We ask whether any one-parameter structural correction to the radial acceleration relation (RAR) can be uniquely recovered from SPARC rotation curves, and answer with an identifiability audit: each candidate is benchmarked against per-galaxy nuisance freedom, with predictive scoring against mass-only and data-quality baselines. In the full sample (N = 126) the answer is no: a hybrid compactness term improves the fit, but zero-point freedom absorbs the gain, and in cross-validation the model fails to out-predict a mass-only baseline and loses to a quality-flag baseline. One regime retains structural information: in gas-dominated, low-acceleration disks -- where MOND's strict locality and $\Lambda$CDM feedback models diverge most sharply -- the RAR residual correlates with compactness ($r=0.46$, $p=1.3\times10^{-4}$), remains significant under hierarchical partial pooling ($\beta=0.23$, $p=1.7\times10^{-5}$; N = 63), and survives canonical joint control for quality, sampling, mass, inclination error, and first-order pressure support ($r=0.30$, $p=0.02$). All significant results pass a Benjamini-Hochberg correction over the declared 27-test family. Three limits temper that survival: it is not significant under rank-based control over the widest proxy set; it resides in faint dwarfs independent surveys do not reach; and after mass control it is shared across the mass-size manifold. Pressure support brackets the interpretation -- isotropic drift correction absorbs a quarter of the amplitude, while a Jeans treatment overcorrects resolved cases -- leaving the physical origin undetermined. The audit's product is the extraction limit: claimed corrections must clear the 0.106 dex per-galaxy nuisance floor, a mass-only baseline, and data-quality stratification.
We present a computational audit of the identifiability limits for structural corrections to the Radial Acceleration Relation (RAR) using a canonical subset of the SPARC database (N = 126). Rather than proposing a new dynamical law, we establish the observational conditions under which such a law would be mathematically recoverable. We resolve three methodological controls that heavily influence RAR interpretations. First, we isolate a -0.39 dex residual offset between the eight galaxies in the lowest-quality observational tier (Q = 3, mean -0.433 dex) and the remaining 118 (mean -0.040 dex). Of five predictions that beam smearing must satisfy, four fail: the radial profile plateaus at -0.331 +/- 0.028 dex rather than decaying to zero, and the offset does not scale with the number of resolution elements across a curve. Beam smearing is disfavoured as the primary driver, though the offset remains a data-quality signature rather than a physical one -- Q = 3 in SPARC flags major asymmetries and strong non-circular motions, conditions under which a rotation curve does not trace the equilibrium potential. Second, we decouple the architectural limits of the dataset into three independently measured quantities -- the no-model point scatter (sigma_M0 = 0.1860 dex), the residual floor after free per-galaxy intercepts (sigma_M3 = 0.1058 dex), and the propagated analytic error floor -- together with the absorbable budget sqrt(sigma_M0^2 - sigma_M3^2) = 0.1530 dex derived from the first two. Finally, we provide an 8-cell protocol grid to reconcile Leave-One-Out (LOO) Mean Squared Prediction Error (MSPE) ratios. We demonstrate that reported structural-dynamical couplings must be evaluated with strict adherence to residual definitions (median vs. mean, signed vs. absolute) and baseline denominators to avoid adopting labeling artifacts as new physics.
The Covarying Coupling Constants (CCC) framework, developed to account for high-redshift JWST observations, contains a mechanism -- a covarying-constant effective mass field keyed to local density -- that modifies galactic dynamics without particle dark matter. We test it against the full Spitzer Photometry and Accurate Rotation Curves (SPARC) sample of 175 disc galaxies, extending an earlier study of a few objects. Working in an inverse formulation, in which each model predicts the baryonic rotation curve from the observed one, we compare CCC against Modified Newtonian Dynamics (MOND) and one- and two-parameter Navarro-Frenk-White (NFW) haloes on identical footing, using the reduced $\chi^2_\nu$. We show that the published sharp density turn-off in the earlier study is unphysical and replace it with a smooth transition -- the density-space analogue of the MOND interpolating function, introducing no new parameter. One-parameter smooth-CCC then performs comparably to galaxy-by-galaxy fitted MOND (the lower $\chi^2_\nu$ in 56 per cent of galaxies, mean $\chi^2_\nu$ of 2.58 versus 2.65; the paired difference is not significant), while two-parameter NFW shows a substantially broader fit-quality distribution and a larger tail of poor or boundary-limited fits (mean $\chi^2_\nu \approx 7$). The CCC turn-off density is not universal (scatter 0.82 dex) and correlates with galaxy size, qualitatively consistent with a spherical reconstruction applied to flattened disc systems. Recast as an acceleration, however, $a_t = V_{\rm flat}^2/R_t$ has scatter 0.33 dex (on the 91-galaxy resolved subset) -- matching the MOND scale $a_0$ (0.34 dex) -- and comparable magnitude of order $2 \times 10^{-10}$ m/s$^2$, with its size correlation removed. Though not designed for galactic dynamics, CCC describes rotation curves as well as galaxy-by-galaxy fitted MOND.
We present a reproducible computational validation and failure analysis of the empirical omega kinematic correction introduced by Flynn and Cannaliato (2025). The algorithm is deliberately minimal: one coefficient per galaxy is calculated from the innermost and outermost measured rotation-curve points and applied to the full observed radial profile before comparison with a baryonic reconstruction assembled from SPARC gas, disk, and bulge components. We preserve the predecessor's frozen 84-galaxy benchmark and publish its exact membership so that the transformation, not sample re-selection, is the object of validation. Without fitting the transformation to the baryonic residual, the primary maximum-disk reconstruction reduces the mean observed-baryonic discrepancy from 51.82 to 30.15 km/s across the frozen 84-galaxy benchmark. Bounded mass-to-light-ratio optimization further reduces the descriptive sensitivity-fit value to 25.45 km/s, while the simple Keplerian reference has a mean RMSE of 74.20 km/s in our earlier analysis [15]. Recalculation from the 84 per-galaxy records shows a resolved mass-to-light optimization benefit (delta RMSE>0.05 km/s) in 53 galaxies and no resolved change in 31. Six galaxies do not beat the Keplerian reference; all six occur at Upsilon_max<= 0.111, whereas their omega values are not concentrated at the high end of the sample. We specify the complete deterministic workflow, native units, endpoint invariants, uncertainty propagation, and formula-level regression checks required to prevent grouping and sign errors. The complete 84-galaxy panel set, population-level error distributions, and failure diagnostics are retained as inspectable outputs. The result is a reproducible astronomical data-transformation benchmark rather than a proposed force law or replacement for dark matter or modified gravity.
To confirm $\Lambda$CDM deviations are due to missing physics (not systematics), one should demonstrate that the model fitting parameters exhibit qualitatively similar redshift drift across independent observables. This is the only way one guarantees new physics. Here, we show that a recent Dark Energy Spectroscopic Instrument (DESI) DR2 Full-Shape (FS) modelling Lyman-$\alpha$ constraint at $z_{\rm eff} = 2.33$ combined with earlier DR1 FS modelling constraints with $0.295 \leq z_{\rm eff} \leq 1.491$ leads to a straight line $\Omega_m(z) = m z + c$ with slope $m = 0.022 \pm 0.012$, $1.8 \sigma$ removed from constant $\Omega_m$. Akaike Information Criterion and Bayesian evidence confirm that constant $\Omega_m$ and increasing $\Omega_m(z)$ are statistically indistinguishable. Through the $Om(z)$ diagnostic, we review how increasing and decreasing $\Omega_m(z)$ trends map to phantom and quintessence dark energy (DE) regimes, respectively. While FS modelling constraints map to phantom DE, the decreasing and increasing $\Omega_m(z)$ trends in DESI BAO and DESI with external data make a phantom crossing inevitable. Since dynamical DE is but one interpretation for $\Omega_m(z)$ trends, it is imperative that different datasets converge on their $\Omega_m(z)$ trends before one jumps to physical conclusions. We forecast how DESI FS modelling $\Omega_m$ constraints will improve up to the final data release and explore the implications for model selection.
Direct inversion in the iterative subspace (DIIS), introduced in 1980, remains the practical default for accelerating Hartree-Fock and Kohn-Sham self-consistent-field (SCF) calculations. Many later methods improve robustness or iteration count, but the near-zero overhead of DIIS makes a broad reduction in total wall time difficult. We introduce AURORA-SCF (auxiliary-curvature unified Riemannian orbital-response acceleration), which evaluates energy and gradient only with the requested target Hamiltonian while obtaining most orbital curvature from an independent valence-STO-3G model. A target-level, transported L-BFGS history corrects the model mismatch; a shifted matrix-free solve, trust region, and geodesic orbital update control the step. In 16 direct CPU RHF pairs spanning 137-1484 atomic orbitals, AURORA-SCF was faster in every case, reducing mean wall time by 26.2% and target J/K builds by 33.3%. In a separate set of 63 converged, energy-matched density-fitted GPU pairs spanning seven molecules, closed- and open-shell formalisms, and HF, PBE, B3LYP, and M06-2X, it was again faster in every included pair, with mean reductions of 26.5% in wall time and 31.9% in target J/K builds. Focused direct CPU and GPU sweeps show mean wall-time reductions of 30-34%. These results establish a specific advance beyond the four-decade DIIS default: transferred, secant-corrected curvature can reduce total SCF wall time, not merely iteration count, without changing the target stationary equations. The same optimization pattern also suggests a route to faster orbital optimization elsewhere in quantum chemistry and to multifidelity optimization across scientific computing.
Background: Localized structure in the equilibrium squared sound speed can affect neutron-star observables, but modifying $dP/d\epsilon$ requires thermodynamically consistent reconstruction and assessment over the complete declared domain. Purpose: We quantify the response to positive and negative localized sound-speed changes around a unified BSk24 baseline while keeping the deformation geometry, admission criteria, reconstruction, and fixed-mass comparison protocol fixed. Method: A Gaussian profile with quintic smootherstep activation is added to $c_{\rm s}^2$. Proposals violating $P>0$ or $0<c_{\rm s}^2\leq1$ anywhere in the retained domain are rejected before reconstruction. Passing cases are reconstructed as effective cold one-fluid barotropes and evolved with the Tolman-Oppenheimer-Volkoff and tidal equations. Results: The $A=0$ case reproduces the undeformed control exactly. A localized change produces a persistent pressure offset, relocates the fixed-mass central state, and yields a mass-dependent, nonlinear, sign-asymmetric response. For $A=-0.8$ and $+0.8$, respectively, $\Delta\Lambda/\Lambda_0=(-46.02\%,+35.33\%)$ at $1.4\,M_\odot$ and $(-63.52\%,+87.17\%)$ at $2.0\,M_\odot$. The reached stiffened feature remains core connected at the reporting endpoints, whereas the softened feature becomes an off-center shell at high mass. Conclusions: These phenomenological BSk24-anchored effective barotropes illustrate how a local sound-speed intervention propagates through thermodynamic reconstruction and stellar structure. They are not BSk24 predictions or evidence for a microscopic composition or phase transition.
Ioannis Papathanasiou· 0 citations
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