A) What differs, and how to falsify it (clean, testable claims)

Scope first: By construction, SPSP–SSC matches GR + SM in screened/validated regimes (the paper’s stated domain). Differences can only show up when either (i) screening is imperfect, or (ii) the boundary-value setup for the elliptic sorting field Φ is not satisfied (e.g., during strongly time-dependent horizons). That makes the theory easy to falsify:

1) No long-range extra force, no dipole radiation

Prediction: Because Φ is a non-propagating elliptic constraint (no kinetic term), there is no fifth-force mediator and no −1PN dipole radiation in binaries. Leading radiation remains quadrupolar (GR value), and GWs are luminal in screened domains.

Falsify by:

• Detecting a long-range fifth force or composition-dependent acceleration (violates A3/A5).
• Seeing a dipole term in compact-binary phasing bigger than the paper’s bound (target: dipole <10^-3 of the GR quadrupole).
• Measuring GW speed ≠ c in the local universe.

2) Exterior equals GR—unless the boundary value problem fails

Prediction: If sources are compactly supported and Φ has homogeneous data on the enclosing surface (A6′), then Φ=0 in the exterior and the outside metric is just GR. Any deviation must come from a failure of those exterior conditions.

Falsify by:

• Observing repeatable, exterior gravity anomalies around isolated bodies (beyond PPN with γ=β=1) without changing the boundary data (would break Theorem T6).

3) Cosmology: “almost-GR” pattern of deviations

Prediction (screened linear scales): No gravitational slip: Φ_Newton−Ψ_Newton=0. Growth, ISW, lensing match ΛCDM up to O(ε_scr).

Where differences could appear: On horizon-scale / unscreened domains, deviations scale with a small screening parameter ε_scr. The pattern is constrained (no new wave mode; any deviation looks like a static constraint leakage, not a propagating scalar).

Falsify by:

• Measuring a percent-level slip on linear scales that cannot be absorbed into ε_scr ≪ 1.
• Detecting GW amplitude/“friction” anomalies (effective Planck-mass running) in the late universe—disallowed here.

4) Strong-field dynamics near changing horizons

Prediction: During rapid horizon growth, if A6′ momentarily fails, there could be tiny, transient near-zone imprints (elliptic, non-radiative) that only modify initial data of ringdown—not the QNM spectrum. No extra polarizations.

Falsify by:

• Robust detection of non-tensor GW polarizations or a new QNM family inconsistent with GR’s spectrum.

5) Particle physics at low energy is exactly the SM

Prediction: Low-energy gauge group SU(3)×SU(2)×U(1) with SM hypercharges (derived via anomaly constraints), one Higgs doublet, and standard one-loop β functions. No light Z′, no extra chiral matter.

Falsify by:

• Discovering a new light gauge boson or anomaly-inducing fermion that cannot be decoupled while keeping the stated assumptions (minimality, anomalies canceled per generation).
• Finding running of couplings at one-loop that contradicts the SM coefficients.

B) Public “research notes” (what was used to get the claims above)

RN-1 (Setup & core equations)

Action S = ∫√-g [^R⁄_16πG + L_m − Φ(ρ−ε)] with GHY boundary term.

Vary g_μν: G_μν = 8πG T_μν in screened domains (A3 fixes the same G).

Vary Φ: ∇²Φ = 4πG(ρ−ε) (no (∇Φ)² ⇒ non-propagating).

Key: Φ is a constraint, not a field with its own wave equation.

RN-2 (Degrees of freedom)

ADM analysis: primary/secondary constraints close; Dirac algebra intact; 2 tensor DOF, no scalar mode.

→ No dipole radiation channel and no fifth force.

RN-3 (Exterior GR equivalence)

With A6′ (compact support + homogeneous boundary data on an enclosing surface), maximum principle for Laplace ⇒ Φ=0 outside.

→ Exterior = GR unless A6′ fails.

RN-4 (PPN & GWs)

Harmonic-gauge linearization: GR propagator; PPN parameters γ=β=1; GW flux pure quadrupole; GW speed = c in screened domains.

RN-5 (Cosmology)

SVT: no slip in the screened limit (Φ_N−Ψ_N=0); any deviation is O(ε_scr) and elliptic-patterned (no extra propagating scalar).

→ Distinguishes this from many modified-gravity models that predict slip or GW damping.

RN-6 (Where differences could live)

Imperfect screening: define ε_scr ≡ sup|δP|/Λ⁴. Any deviation on a given domain is at most O(ε_scr), with no new wave pole.

Boundary failures (time-dependent horizons): only initial-data tweaks to ringdown; spectrum unchanged.

RN-7 (SM sector)

Assumptions (compact YM factors + one U(1), minimal Higgs doublet, anomaly cancellation) ⇒ unique SM hypercharges and standard one-loop β’s.

→ Any confirmed low-energy extension (light Z′, extra chiral gen) breaks the minimality/anomaly setup used here.

RN-8 (Falsifier matrix—quick mapping)

• See dipole GW radiation / extra polarizations / GW speed ≠ c → violates non-propagating Φ + 2-DOF result.
• Measure PPN γ,β≠1 in a screened environment → contradicts PPN derivation.
• Detect cosmological slip on linear scales beyond an O(ε_scr) envelope → inconsistent with screened SVT.
• Find low-energy non-SM gauge content → contradicts the low-energy uniqueness proof.

RN-9 (What would not falsify it)

Any anomaly confined to an unscreened, horizon-scale regime that can be quantitatively fit by a small ε_scr and preserves the “no new propagator” character would be a signal, not a refutation.

TL;DR: In its stated domain, SPSP–SSC deliberately reproduces GR + SM. It differs from many alternatives by predicting no extra mode, no slip, no GW damping—and gives a tight falsifier list: any fifth force, dipole radiation, non-luminal GWs, PPN γ,β≠1, linear-scale slip, or new low-energy gauge content would rule it out under its assumptions. The “research notes” above show how each claim follows from the constraint nature of Φ, the boundary-value result, the ADM DOF count, and the anomaly-based SM construction.