Technical FAQ — SPSP–SSC
Short answers to common expert questions about the Single Point Super Projection – Single Sphere Cosmology (SPSP–SSC) formalism.
One-line summary. SPSP–SSC reproduces GR+SM+QM exactly in validated regimes and introduces a single, non-radiative elliptic constraint that is active only at projection boundaries (e.g., horizons). This yields hard falsifiability (no scalar dipole radiation, GR phasing, ΛCDM linear cosmology) while keeping the local effective theory identical to standard physics.
Core Structure
Q1. What is the action? What’s new?
The validated-regime action is
New piece: the sorting potential \(\Phi\) appears without a kinetic term. Variation gives an elliptic constraint; no new propagating fields are introduced.
Q2. What equation does the \(\Phi\) variation impose?
Elliptic (Poisson-type), slice-wise. No wave operator, hence non-radiative.
Q3. Does this add any propagating degrees of freedom?
No. The primary constraint \(\pi_\Phi\!\approx\!0\) is preserved by a secondary elliptic constraint; the Dirac algebra closes as in GR. Only the usual 2 TT graviton modes propagate.
Effective Theory & Corrections
Q4. Does SPSP–SSC generate higher-derivative operators at low energy?
No. In validated regimes, the local Lagrangian is exactly Einstein–Hilbert + SM. There is no tower of curvature-squared (e.g. \(R^2\), \(R_{\mu\nu}R^{\mu\nu}\)) or higher-derivative matter terms induced by \(\Phi\), because \(\Phi\) has no kinetic term and no radiative dynamics. Novelty appears only as bounded boundary diagnostics (e.g., horizon consistency conditions), not as local EFT operators.
Q5. How does this compare to EFT gravity?
EFT gravity: GR + suppressed higher-curvature operators. SPSP–SSC: exact GR propagation locally, plus a global elliptic constraint active at boundaries. Orthogonal approaches; SPSP–SSC does not compete via a higher-derivative expansion and thus avoids additional low-energy Wilson coefficients.
Radiation & Gravitational Waves
Q6. Is there scalar dipole radiation?
No. Because \(\Phi\) is elliptic, there is no radiative scalar channel. Binary energy loss is purely GR quadrupole (two TT polarizations at \(c\)).
Q7. What are the falsification bounds?
- Pulsars: fractional excess \(\Delta_{\rm dip}\equiv(\dot P_{\rm obs}-\dot P_{\rm GR})/|\dot P_{\rm GR}|\), \(\ \boxed{|\Delta_{\rm dip}|<10^{-3}}\) (post-systematics).
- GW phasing: −1PN coefficient \(\beta_{-2}\) in \(\Psi(f)=\Psi_{\rm GR}(f)+\beta_{-2}f^{-7/3}+\cdots\), \(\ \boxed{|\beta_{-2}|<\beta_{\rm thr}}\) where \(\beta_{\rm thr}\) maps to \(|\mathcal F_{\rm dip}|/\mathcal F_{\rm quad}<10^{-3}\).
Q8. GW speed and polarizations?
Identical to GR in validated regimes: luminal propagation; only + and × polarizations.
Cosmology
Q9. Background and linear perturbations?
ΛCDM-equivalent background \(H_{\rm eff}\) and GR-identical linear SVT system in the validated window. No linear anisotropic stress from \(\Phi\); \(\Phi_g=\Psi\).
Q10. Where might deviations show up?
Only at ultra-large scales or in horizon diagnostics via bounded boundary terms (e.g., echo-like features). These are explicitly falsifiable and do not affect local EFT predictions.
Quantum Mechanics & Information
Q11. Does the model preserve standard QM (Born rule, entanglement, CHSH)?
Yes. The SPS is a qubit in a Hilbert space with a fixed projector \(P\) (elliptic superselection): \(P\rho P=\rho\). Born rule, unitary evolution on the physical subspace, entanglement, and CHSH violations are exactly as in QM; no signalling.
Q12. Do we need to quantize the metric?
No. The exterior dynamics are GR+SM; the lock-in arises from the elliptic constraint projector. This avoids introducing new quantum gravitational DOF in validated regimes.
Consistency, Causality, Conservation
Q13. Is causality respected?
Yes. The propagating sector is GR+SM+QM. The \(\Phi\) constraint is elliptic (instantaneous balance), not a superluminal signal. No additional light cones are introduced.
Q14. Stress–energy conservation?
Yes. Diffeomorphism invariance and the constraint imply \(\nabla^\mu T^{\rm tot}_{\mu\nu}=0\). In validated regimes this reduces to the usual continuity/Euler equations.
Black Holes & Boundaries
Q15. What changes near horizons?
Exterior geodesics, lensing, and ringdown match GR. Novelty is confined to bounded boundary diagnostics (e.g., interior recycling kernels) that can produce tiny, testable echo-like correlations without modifying the exterior wave equation.
Q16. Are boundary effects tunable to fit data?
No arbitrary tuning is needed: the diagnostics are bounded (e.g., normalized correction \(\Delta B_{\rm norm}\!\approx\!0.02\)) and serve as falsifiable predictions, not free parameters for curve-fitting.
Mathematical Outlook
Q17. Is there a link to spectral or number-theoretic structures?
Yes, at the conceptual level: recursion-wall invariants are robust under zeta-zero “scrambling,” suggesting independence from numerology and pointing to a deeper spectral stability (useful for proofs, not required for predictions).
Q18. Does this imply new low-energy constants?
No. Since there is no higher-derivative tower, there are no additional Wilson coefficients at low energy. The lock-in is structural, not parametric.
Implementation Note
Clarity statement. All exterior predictions use unmodified GR geodesics and SM/QM dynamics; SPSP–SSC effects appear only through bounded elliptic boundary diagnostics. This preserves every validated prediction while keeping novelty sharply testable.