RAR Scatter

New Prediction #2 (NP2): The scatter in the Radial Acceleration Relation depends on environment. Does it? On the one run that measured environment, no. SPARC galaxies placed in the Cosmicflows-4 density field give r² = 0.0001 (N = 141, p = 0.89), against a registered prediction of more than 20% of the scatter, so the kill fired (TEST-03s on Tier 1: Existing Data). Until 2026-10-21 this paragraph called the effect “real and statistically significant (p = 5×10⁻⁶, R²=0.14)”. That number is real, but it measures RAR scatter against Hubble type, not environment (below). Correction (2026-07-04): this is not a prediction standard models avoid — MOND's External Field Effect (EFE) also predicts environment-dependent RAR scatter, so a detection here does not by itself discriminate Synchronism from MOND.

Local density, point by point (the within-galaxy version): the boost each SPARC point requires scatters 0.161 dex conditioned on local baryonic density and 0.118 dex conditioned on g_bar (1.37× wider; 1.34–1.77× across gas and scale-height treatments; 2,622 points). At fixed g_bar, density adds nothing: partial correlation +0.0012 (explorer 2026-08-02), partial slope +0.003 with 95% CI −0.022 to +0.027 on the 2,438 points behind the density fit (explorer 2026-11-04). No γ, ρ_crit or compander enters. Details on Honest Assessment.

What Is RAR Scatter?

The Radial Acceleration Relation plots observed gravitational acceleration (g_obs) against the acceleration predicted from baryonic mass alone (g_bar). Across thousands of galaxies, this relation is remarkably tight — but not perfectly tight. The scatter around the mean relation is measured as σ_int (intrinsic scatter in dex).

Standard models — both CDM and basic MOND — predict that this scatter should be constant regardless of a galaxy's environment. A galaxy in a dense cluster should scatter the same amount as an isolated field galaxy.

Synchronism's Prediction

The coherence function depends on local density. Galaxies in dense environments (clusters, groups) experience a different coherence gradient than isolated galaxies. This means the RAR scatter should vary with local density. Specifically:

The Test

Using the ALFALFA-SDSS cross-matched sample, σ_int = 0.086 dex was measured on the optimal quality cut (N = 677) — the full cross-match (N = 14,435) gives 0.118 dex; pairing the headline N with the optimal-cut statistic was a sample splice, corrected 2026-07-10 (2026-10-24: the number is not a BTFR scatter: it is independent of V (shuffling V across galaxies gives 0.0870 vs 0.0864; explorer 2026-10-23), the residual of an in-sample photometric mass model, so it has no CDM verdict; see CDM Discrimination). The p = 5×10⁻⁶, R² = 0.14 environment-density statistics below are notfrom this sample: they trace to a SPARC-scale (N≈171) Hubble-type/morphology regression (archive Session 377), mislabeled as this test's result since 2026-04. The result:

Until 2026-10-21 these tiles read “p = 5 × 10⁻⁶: statistical significance of environment effect”, “R² = 0.14: fraction of scatter explained” and “86%: scatter remains unexplained”.

What This Means

There are two results here, and only one is about environment. Hubble type does predict RAR scatter on SPARC (p = 5×10⁻⁶, R² = 0.14, surviving five confound controls; Sessions 376–378). Session 381 asked whether type was standing in for environment, and found it was not. Within each type an isolation proxy predicts nothing (r = +0.003, p = 0.97), and rotation-curve roughness absorbs the type signal (type is non-significant once roughness is controlled, p = 0.61): late-type galaxies have rougher curves. Environment, measured directly with an external density catalogue, explains none of the scatter (r² = 0.0001). This page previously read the type result as an environment effect that was “real” but short of the R² > 0.20 bar. Basic MOND (no EFE) does not predict environment dependence, but MOND with the External Field Effect does — EFE is a standard part of MOND phenomenology, not an ad-hoc addition, so this result does not separate Synchronism from the MOND family. CDM simulations with baryonic feedback can also potentially produce environment-dependent scatter.

Honest Caveat

The coherence model's environment prediction explains none of the RAR scatter (r² = 0.0001 against a registered > 20%). By its own standard this test has failed, not merely under-delivered. Most of the scatter likely comes from observational systematics (distance errors, inclination corrections, mass-to-light ratio assumptions) rather than any physical model. MOND plus standard M/L corrections already accounts for essentially all of the variance. See CDM Discrimination for how this same measurement bears on the CDM comparison.