Galaxy Rotation Curves

Failed — density-keyed form ΔBIC +2843; γ = 2 compander in acceleration ΔBIC +184 Reparametrization — Acceleration-keyed fit is exactly MOND's simple μ

Sub-note: the registered ALFALFA test, TEST-03, was never run as registered (see correction below), so that one test is untested. Until 2026-09-19 that was this page's only badge, which undersold the page's own opening verdict; the two badges above are the ones the Galaxy Plotter already carried for the same content.

Galaxy rotation curves are the most important empirical test for any theory of gravity at galactic scales. Stars and gas in the outer regions of disk galaxies orbit faster than Newtonian gravity predicts from visible mass alone. The Radial Acceleration Relation (RAR) captures this: observed acceleration correlates tightly with the acceleration predicted from baryonic mass, but systematically exceeds it below a critical scale.

Does Synchronism replace dark matter? No, not on current evidence. The idea was that gravity's strength depends on how densely matter is packed, which would make the extra pull without invisible matter. Written that way, keyed on density, the equation does not fit galaxies. In a real disc it barely changes gravity at all, which you can see on the Galaxy Curve Plotter. A version keyed on acceleration, with one dial fitted, does fit, but at that setting it is exactly MOND's formula. So it carries MOND's successes and MOND's problems, including the Solar System test below, and it never does better. Everything after this box is the technical detail behind those three sentences.

Read this first (promoted to the top 2026-07-23): the headline equation never reaches this page's fits. When this box was written no chain from C(ρ) to g_obs was stated anywhere in the framework. Two have since been written down (division g_obs = g_bar/C, and a field equation that turned out to be Refracted Gravity's; see how C enters dynamics), and the density-keyed law has been fitted through them and lost. But none of the fits on this page use it — the galaxy fits shown below use McGaugh's standard RAR interpolating function (MOND phenomenology), with Synchronism contributing only a scatter hypothesis on top (since refuted by the 2026-07-14 environment run, filed on Tier 1 as TEST-03s — not the Freeman-law card TEST-08). The structural reason is in the next paragraph; the tested-and-killed compander variants are further down.How C entered the RAR fit, in one sentence (added 2026-09-08; asked by two visitor personas who showed the alternatives give different force laws): the compander was used as an implicit interpolating function keyed on g_obs — the script solves g_bar = g_obs·tanh(γ ln(1 + g_obs/a₀′)) for g_obs with a₀′ profiled (simulations/sparc_tanhlog_profile.py, research repo, line 85). At γ = ½ that is Milgrom's simple μ with a₀ = 2a₀′. It was not evaluated explicitly on g_bar (which would give an additive floor g_bar + 2a₀′, not MOND), and not on ρ. So every quantitative galaxy fit on this page is a fit in MOND's own variable; the density-keyed law is tested on the Honest Assessment (head-to-head ΔBIC +2843, the Oort limit, and the globular-cluster fork).

One structural reason to expect this fit to reparametrize rather than derive MOND: C(ρ) is a function of local density, while the RAR is organized by g_bar, a non-localenclosed-mass acceleration. A pointwise map cannot in general reproduce an acceleration-space relation across systems with different mass geometries except by per-system calibration — see the local-vs-non-local structural no-go. The Galaxy Curve Plotter's hand-tuned radius stand-in is that no-go showing through in a single demo.

C-convention note (2026-08-04): the site ran three mutually exclusive readings of the substitution above: this plotter codes v² = v_b² + (V_flat·C)², i.e. g_obs = C·g_bar shifted into an amplitude term; the f_DM = 1 − C identity on Tier 1 implies g_obs = g_bar/C; and MOND Unification's prose then said g_obs = C·g_bar directly — since corrected there to g_bar/C, so two readings are live today: the plotter's amplitude term and g_bar/C, whose field-equation form (and where the two part company in a disc) is written out on Coherence Function. On the site's own five plotter galaxies these three laws miss the observed curve in three different directions — roughly 10²–10³× high, converging on Newtonian, and 10²–10³× low — and no calibration reconciles them, because the disagreement is a functional-form mismatch (delivered boost falls exponentially with radius under an exponential disk; a flat curve needs it to rise roughly linearly), not an amplitude one. This plotter shows the amplitude reading only; it is not necessarily the framework's asserted one.

The literature already contains both this obstruction and its known escapes (noted 2026-07-10; corrected 2026-07-27): density-dependent transitions are a mature field (symmetron/chameleon screening). This paragraph previously claimed that “the ρ-vs-g_bar variable mismatch is the standard reason screened scalars don't reproduce MOND.” That attribution was never sourced and is wrong: the screening literature does not make it, and Burrage, Copeland & Millington, PRD 95, 064050 (2017) reproduce the radial acceleration relation for 153 SPARC galaxies with a scalar keyed on local volumetric ρ(r) and universal Lagrangian parameters. Their extra force is the gradient of a function of ρ, not a multiplier on g — which is what lets a density-keyed field track an acceleration-keyed relation, and is precisely what C(ρ) does not do. See the counterexample paragraph on For Researchers. The other constructive escape is superfluid dark matter (Berezhiani & Khoury 2015): a local density criterion switches on a condensate, but the MOND-like force is carried by the condensate's phonons — the force scale enters independently of the switch. C(ρ) conflates switch and force into one local function; that conflation is what the data kill. See the escape taxonomy on For Researchers.

Dataset Results

SPARC Dataset

175 galaxies with high-quality photometry and resolved rotation curves (Lelli, McGaugh & Schombert 2016). The gold standard for RAR studies. [Public data]

Tight RAR confirmed (σ_int ≈ 0.057 dex) — McGaugh et al. 2016 measured value, restated
Coherence function fits within observational scatter
Environment-dependent effects visible but sample too small for strong statistics

ALFALFA-SDSS Dataset

14,585 galaxies from the ALFALFA HI survey cross-matched with SDSS photometry — that is the registered cross-match; the definitive session actually analysed 14,435 after a quality cut. Unresolved rotation curves but massive statistical power. [ALFALFA data] [SDSS DR17]

Environment-dependent RAR scatter detected at p = 5 × 10⁻⁶, R² = 0.14 — but this statistic is SPARC-scale (N ≈ 130–175), not a valid measurement of this 14,585-galaxy sample (see correction below). The registered TEST-03 environment-density test on this sample was never run.
σ_int = 0.086 ± 0.003 dex — CDM-consistent (z = +0.5 in the source session's definitive run), not below CDM. An earlier −6.2σ “below CDM” reading from an intermediate session was retracted in-archive as premature once distance-noise modeling was added; the verdict is also modeling-choice-dependent (z ranges +0.5 to +64). See CDM Discrimination for the full history.
Cluster vs. field galaxies show different scatter — the effect is real but sub-threshold, not a confirmed prediction

The Interpolating Function

Attribution: The equation below is the standard RAR interpolating function from McGaugh, Lelli & Schombert (2016) — already in the literature for a decade and widely used to fit SPARC. Synchronism's specific contribution is not the function itself, but the environmental scatter ansatz on top of it (the claim that σ_int depends on local density). All fit-quality claims refer to that ansatz and to the McGaugh-2016 baseline together.

g_obs = g_bar / (1 − e^{−√(g_bar/a₀)})

RAR interpolating function (McGaugh et al. 2016)

In Synchronism, the acceleration scale a₀ ≈ cH₀/(2π) is a 40-year-old dimensional coincidence (Milgrom 1983), discussed by Famaey & McGaugh (2012), McCulloch, Verlinde, and Smolin under different theoretical umbrellas. The 2π prefactor is chosen to match the observed value; cH₀/(2π) ≈ 1.04×10⁻¹⁰ m/s² at the site-standard H₀ = 67.4 undershoots the observed 1.2×10⁻¹⁰ by ∼13%. Synchronism's contribution is the coherence-function mechanism that provides areason for this scale — not the identification itself. See Honest Assessment and Parameter Derivations for prior-art acknowledgment and the canonical reparametrization framing.

Key Results Summary

0.086

σ_int (dex) — intrinsic scatter

5 × 10⁻⁶

p-value for environment effect

R² = 0.14 belongs to SPARC (N≈171), not this sample — see correction

14,610

galaxies run (175 SPARC + 14,435 ALFALFA–SDSS (quality cut))

mechanism tested on 175 SPARC curves; the TFR scatter test never ran as registered

Structural Failure: Dark Matter Mechanism (March 2026)

Synchronism's CFD viscosity interpretation mapped low coherence (dark matter) to high viscosity — predicting dark matter should be stickier than baryons. The Bullet Cluster (1E 0657-558) shows the opposite: dark matter halos pass through each other with negligible self-interaction (σ/m < 0.47 cm²/g, Harvey et al. 2015). That specific ansatz has the wrong sign — see the full failure analysis.

Scope note (added 2026-07-09): this is a documented failure of the specific CFD viscosity ansatz, not of Claim 3's headline form (“dark matter is incomplete decoherence”), which asserts a modified gravitational response, not a substance with a viscosity to get the sign of. The Bullet Cluster still refutes any local-density-sourced-gravity reading of Claim 3, via a different and stronger argument: the lensing-mass peaks track the collisionless galaxies while the X-ray gas — most of the baryonic mass — is stripped and lags behind (Clowe et al. 2006, ApJ 648, L109). Any theory where gravity responds to localbaryon density must put the extra gravity where the baryons are; it isn't there. This is the same local-vs-non-local no-go documented above, applied at cluster scale — not a second, independent failure. (MOND needs additional collisionless mass at cluster scale for the same reason: Angus, Famaey & Zhao 2006.)

The galaxy rotation fit results on this page are independent of the CFD interpretation and stand as-is (reparametrization of MOND with an environmental scatter term).

Honest Caveat

The environment-dependent scatter is real and statistically significant (p = 5×10⁻⁶), but the R² = 0.14 / p = 5×10⁻⁶ pair is only mutually consistent at SPARC scale (N ≈ 130–175) — see correction below. Furthermore, standard MOND plus mass-to-light ratio corrections already explains essentially all of the RAR variance. Synchronism adds at most a small, detectable effect on top of what MOND already provides — it does not replace MOND's success, and MOND's own External Field Effect predicts the same qualitative environment dependence (Chae et al. 2020/2021), so the effect does not discriminate the two.

Correction (2026-07-09) — TEST-03/TEST-05 provenance: This page previously said R² = 0.14 was TEST-03's result on this 14,585-galaxy sample and that it tripped TEST-03's kill criterion. It doesn't: at N = 14,585, R² = 0.14 implies p of order 10⁻⁵⁰⁰, not 5×10⁻⁶ — the pair is self-consistent only at SPARC scale, TEST-05's sample. TEST-03's actual environment-density result on this sample was never computed as registered. TEST-05, which does own this statistic on its registered terms, met its own criterion (rejecting independence) — briefly reclassified MOND-shared (2026-07-09), a tie dissolved on adjudication 2026-07-15: the two frameworks' environment levers differ by ~50×–5,000× (local density vs external acceleration), so the axis discriminates; honest status is “never run as registered.” Full trace on Tier 1: TEST-03 and TEST-05.

ΔBIC note: The incremental value of the environmental scatter term above baseline MOND has not been quantified via ΔBIC on the ALFALFA-SDSS dataset. A separate ΔBIC analysis was run for the RAR transition-shape question (see below) — which is the more fundamental discriminating question.

RAR Transition Shape: The Decisive Test — CLOSED (2026-05-21)

The environment-dependent scatter tests (TEST-01, TEST-05) probe the size of deviations from MOND's RAR. A more fundamental question is whether the compander's functional form (μ_Syn = tanh(γ ln(1+x)), γ=2) differs from McGaugh's interpolating function ν(x) = 1/(1−e^−√x) in the shape of the transition — the only test that could discriminate the two frameworks without assuming any environmental coupling.

This test was run on 2807 real SPARC points (Lelli-McGaugh-Schombert 2016, 10% velocity-error cut) with a₀ free and standard M/L priors. Result:

Model	RMS (dex)	ΔBIC vs McGaugh
McGaugh ν (standard MOND)	0.1437	— (reference)
Compander μ, γ=2 pinned	0.1485	+184
Compander μ, γ free (best fit: γ=0.49)	0.1437	+7.1

Kill criterion triggered. ΔBIC = +184 ≫ 10 refutes the γ=2 compander as the galaxy mechanism. Conservative correction for intra-galaxy point correlation (effective N≈500–1000): ΔBIC ≈ 33 — still decisive. The residual is a coherent S-shaped ≈0.05–0.10 dex signature at the transition, significant at ~8σ per bin.

Note on γ=2: γ=2 follows from N_corr=1 (individual stars taken as uncorrelated), but N_corr is asserted, not independently counted. The SPARC-preferred γ≈0.49 back-implies N_corr≈17, contradicting the independent-stars premise. γ=2 is the most charitablepin for galaxies given the framework's own logic — not a prediction derived from independent evidence.

The fork that closes the question: free-γ converges to γ≈0.49 with RMS identical to McGaugh to four digits. ΔBIC=+7 is entirely the BIC penalty for the extra parameter — the fit improvement is zero. Made quantitative (2026-07-27, external-reviewer point): with N = 2807, ln N = 7.94, so one added free parameter costs +7.94 in BIC before any likelihood is considered. The observed +7.1 therefore implies Δχ² ≈ −0.84 — the free-γ compander fits the data marginally better than McGaugh's ν and loses purely on the complexity charge for a knob MOND does not need. That is a sharper statement than “collapses to MOND equivalence”: the compander is a strictly worse-parameterized reparametrization of the RAR, buying Δχ² < 1 for one degree of freedom. (Bookkeeping: a₀ is floated in both arms, so Δk = 1 — McGaugh's ν is fitted with k = 1 (a₀), the free-γ compander with k = 2 (a₀, γ); see explorer/scripts/rar_transition_shape_real_sparc.py, where the BIC is computed as bic(ssr_F,2) − bic(ssr_M,1).) Note the contrast with the γ=2 row: ΔBIC = +184 there is pure likelihood (Δk = 0). The two numbers do different work and are not one ladder. There is no γ for which the compander is both (a) distinct from MOND and (b) consistent with SPARC. Pin γ=2 → refuted. Fit γ → MOND.

Why 0.49? Mechanism identified (2026-07-22 form-selection run): γ controls the Newtonian-return exponent — algebraically, tanh(γ·ln(1+y)) approaches 1 like (1+y)^−2γ, so the return exponent is q = 2γ. Within a one-parameter family, the SPARC transition shape maps onto q ≈ 1 (a free Hill fit on the same data gives n = 0.975); the asymptotic return itself is not constrained by SPARC — the data reach only x ≲ 10, and McGaugh's exponential-return function fits the same 2,807 points with the same RMS. q = 1 is the value hard-coded in MOND's “simple” μ-function. γ = 0.49 was never a constant awaiting derivation; it is the tanh family's encoding of MOND's simple μ. The framework's asserted γ=2 means q=4 — re-Newtonianizing far too abruptly — which is the +184 kill restated mechanistically.

Stated exactly, not asymptotically (added 2026-09-07, visitor graduate-physics persona). The paragraph above argues MOND-equivalence through a tail exponent. It holds identically, and the exact version is both shorter and more damning. Because e^γln(1+x) = (1+x)^γ,tanh(γ ln(1+x)) = [(1+x)^2γ − 1] / [(1+x)^2γ + 1]with no approximation. At γ = ½ the exponent cancels and this collapses to a Möbius transform of its argument x (in this passage an acceleration ratio, not a density):C(x) = x/(x+2) = μ_simple(x/2)— MOND's simple interpolating function for all x, not just in the tail, with a₀ → 2a₀. The free-γ SPARC fit lands at 0.489, which is 2% from the unique γ at which this model does not resemble MOND but is MOND. The same cancellation runs the cosmology sector: at γ = ½, (1−C)/C = 2/x, so the substituted dark-energy density ρ_DE = ρ_m(1−C)/C = 2ρ_crit — ρ_m cancels identically and a cosmological constant falls out. One special point, two variables: exactly MOND-simple when x is an acceleration (the galaxy fit's variable), exactly Λ when x is the mean matter density (the cosmology's). The galaxy fit (γ = 0.489) and DESI DR2 (γ = 0.487) both land there, but they are fits of the same function in different variables, so this is each sector's incumbent fitting its own data, not one parameter measured twice. The density-keyed galaxy law, which shares cosmology's variable, fits SPARC best at γ → 0.046 and is refuted (corrected 2026-09-24; this used to read “one algebraic fact with two faces”). See Coherence Function and Dark Energy.

The fitted γ has a consequence beyond MOND-equivalence: the Solar System (TEST-25). A QUMOND interpolating function used for galaxies also acts in the Solar System. There the Galactic field induces a small quadrupole in the Sun's potential, and Cassini bounds it. That quadrupole is set near the Sun's MOND radius, √(GM☉/a₀) ≈ 7,000 AU, where the Sun's field is about a₀, so it tests the interpolating function in its transition. A pre-registered joint squeeze checked the Cassini bound against the full SPARC-retained γ interval (ΔBIC ≤ 10 ⇒ γ = 0.425–0.600). It found a robust empty intersection: at the SPARC fit the compander fails Cassini by +17.95σ (unmarginalized; +17.7σ to +18.0σ across the interval).

This failure is shared with MOND's own functions. On the same instrument, McGaugh's RAR function ν = 1/(1−e^−√y), the one fitted on this page, fails by +15.9σ to +20.9σ. Milgrom's simple function fails by +15.3σ to +20.1σ. The grid covers a₀ ∈ {1.128, 1.20}×10⁻¹⁰ and TEST-25's three external-field values. Desmond, Hees & Famaey (2024, MNRAS 530, 1781) report 8.7σ after marginalizing. In the δ-family, which contains McGaugh's function at δ = 1, nothing enters the Cassini 95% interval until δ = 4, and then only at 3 of 6 grid points. Whether δ ≈ 4 still fits SPARC was not computed. So TEST-25 closes one scale-universal tanh-log QUMOND realization, and it closes the RAR-preferred MOND functions just as hard. See TEST-25 for the scope statement (it does not reach modified inertia, dark-matter models, or the umbrella ontology). Script and pre-registration: maintainer/scripts/cassini_q2_mond_interpolating_functions.py.

A separate, larger effect: the direct tail. The compander returns to Newton as a power law, 1−C ≈ 2(1+x)^−2γ, while McGaugh's function returns exponentially. At Saturn (x ≈ 5×10⁵) the fractional anomaly is ≈ 5×10⁻⁶ against e⁻⁷⁰⁷. Small as a fraction, it is not small as an acceleration: with g ≈ 6.5×10⁻⁵ m/s² it is δg ≈ 3×10⁻¹⁰ m/s², an a₀-sized extra pull (for any simple-μ-class return, ν−1 ≈ a₀/g, so δg ≈ a₀). The Cassini-bound external-field quadrupole gives δg ~ Q₂·r ≈ 3×10⁻²⁷ s⁻² × 1.43×10¹² m ≈ 4×10⁻¹⁵ m/s² at the same place — about 10⁵ times smaller. Nor can the tail hide in GM☉: a near-constant δg makes δg/g grow as ~r² from planet to planet. The literature finds this branch (simple μ, slow power-law return) already disfavoured by planetary ephemerides, independently of the external-field effect (Hees et al. 2016; Blanchet & Novak 2011). That is a literature result: it has not been re-executed on this site, and the size of the exclusion for the compander specifically is not yet computed. It is also inherited, not framework-specific — at γ = ½ the compander is simple μ. The executed test on this page remains TEST-25's Q₂ computation above.

Revision note

This box used to explain the empty intersection as a tail-shape mismatch, with the exponential tail “indistinguishable from zero at any precision.” It concluded that the compander sits in the simple-μ branch the Solar System had closed while McGaugh's branch survives. That compared the direct anomaly at Saturn, but Cassini bounds the external-field quadrupole set near 7,000 AU, and there McGaugh's function fails too. A visitor persona (graduate physics) raised it, and a pre-registered run on TEST-25's instrument confirmed it. An earlier correction on this box had already fixed the naming (simple μ returns as a power law; the exponential return belongs to McGaugh's RAR ν). Until 2026-09-22 the box then called the direct tail “a separate, smaller effect” that did not bear on the Solar System verdict. That compared fractions, not accelerations; in acceleration it is about 10⁵ times the Cassini Q₂ effect at Saturn (visitor graduate-physics and researcher personas, 2026-09-22). The Hill-fit sentence above also previously called the n = 0.975 fit an independent cross-validation; it uses the same SPARC data.

Galaxy tests that selected Synchronism over MOND: 0, by execution (this RAR-shape test cannot separate them at free γ). Script + full analysis: explorer/scripts/rar_transition_shape_real_sparc.py, finding: explorer/findings/rar-transition-shape-real-sparc-result.md.

Wide Binaries

The RAR environment test refuted its registered amplitude (Session 177's claim, r² = 0.0001 on 2026-07-14; this line previously credited TEST-03 with tripping a kill criterion, a metric conflation corrected on Tier 1 in July), and the RAR transition-shape test (above) has now closed the main galaxy-scale question. The wide binary test (TEST-02) was previously identified as a discriminator, but with the compander collapsing to MOND at its best-fit γ, the wide-binary question is now whether MOND+EFE and the compander (at fitted γ≈0.49) diverge in a density-stratified wide-binary sample. Wide stellar binaries (separations > 0.1 pc) probe the sub-a₀ acceleration regime in a fundamentally different mass and density environment from galaxy rotation curves — no dark matter halos, no baryonic feedback, just two stars in a nearly Keplerian orbit.

The key papers are Pittordis & Sutherland (2023) and Hernandez et al. (2024), using Gaia DR3. They disagree on the strength of the MOND signal. Synchronism predicts a density-dependent wide binary anomaly (stronger anomaly in denser stellar fields). Gaia DR3 is public; stratifying the sample by local stellar density is a tractable one-week analysis. See TEST-02 for the kill criterion.

MOND+EFE / wide-binary avenue: CLOSED (2026-06-03) MOND with the External Field Effect (EFE, Bekenstein-Milgrom 1984) also predicts environment-dependent wide-binary dynamics. The quantitative divergence was computed on 2026-06-03: a bounded C(a) is the only form whose EFE prediction differs from MOND (TDG velocity dispersion σ ≈ 14.5 vs 41 km/s in Tidal Dwarf Galaxies), but that same boundedness caps the acceleration boost at ≈3.17 while ~42% of SPARC RAR data points require boosts above that (up to ~34×), giving RMS 0.224 vs McGaugh's 0.146. The boost ceiling and RAR fit trade off monotonically with opposite sign — no ceiling simultaneously fits the RAR and stays distinct from MOND+EFE. This is the same fork as the RAR transition-shape test: the one non-degenerate form is refuted by the data. Wide-binary density stratification cannot discriminate Synchronism from MOND+EFE. See TEST-02 and Honest Assessment for the full picture.

GW170817 and the Speed of Gravity

The binary neutron star merger GW170817 constrained |c_GW − c|/c < 10⁻¹⁵, killing TeVeS, Bekenstein-Sanders, and large swaths of Horndeski parameter space (Sakstein & Jain 2017, Ezquiaga & Zumalacárregui 2017). Synchronism is marketed in part as a modified-gravity alternative, so this constraint is relevant.

Synchronism's posture: The coherence function C(ρ) is not a tensor-vector-scalar theory and does not introduce new propagating tensor degrees of freedom. It does not modify the graviton kinetic term or introduce derivative couplings of a scalar to the metric that would change gravitational wave speed. Therefore the framework's prediction is c_GW = c by construction, and GW170817 does not apply.

Open gap: This statement has not been formally derived from the framework's equations. The coherence field couples to density (ρ), not directly to the metric, but the precise relationship between C(ρ) and the effective gravitational action at GW propagation scales has never been written down. Until it is, “GW170817 doesn't apply” is a reasonable expectation but not a proven constraint.

Cosmological extension — disfavored 2.4σ on σ₈ amplitude (reframed 2026-07-02): Session 107's prediction of suppressed growth (fσ₈ ≈ 0.418) was compared against DESI DR1. Full-shape result (arXiv:2411.12021): combined σ₈ = 0.841 ± 0.034 vs predicted 0.76 → 2.4σ tension on the σ₈ amplitude, a GR-conditioned statistic. The registered kill criterion (fσ₈(z = 0.51) > 0.46 at >3σ) was not met: ~1.5σ, underpowered as registered (this page kept the retired “triggered” wording until 2026-09-11, two months after Tier 1 and Honest Assessment dropped it). The LRG1 fσ₈/(fσ₈)_fid = 1.16 ± 0.13 “enhancement” is a single ~1.2σ bin, not load-bearing. Verdict: post-hoc retrodiction, disfavored 2.4σ on amplitude. (Prior 2026-05-25 “correction” was itself an error — misattributed z≈0.07 PV value.) Honest Assessment: TEST-04a →

Next: RAR Scatter →CDM Discrimination →Galaxy Curve Plotter →

Prerequisites

Understanding these concepts first will help:

Dark Matter ReframedPatterns interacting indifferently: gravity only, no EM Critical Densityρ_crit = A V_flat²: the transition point

Related Concepts

RAR ScatterEnvironment-dependent RAR scatter — registered >20% amplitude, refuted as registered (r² = 0.0001)CDM Discriminationσ_int = 0.086 dex: CDM-consistent (z=+0.5), not below-CDM Galaxy Curve PlotterPlot SPARC rotation curves with Synchronism overlays