Architecture of the SPSP–SSC Bridge

What this page is: a compact, rigorous map of the bridge layered architecture (foundation → local physics → observables), with clear equations on the left and intuitive analogies on the right. The bridge is an elliptic constraint that locks exterior predictions to GR+SM and embeds QM via a fixed projector. No new radiative degrees of freedom; novelty is confined to bounded boundary terms and interior diagnostics (falsifiable).

Layer I — Foundational BridgeElliptic constraint (non-radiative)Dirac/ADM constraints intact Layer II — Local PhysicsSorting dynamics (screened)No extra propagating DOF Layer III — ObservablesGR geodesics + SM interactionsQM via fixed projector Bounded boundary termsInteriors / echo diagnostics Falsifiable frontier
Layer I — Foundation

Mathematical Conduit (Elliptic Constraint + Lock)

Validated-regime action (schematic):

\[ S=\!\int d^4x\,\sqrt{-g}\Big[\tfrac{M_P^2}{2}R+\mathcal L_{\rm SM}(\psi,g)\;-\;\Phi\,(\rho-\varepsilon)\;+\;\text{screened/boundary}\Big]. \]

Bridge constraint (elliptic, non-radiative):

\[ \mathcal C:\quad \nabla^2\Phi = 4\pi G\,\rho \quad\text{(validated Poisson-like balance)}. \]

Metric equations in the lock:

\[ G_{\mu\nu} = 8\pi G\,T_{\mu\nu},\qquad \text{(no extra propagating DOF; TT modes only)}. \]

Hamiltonian picture: primary constraint \(\pi_\Phi\!\approx\!0\); Dirac/ADM algebra intact; \(T^{(\Phi)}_{\mu\nu}\) contributes only constrained/boundary terms.

Analogy (for intuition)

Differential / escrow gear: Layer I is like a rigid, lossless mechanical differential that couples two shafts: it does not “add power” nor “translate language”; it enforces a relation so both ends remain consistent under load.

Not an interaction, a condition: The bridge is a boundary/constraint structure — more like perfect grounding or clamping than a new field. Electromagnetic or centrifugal effects we notice are local phenomena compatible with, not caused by, the constraint.

Layer II — Local Physics

Sorting Dynamics (Screened; No New Radiation)

Local sorting equation (validated regime):

\[ \nabla^2\Phi = \alpha\big(\rho-\varepsilon\big) + \delta\mathcal P,\qquad \delta\mathcal P\rightarrow 0 \ \text{(labs/Solar System)}. \]

Here \(\Phi\) acts as a projector-like potential that enforces balance; in validated regimes this reduces to the Poisson-like constraint above. No scalar dipole channel, no extra polarizations.

Analogy (local manifestation)

Think of \(\Phi\) as a perfectly tuned jig. Forces (centrifugal, EM, pressure) act locally, but the jig ensures the assembly stays within tolerance. Local effects can be complex, yet the global lock guarantees the exterior looks exactly like GR+SM.

Layer III — Observables

Exterior Predictions (GR + SM; QM via Fixed Projector)

Geodesics & light-time (unchanged):

  • Light bending: \(\Delta\phi = \dfrac{4GM}{bc^2}\)
  • Shapiro delay: \(\Delta t \simeq \dfrac{2GM}{c^3}\ln \dfrac{4r_E r_R}{b^2}\)
  • Weak-lensing SIS: \(\theta_E = 4\pi \dfrac{\sigma_v^2}{c^2}\dfrac{D_{ds}}{D_s}\)

Quantum embedding: A fixed projector \(P\) from the bridge enforces \(P\rho P=\rho\); otherwise standard Hilbert space, Born rule, CHSH violations, and no-signalling are preserved.

Analogy (instrument panel)

Outside the “engine bay,” the dials behave exactly as the factory spec (GR, SM, QM). Any deviation (e.g., scalar dipole radiation) would be an immediate fault light — and would falsify the bridge.

What’s novel (and testable)?

  • Strict absence of dipole radiation (no \(-1\)PN term): \(|\mathcal F_{\rm dip}|/\mathcal F_{\rm quad} < 10^{-3}\) bound.
  • Echo-like interior diagnostics bounded by \(\Delta B_{\rm norm}\approx 0.02\) (projection-wall universality).
  • Ultra-large-scale projections (if any) confined to boundary/overlap structure; standard \(\Lambda\)CDM elsewhere.

Everything else remains exactly GR+SM+QM where tested.

Intuition

Consolidated Analogies (kept separate from math)

Escrow / conduit: The bridge is a rule that binds two accounts; nothing is “exchanged,” but balances are enforced. That’s Layer I.

Differential gear: It rigidly relates outputs without adding power; it preserves consistency under load. That’s the lock to GR.

Hand–table charge (cautionary): For intuition only: two hands on a grounded table won’t create current by themselves — the ground condition enforces potentials. Likewise, the bridge enforces relations; local physics supplies forces/flows.

These are images to build intuition; the formal content is the elliptic constraint + GR field equations + fixed projector for QM.