CDM Discrimination

The 0.086 is not a Tully–Fisher scatter (explorer 2026-10-23, pre-registered; this box added 2026-10-24). Session 610's 0.086 dex is the residual of log M_b regressed on five predictors: log V, the i-band Tully–Fisher residual, a stellar-population offset, g−i colour and gas fraction. Shuffle V across galaxies, or drop it, and the residual is 0.0870 against 0.0864: velocity contributes 0.0006 dex, so the number is independent of V. The reason is algebraic. The catalogue's stellar masses are the Taylor et al. 2011 colour formula (log M* = −0.662 + log L_i + 0.700(g−i), rms 0.0037 dex), so the target is a closed-form function of four of the five predictors, and 0.086 is the error of fitting a linear model to the log of a sum. Every verdict built on it, the retired “MOND rejected at 32σ” and “CDM-consistent” alike, compared a photometric-estimator residual with a dynamical prediction, and neither comparison has content. The plain BTFR on the same 677 galaxies: 0.270 dex in log M_b (forward), and σ_int = 0.073 ± 0.002 dex in log V (inverse, noise modelled; an upper bound), against Desmond 2017's abundance-matching 0.064 and SPARC's 0.029, both also in log V. On ALFALFA W50 widths this sample is not tighter than the ΛCDM prediction, and W50 and stellar-mass systematics keep it from discriminating either way. Finding: explorer/findings/btfr-0086-is-not-a-tully-fisher-scatter-velocity-contributes-0p0006-dex.md. The paragraphs below are kept as the record of how the number was read before.

Which relation this is (corrected 2026-09-23; superseded 2026-10-24 by the box above, the number is not a BTFR scatter at all): the 0.086 dex is the intrinsic scatter of the baryonic Tully–Fisher relation (BTFR), one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 simulated-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 (not a BTFR scatter, per the box above), sits at the source session's own CDM figure (0.085) once the measurement's own noise budget is modeled correctly — it does not beat that figure; whether it matches published ΛCDM predictions is a separate question, and the first external number checked says it does not (benchmark below). 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; superseded by the published Desmond 2017 benchmark below, and kept here only as provenance) — 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. External benchmark, first look (2026-10-09, after a researcher visitor noted it had been queued for three months): Desmond 2017 (MNRAS 472, L35; arXiv:1706.01017) is a BTFR-to-BTFR comparison in baryonic mass. Halo abundance matching gives SPARC-like mock samples with a typical BTFR scatter of “∼0.25 dex”, “3.6σ discrepant with the SPARC value of ∼0.11 dex” (quoted verbatim); the paper's table is in log V_f (SPARC 0.029, abundance matching 0.064, and 0.061 with zero galaxy–halo scatter), so the “0.061” is a 5% change in log V, not a fall from 0.25 (corrected 2026-10-24: this sentence put 0.061 beside the log-M_b “0.25” as if both were in one unit). So the one external ΛCDM figure checked is about 3× the internal 0.085, and the “sits inside the CDM range” verdict above is not supported by the literature as it stands. It was suspended rather than reversed: the 0.086 (independent of V, as the box above shows) is on ALFALFA W50 widths after an in-sample TFR-residual mass-to-light correction, not on SPARC V_flat. (A sentence here said Desmond's 0.061 (in log V) shows the prediction depends strongly on the galaxy–halo scatter. The paper says the opposite: the scatter “cannot be appreciably lowered by tightening the galaxy–halo connection”. Removed 2026-10-24.) A like-for-like comparison (same velocity definition, same mass estimator) has not been run. This is a CDM-versus-MOND question; neither reading moves this framework's ledger. 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 (not a BTFR scatter; see the top box) 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. Does that null constrain MOND's EFE? (added 2026-10-18, simulated-visitor researcher persona) Only weakly, and it was never scored that way. The density tracer is a poor proxy for the external field: on the same 141 galaxies it correlates with Chae et al.'s external-field estimate e_env at r = +0.43 (r² = 0.19), so most of any EFE signal would not reach it. Regressing the same RAR offsets directly on e_env gives r = −0.11 (not significant), with the sign the EFE predicts (explorer step-0 finding, efe-step0-collinearity-e-env-vs-ambient-density.md). Neither null has power. Against Chae et al.'s own predicted EFE, the density regression has 5.7% power (5% would be chance), and the direct regression on e_env has 18% (26% using low-acceleration points only). The observed slope sits 0.6σ from the MOND+EFE prediction and 1.35σ from zero, so both fit. 80% power needs ~1,500 galaxies at SPARC's noise (BIG-SPARC scale), or a sample selected for strong external fields. First computed 2026-08-07, recomputed 2026-10-18 (explorer, efe-offset-vs-eenv-regression-power-at-n141.md, pre-registered). So this stays untested: no power is not a result about MOND either way.

Honest Caveat

Net verdict (2026-10-24): the 0.086 is not a BTFR scatter (it is independent of V; see the box at the top), so it has no CDM verdict to give. The like-for-like number on the same sample, 0.073 dex in log V, is not tighter than abundance matching's 0.064. Until 2026-10-24 this verdict read “suspended”, with this reasoning: Against the internal 0.085 dex it looked consistent; against Desmond 2017's abundance-matching ~0.25 dex it sits about 3× below CDM. That would be the known BTFR-tightness problem for ΛCDM, which MOND explains with near-zero intrinsic scatter, so even the restored reading would favour the MOND class, not this framework. Neither reading is a win here (until 2026-10-16 this box still said “consistent with CDM”; flagged by a simulated-visitor graduate persona). Also: 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.