sStarDerived
plain-language theorem explainer
Packages the S-star periapsis QG channel as a derived prediction at rung 44 with unit geometric prefactor, so the timing residual scales as φ^{-44}. Strong-field gravity and Sgr A* timing analysts cite it when reading Recognition Science periapsis residuals against data. Fields are filled literally; the equality is discharged by unfolding the correction value and closing with ring.
Claim. The S-star periapsis channel is the derived QG prediction with observable "periapsis timing residual $\delta t/P$ near Sgr A*", rung $r=44$, geometric prefactor $1$, and correction value $\varphi^{-44}$, together with proofs that the correction equals $1\cdot\varphi^{-44}$ and is strictly positive.
background
Recognition Science assigns each length scale a φ-ladder rung $r(L)=\log_\varphi(L/\ell_{\mathrm{sub}})$; recognition corrections at that address scale as $\varphi^{-r}$ relative to the Planck value. For astrophysical black holes the strong-field rung is $s=44$, fixed by the half-area horizon cell count $N=A/\ell_{\mathrm{sub}}^2=\varphi^{2s}$. The same rung appears in the baryon asymmetry $\eta_B=\varphi^{-44}$.
A derived channel prediction packages name, observable, integer rung, real geometric prefactor, a correction value, a proof that the value equals $\mathrm{prefactor}\cdot\varphi^{-\mathrm{rung}}$, and positivity. The S-star correction sibling is defined as $\varphi^{-\mathrm{strongFieldRung}}$, i.e. $\varphi^{-44}$.
This gravity module derives the φ-powers for PTA, EHT, S-star, Cassini, and ringdown from those scale addresses rather than fitting them.
proof idea
Structure instance, not a deep proof. Name, observable, rung $44$, and prefactor $1$ are set by literals; the correction field points at the sibling S-star correction value. The equality field unfolds that sibling and the strong-field rung definition, then closes by ring. Positivity is the already-proved positivity lemma for the same correction value.
why it matters
Feeds the five-channel list derivedChannels, the theorem that four channels share rung 44, and the master certificate that records count, positivity, the shared-rung fact, and ringdown at rung 1. Fills the S-star row of the module table: periapsis residual at the strong-field rung with pure $\varphi^{-44}$ scaling (unit prefactor, no path-integral or projection multiplier). Anchors the structural coincidence that strong-field gravitational injection and baryon asymmetry sample the same rung-44 address on the φ-ladder. Status is structural (0 sorry); no open scaffold remains on this declaration.
Switch to Lean above to see the machine-checked source, dependencies, and usage graph.