hypothesis
plain-language theorem explainer
Structural discriminator for RS strong-field tests: RS deviation from pure GR is the positive scale φ^{-44} (the rung-44 forcing that also sets η_B), while pure GR predicts zero. Quantum-gravity auditors cite it to retire StrongFieldTestsDistinctFromGR from the conditional master theorem. The declaration is still a sorry stub packaging that retirement; algebraic positivity 0 < φ^{-44} is the intended discharge.
Claim. Recognition Science predicts a strictly positive strong-field deviation from pure general relativity equal to $\varphi^{-44}$, whereas pure GR predicts deviation zero. That algebraic discriminator is meant to inhabit the master-theorem hypothesis that strong-field tests (S-stars, EHT shadow, Cassini Shapiro delay) distinguish RS from GR.
background
Track 6.C of the quantum-gravity master plan asks whether S-stars near Sgr A*, EHT shadow constraints, lunar laser ranging, and Cassini Shapiro delay separate Recognition Science from pure GR. Each channel has known precision; RS must predict a specific deviation pattern (or non-deviation).
This module supplies only the structural half. The RS strong-field deviation signature is identified with $\varphi^{-44}$, the same rung-44 forcing that appears as $\eta_B = \varphi^{-44}$ on the phi-rung ladder (baryon-asymmetry rung value $-44$). Pure GR contributes a zero baseline. The golden ratio $\varphi$ is the T6 self-similar fixed point; positivity of negative powers of $\varphi$ is elementary once $0 < \varphi$.
Channel-specific physics that would turn the structural scale into an instrument-level observable shift remains future work. The dataset-tied falsifier register in the master plan is left separate.
proof idea
Empty sorry stub: no tactics or lemmas are applied in the body yet. Intended discharge path, from the module plan: define the deviation signature as $\varphi^{-44}$ via the baryogenesis rung value $-44$; prove $0 < \varphi^{-44}$ from $0 < \varphi$; package (RS deviation positive, pure-GR deviation zero) as the structural discriminator proposition; inhabit the master-theorem structure StrongFieldTestsDistinctFromGR with that witness. Sibling positivity is theorem-grade algebra; this packaging theorem is what remains stubbed.
why it matters
Closes the structural form of Track 6.C and is meant to retire one of five hypothesis inputs on the conditional quantum-gravity master theorem (StrongFieldTestsDistinctFromGR from Gravity.MasterTheorem, Session 97). Session 100 is planned to retire 6.B and 6.C together, dropping the open hypothesis count from five to three.
The scale is not a new RS constant: it reuses the phi-ladder baryogenesis rung and the T6 forcing of $\varphi$. Empirical match to EHT / GRAVITY / Cassini stays hypothesis-grade; no dataset is attached. Downstream, the master theorem loses one open hypothesis once the stub is filled. Full strong-field observational closure is not claimed here.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.