CDM Discrimination

Cold Dark Matter (CDM) models predict a range of intrinsic scatter in the Radial Acceleration Relation (RAR) from halo-to-halo assembly diversity. The measured value, 0.086 ± 0.003 dex, sits inside that predicted range once the measurement's own noise budget is modeled correctly — it does not beat CDM. Benchmark disclosure (2026-07-10): the “CDM prediction” used here is the source session's own internal figure (≈0.085 dex from halo-concentration scatter, Session 610) — no external published CDM scatter estimate (semi-analytic or hydrodynamic-simulation) has been cited or checked against, so the CDM-consistency verdict is internally coherent but not yet anchored to the literature's range. An external-benchmark check is queued. The number comes from an optimal N = 677 subsample (Mendel stellar masses) drawn from the larger 14,585-galaxy ALFALFA-SDSS cross-match used elsewhere on this site — not from “14,760 galaxies,” a figure that matched no accounting in the underlying analysis and has been removed.

Why This Verdict Flipped: A Case Study in Noise Modeling

The interesting part of this result isn't the final number — it's that the verdict on the same measurement reversed across the analysis, and the reversal is fully documented in-archive:

• An intermediate session measured σ_int = 0.072 dex and read it as −6.2σ below the CDM prediction — a striking, headline number.
• The next session in the chain found that distance-measurement noise dominates the scatter budget and had not been properly subtracted — the −6.2σ reading depended on treating noisy distance errors as if they were intrinsic physical scatter.
• The program's own definitive re-analysis, correcting for distance noise, revised the estimate to σ_int = 0.086 dex and explicitly labeled the −6.2σ reading premature. Its own verdict: CDM-consistent at z = +0.5 — well within one standard deviation of the CDM prediction, not a tension.
• The program's final accounting goes further: the CDM-consistency statistic itself is modeling-choice-dependent, ranging from z = +0.5 to z = +64 depending on which noise and error assumptions are used. A number that swings that widely with modeling choices cannot support a “definitive” discrimination claim in either direction.

This page (and, until 2026-07-04, Honest Assessment and Galaxy Rotation) kept quoting the retracted −6.2σ framing years after the source program itself reversed it — a compilation surface citing a root claim the archive had already retracted. MOND Comparator had the correct framing (“Matches, z = +0.5”) the whole time; it just wasn't cross-checked against the other pages.

Even On the Most Favorable Reading, This Doesn't Discriminate Synchronism from MOND

Two further problems would remain even if the tight-RAR argument were accepted at face value:

• “RAR too tight for CDM” is a contested claim in the literature, not a settled one — several CDM hydrodynamical simulations (Keller & Wadsley 2017; Dutton et al.; later EAGLE-based work) reproduce a tight RAR, and intrinsic-scatter estimates are sensitive to error modeling and radial-range choices.
• Even granting the argument, it favors modified-gravity-class theories (MOND-like) over particle CDM — it says nothing about Synchronism specifically versus MOND, which is the comparison that actually matters for this framework. MOND naturally predicts a near-zero intrinsic RAR scatter, so a tight RAR is squarely MOND's prediction, not a Synchronism-specific one.
• The environment-dependence test (the other half of this page's original claim) is not a Synchronism-vs-MOND discriminator either — MOND's External Field Effect (EFE) also predicts environment-dependent RAR scatter. TEST-05's null-independence rejection (p = 5×10⁻⁶, R² = 0.14 on SPARC scale — a Hubble-type/morphology dependence, not ambient density) met its own registered criterion — corrected 2026-07-09 from “failed” to MOND-shared, then re-adjudicated 2026-07-15: the tie dissolves on lever magnitude (MOND+EFE couples to external acceleration, ~0.09 dex modulation; C(ρ) to ambient density, ≤2×10⁻³ dex — environment dependence is a discriminating axis, and the registered density-classified run executed 2026-07-14 in the research repo gives r² = 0.0001: refuted by execution); see Tier 1: TEST-05 for the adjudication and the TEST-03 provenance error it had been conflated with.

Honest Caveat

Net verdict: σ_int = 0.086 dex is consistent with CDM, not a constraint on it; the framework's registered environment prediction was refuted when run as registered (r² = 0.0001 vs a >20% claim, 2026-07-14); and no reading of either result separates Synchronism from MOND, which remains the framework's actual competitor on galaxy dynamics. This page exists now primarily as a documented case study in how a noise-modeling correction can flip a headline verdict, and in how compilation pages can keep citing a claim long after its own source has retracted it.