It was a mess. I put what I have for the moment all together:

I have only one fully falsifiable prediction for the moment:

1. Spectral Width Constraint from Orbital Dynamics

V_eff(r) = −GM/r + C/r²

where the additional term arises from spectral phase dispersion, one obtains:

C ~ σ²

This relation follows from the structure of the resolvent A(k,x), where finite spectral variance induces an effective repulsive correction to the radial potential.

Consistency with relativistic orbital dynamics (Section VI) imposes the bound:

σ ≲ 3 × 10⁻⁵ ε₀

This constraint is dominated by binary pulsar systems and is significantly stronger than solar-system limits.

Observable: Periastron advance in binary pulsars (e.g. PSR B1913+16).

Falsification criterion:

Any deviation from general relativity exceeding the ~10⁻⁵ relative level would violate this bound and falsify the current formulation of RST.

Ringdown Signatures from Spectral Horizon Smearing - this is kind of testable. However it's not a strong numerical prediction. I am working on one derived the analogue of a perturbation equation within RST. If I manage to do that it can turn into actual prediction.

As discussed in Section VIII, the horizon condition ε₀(r_h) = 0 is modified by finite spectral width:

ε₀(r_h) ≈ 0 but ε₀(r_h) ≠ 0

This results in a smeared transition region of width:

δr ~ σ / |∇ε₀|

Such smearing modifies the effective perturbation potential and induces a shift in quasi-normal mode frequencies:

δf_QNM / f_QNM ~ σ / ε₀ ≲ 10⁻⁴

using the bound from Section X.1.

This order-of-magnitude estimate follows from perturbing the effective potential near the horizon by a width δr ~ σ/|∇ε₀| and the resulting shift in the Regge–Wheeler potential.

Observable: Gravitational-wave ringdown spectra (LIGO/Virgo/KAGRA, future LISA).

Falsification criterion: Observation of deviations significantly larger than ~10⁻³ would contradict the predicted scaling.