologically, a small homogeneous residual of the intrinsic-resolution field behaves as an effective cosmological constant, scaling with the Hubble parameter squared, providing a concrete observational target.