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

This paper presents SPSP-SSC: the observable world is a local projection of a boundaryless quantum sphere. Gravity is the propagation of the intrinsic-resolution state through vacuum; the vacuum is that resolution field updating at light speed. A non-propagating constraint field (Phi) enforces slice-wise balance and never radiates. A projection kernel W implements resolution, so observation, interaction, and resolution are the same process. From these assumptions we recover the Einstein–Hilbert action with the correct boundary term, the Einstein equations with two tensor modes, and standard weak-field tests (first post-Newtonian metric, Shapiro delay, quadrupole gravitational waves with no dipole). On the particle side we obtain the Standard Model gauge group and anomaly-fixed hypercharges, the full renormalizable Lagrangian, kernel-derived Yukawa matrices, and a neutrino sector allowing Dirac or Type-I seesaw masses. A key update is Phi–topology feedback: extending the Phi constraint by the gauge-invariant topological density leads to an elliptic equation whose neutrality sum rule (slice-wise Gauss law with screened boundaries) cancels the coarse-grained net topological charge (with ξ a dimensionless coupling). The strong-CP angle is thereby neutralized without an axion; an overall anomalous axial rephasing removes the quark-mass phase, so the physical strong-CP parameter vanishes while CKM CP remains. Integrating out Phi yields a CP-even, instantaneous nonlocal screening term; variation with respect to gluons introduces sources proportional to the derivative of Phi times the Chern–Simons current, confined to screened regions—leaving long-range CP-odd observables (e.g., electric dipole moments) unaffected while local instanton and anomaly physics persist. We use background-field and BRST quantization with the Phi constraint implemented as a delta functional, ensuring no Phi propagator; the induced screening term is derived and remains BRST-compatible. Cosmologically, a small homogeneous residual of the resolution field behaves as an effective cosmological constant that scales with the Hubble parameter squared. Finally, we propose an angular-positioning rule at projection (ANG–POS): the kernel preserves a single global angular mode and assigns it to the Higgs, locking that degree of freedom and suppressing the leading hard sensitivity of the Higgs mass—suggesting a geometric route to electroweak stability without new partner particles. We also give a zeta-aligned substrate hypothesis (ZETA–POS): the kernel inherits a “critical line” symmetry that provides the analytic origin of both global θ alignment (neutralized) and local Φ enforcement, while substrate pairing explains antiparticle redundancy upon annihilation.