strong_field_one_statement
plain-language theorem explainer
Packages the Track 6.C structural discriminator into one conjunction: the RS strong-field deviation φ^{-44} is strictly positive, the distinct-from-GR proposition holds, and the master-theorem hypothesis StrongFieldTestsDistinctFromGR is inhabited. Gravity and quantum-gravity auditors cite it to retire that hypothesis from the conditional master theorem. The proof is a three-component term assembly of existing positivity, proposition, and witness results.
Claim. The following three claims hold simultaneously: $0 < \varphi^{-44}$; the structural discriminator asserting that the RS strong-field deviation is strictly positive (hence distinct from pure GR's zero baseline) is true; and the master-theorem hypothesis type "RS strong-field tests are distinct from pure GR" is inhabited.
background
Track 6.C of the quantum-gravity master plan asks for strong-field discriminators against pure GR (S-stars near Sgr A*, EHT shadow, Cassini Shapiro delay, etc.). This module ships only the algebraic half: a single φ-rational scale that is forced nonzero, not the channel-by-channel observables.
The deviation signature is defined as $\varphi^{-44}$, the same rung-44 forcing that appears as the baryogenesis ratio $\eta_B = \varphi^{-44}$ on the phi-rung ladder. Pure GR predicts zero structural deviation at this level, so positivity alone is the discriminator proposition.
Upstream, the master theorem exposes a structure StrongFieldTestsDistinctFromGR whose field is a Prop plus a proof that it holds. A local witness fills that structure by pointing the Prop at the positivity statement and supplying the positivity proof. The one-statement theorem simply conjoins positivity, the discriminator Prop, and nonemptiness of that structure.
proof idea
Term-mode triple constructor. First component is the positivity theorem for $\varphi^{-44}$ (unfold the definition and apply positivity of integer powers of $\varphi > 0$). Second component is the discriminator proposition theorem, itself a one-line re-export of that positivity fact. Third component is Nonempty introduced by packing the local witness that inhabits the master-theorem structure (Prop field set to the discriminator, holds field set to its proof). No new algebra is performed here.
why it matters
Closes the structural form of Track 6.C in the quantum-gravity master plan: RS carries a positive $\varphi^{-44}$ strong-field signature while pure GR does not. The witness retires StrongFieldTestsDistinctFromGR from the hypothesis list of the conditional quantum-gravity master theorem, converting an open structural obligation into a proved input.
The rung-44 scale ties gravity's strong-field discriminator to the same phi-ladder forcing used for baryogenesis ($\eta_B = \varphi^{-44}$), so the claim sits inside the broader RS constants and ladder program rather than as an ad-hoc gravity patch. Empirical match to EHT, GRAVITY, and Cassini datasets is explicitly left as a separate falsifier-register obligation; this declaration does not claim observational confirmation, only algebraic distinctness and hypothesis inhabitation. No downstream users are recorded yet; the intended consumer is the master theorem assembly.
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