CDM Discrimination

Which relation this is (corrected 2026-09-23): the 0.086 dex is the intrinsic scatter of the baryonic Tully–Fisher relation (BTFR), one point per galaxy, built from ALFALFA's global HI line width W50 and SDSS stellar masses (Session 610 calls it “BTFR scatter”). It is not the scatter of the resolved Radial Acceleration Relation (RAR), which uses many radii per galaxy; the observed SPARC RAR scatter is about 0.057 dex (Li et al. 2018) with intrinsic scatter consistent with zero. This page compared it to RAR literature until a researcher visitor persona asked which relation it was. The two are not interchangeable, so the comparison below is BTFR-to-BTFR where it can be. Cold Dark Matter (CDM) models predict a range of intrinsic scatter in these relations 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 has been queued since 2026-07-10 and is still not done. The papers it should take its CDM numbers from: Ludlow et al. 2017 (PRL 118, 161103; EAGLE/APOSTLE), Keller & Wadsley 2017, Desmond 2017 (abundance matching), Dutton et al. 2019 (NIHAO). Most of them report RAR, not BTFR, scatter, which is the relation mismatch above. 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 for months 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.