strongFieldStructuralCert_inhabited
plain-language theorem explainer
The strong-field structural certificate is inhabited: RS carries a strictly positive φ^{-44} deviation from pure GR, the structural discriminator holds, and the master-theorem hypothesis that strong-field tests differ from GR is witnessed. Gravity and Track-6 verification authors cite this to retire that open hypothesis. Proof is a one-line term packaging the existing certificate instance.
Claim. There exists a strong-field structural certificate: the RS strong-field deviation $\varphi^{-44}$ is strictly positive, the structural discriminator proposition (RS deviation positive, pure GR zero) holds, and the master-theorem hypothesis that RS strong-field test predictions differ from pure GR is inhabited by a concrete witness.
background
Track 6.C of the quantum-gravity master plan asks whether RS strong-field predictions (S-stars near Sgr A*, EHT shadow, Cassini Shapiro delay) differ from pure GR. This module ships only the algebraic discriminator, not channel-by-channel physics.
The RS signature is the rung-44 scale $\varphi^{-44}$ (same forcing that yields $\eta_B = \varphi^{-44}$ on the phi-rung ladder). Pure GR predicts zero deviation on that structural axis. The master theorem in Gravity.MasterTheorem still lists a hypothesis structure whose sole content is a proposition that RS strong-field tests are distinct from GR, plus a proof that the proposition holds.
The certificate structure packages three facts: positivity of $\varphi^{-44}$, the discriminator proposition, and an inhabitant of that master-theorem hypothesis (via a witness that RS and GR disagree on the structural strong-field axis).
proof idea
One-line term proof. The certificate instance already assembles positivity of the $\varphi^{-44}$ deviation, the discriminator proposition, and the master-hypothesis witness. The theorem simply wraps that instance in the Nonempty constructor, so existence of the certificate follows immediately from the prior construction.
why it matters
Closes the structural half of Track 6.C: the master-theorem input that RS strong-field tests differ from pure GR is no longer an open hypothesis; it is inhabited. Downstream, the Track-6 falsifier-sensitivity certificate consumes this inhabitation as part of the discriminator matrix and rival-row coverage for fork F.
Framework link: the deviation scale is the same rung-44 $\varphi$-power that appears in the cosmology ladder for $\eta_B$. Empirical match to EHT, GRAVITY, and Cassini remains a separate falsifier-register obligation; this result only forces a nonzero structural gap from GR.
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