# Predictions and data matching Summary of RST predictions, the data each is matched or matchable against, and current status. See [[RST Charter (Scientific Status)]] for derived vs calibrated status; [[Relational Substrate Theory (RST)#Part VII: Falsification Programme]] for Gates 1–3. --- ## Table | # | Prediction | Observable | Data source | Status | |---|------------|------------|-------------|--------| | 1 | **Rotation curves (RST field equation)** | \(v(r) = \sqrt{r \cdot q'}\) from \(\mu(q'/a_0,n)\,q' = g_N\); \(a_0\), \(n\) fixed; one free parameter \(\Upsilon_{\text{disk}}\) per galaxy | SPARC (171 galaxies, Lelli et al. 2016) | **Done.** [[SPARC Evaluation Verification]], [[SPARC Evaluation Results]]. ~86% acceptable fits; median \(\Upsilon_{\text{disk}} \approx 0.49\)–0.52. | | 2 | **RAR at high \(z\) (Gate 1)** | At \(z=2\): \(a_0(z=2) \approx 3.1\times 10^{-10}\) m/s², \(n(z=2) \approx 2.34\); asymptotic \(v_{\text{flat}}\) ~32% higher than local analogue; transition radius ~42% smaller | JWST / ALMA resolved kinematics at \(z > 1\) | **Predicted.** Algebraic plot and numbers: [[RST Equilibrium Proof - Code]], [[RST Equilibrium Proof Results]]. Awaiting high-\(z\) data. | | 3 | **Wide-binary threshold (Gate 2)** | Low-acceleration anomaly at exactly \(a_0 = cH_0/(2\pi) \approx 1.04\times 10^{-10}\) m/s², sharpness \(n_0 = 1.25\) | Gaia DR3/DR4 wide-binary orbital statistics | **Stated.** [[Relational Substrate Theory (RST)#Part VII: Falsification Programme]]. No pipeline yet; data exists. | | 4 | **\(\alpha\)-drift (Gate 3)** | \(\Delta\alpha/\alpha = \kappa \cdot \Delta H/H\); \(\kappa = \partial\ln(V_{L^n})/\partial\ln(H)\) derived; constraints \(\kappa < 5\times 10^{-6}\) | Quasar absorption spectroscopy (e.g. Many-Multiplet) | **Derived.** [[Substrate Eigenvalues]], [[RST Four-Force Bridge]]. Compare \(\kappa\) to published bounds. | | 5 | **Cluster / strong lensing** | RST deflection (disformal term) gives “double” lensing vs baryons-only; mass profile / Einstein radius for given baryon model | Cluster strong-lensing (Einstein radius, multiple images, or mass profile) | **Dataset chosen.** Public data: **CLASH** (25 clusters; [STScI](https://archive.stsci.edu/prepds/clash/), [For Astronomers](https://www.stsci.edu/~postman/CLASH/for_astronomers.html)); alternative **HFF** ([STScI lensmodels](https://archive.stsci.edu/prepds/frontier/lensmodels/)). Download into `expanded theory/cluster_lensing_data/` — see that folder's README. Solver: [[RST Refractive Lensing - Code]], [[RST Lensing Results]]. | | 6 | **Reality Engine ↔ galaxy (optional)** | Map engine outputs (e.g. acceleration vs graph distance, EFE) to physical units; compare to one fiducial rotation curve or MOND curve | One SPARC galaxy (toy mapping) or synthetic MOND curve | **Not yet.** Design: which config (nodes, \(H\), \(W\)) corresponds to “one galaxy”; which engine output maps to \(v(r)\) or \(g_{\text{obs}}(r)\). | --- ## Data pipeline index - **SPARC:** Method and data — [[expanded theory/python calculations/SPARC Evaluation - Code]]; implementation — [[about systems/expanded theory/sparc evaluation/SPARC evaluation - Code]]; results — [[SPARC Evaluation Results]]. - **Gates 1–3:** [[Relational Substrate Theory (RST)#Part VII: Falsification Programme]]; Gate 1 algebra — [[RST Equilibrium Proof - Code]]; Gate 3 \(\kappa\) — [[Substrate Eigenvalues]]. - **Lensing:** [[RST Lensing (Disformal)]], [[RST Refractive Lensing - Code]], [[RST Lensing Results]]. Public cluster data: `expanded theory/cluster_lensing_data/` (README has CLASH and HFF download links).