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A Null Test for Correlations Between Residual Rotation-Curve Parameters and Large-Scale Velocity-Field Kinematics

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May 19, 2026 A Null Test for Residual Rotation-Curve Parameters vs. Velocity-Field Kinematics A Null Test for Correlations Between Residual Rotation-Curve Parameters and Large-Scale Velocity-Field Kinematics FRCMFD Collaboration Methodological Lead: D. HunchNeck AI Auditing: ChatGPT, DeepSeek, Gemini, Copilot Abstract. We test for correlations between baryonic residuals (Δγ_resid) derived from SPARC rotation curves and large-scale kinematic variables from the 2M++ reconstructed velocity field. After controlling for distance — which exhibits strong depth-dependent structure in the shear field (Spearman ρ up to 0.823) — no statistically significant association is detected. Directional alignment (cos θ), shear eigenvalues (λ₁, λ₂, λ₃), and vorticity magnitude (|ω|) all yield partial Spearman correlations |ρ| 0...
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\documentclass[12pt]{article} \usepackage{amsmath, amssymb} \usepackage{graphicx} \usepackage{natbib} \usepackage{geometry} \geometry{margin=1in} \title{ FRCMFD WATCHDOG PAPER — Exploratory Null Test \\ \large A Null Test for Correlations Between Residual Rotation-Curve Parameters \\ and Large-Scale Velocity-Field Kinematics } \author{Derek Flegg} \date{May 2026} \begin{document} \maketitle \begin{abstract} We present an exploratory null test for correlations between the residual rotation-curve parameter $\Delta\gamma_{\rm resid}$ and large-scale kinematic observables derived from the 2M++ reconstructed velocity field. Using a matched sample of 80 SPARC galaxies, we test for associations with directional alignment, shear tensor eigenvalues, and vorticity magnitude. All tests control for distance-dependent structure in the reconstructed field. Raw correlations show weak trends, but all partial correlations (conditioning on distance) are consistent with zero. Bootstrap confidence in...
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FRCMFD PROJECT STATUS UPDATE — METHODOLOGY, ONTOLOGY, AND CURRENT EMPIRICAL POSITION

FRCMFD PROJECT STATUS UPDATE — METHODOLOGY, ONTOLOGY, AND CURRENT EMPIRICAL POSITION This project is NOT seeking AI confirmation or agreement. The purpose of involving multiple AIs is adversarial comprehension, methodological critique, bug hunting, statistical auditing, ontology clarification, and semantic alignment between hypothesis and test design. The workflow is: ontology → mathematical formalization → testable variables → empirical pipeline → data → interpretation NOT: ontology → belief → confirmation. The data decides. PROJECT EVOLUTION (HIGH LEVEL) The project evolved through several distinct phases: • Early RST (2025) exploratory / speculative substrate language nonlinear field intuition finite-state anti-infinite ontology messy but archived, not erased • FRCFMD v1.0 (Apr 2026) formalized nonlinear field equations introduced saturation and substrate response structure moved toward mathematically constrained language • Baseline v1.2 (May 2026) empirical SPARC pipe...
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FRCMFD Paper – Technical Evaluation

FRCMFD Paper – Technical Evaluation 1. Global logical consistency Null hypothesis: γ independent of baryonic and environmental variables is clearly stated and consistently used. Sample sizes: 171 γ fits, 136 with environment (v1.0), 104 (v1.1b), 80 (v1.2) are used consistently across sections and tables. Versioning: v1.0 (raw γ), v1.1b (log Vflat + log L[3.6]), v1.2 (log Vflat + log L[3.6] + log SFR) is consistently described in text, tables, and appendices. No internal contradictions were found between the numerical results in the tables and the narrative summary. 2. Mathematics and statistics 2.1 Rotation curve model and regularization The interpolation formula for V(R) is mathematically well-defined and smooth for γ > 0. The log-normal regularization term R(γ) and total objective L total are correctly specified and dimensionally consistent. The statement that the model “asymptotes to a constant at large R” is correct; the qualif...
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FRCMFD BASELINE PIPELINE v1.0

====================================================================== FRCMFD BASELINE PIPELINE v1.0 ====================================================================== [1] Loaded 136 galaxies γ range: [0.100, 1.500] γ mean: 0.604 ± 0.539 [2] Converting to Supergalactic coordinates... SGX range: [-21.6, 66.3] Mpc SGY range: [-30.4, 109.9] Mpc SGZ range: [-66.0, 48.3] Mpc [3] Interpolating CF4 density... Using: CF4gp_new_64-z008_delta.fits Grid shape: (64, 64, 64) δ range: [-0.7787, 0.7526] δ mean: -0.0704 δ std: 0.2591 [4] Assigning watershed basins... BoA grid shape: (128, 128, 128) Unique basins (valid): [np.int64(1), np.int64(2), np.int64(3), np.int64(4), np.int64(5), np.int64(6), np.int64(7), np.int64(8)] Out of bounds (basin = -1): 0 [5] Computing Δγ residuals... Median γ: 0.4848 Δγ range: [-0.385, 1.015] Δγ std: 0.539 [6] Running statistical tests... γ vs CF4 density δ: Spearman r = 0.0822, p = 0.3416 Δγ vs CF...
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F563-V2 F565-V2 F567-2 F568-1 F568-3 F568-V1 F571-8 F571-V1 F574-1 F574-2 F579-V1 ESO079-G014 ESO116-G012 ESO444-G084 ESO563-G021 IC2574 IC4202 LSBC D563-03 LSBC D564-08 PGC51017 KK98-251 LADDER: Revisiting the Cosmic Distance Ladder with Deep Learning Approaches and Exploring Its Applications Rahul Shah, Soumadeep Saha, Purba Mukherjee, Utpal Garain, and Supratik Pal Published 2024 July 26 • © 2024. The Author(s). Published by the American Astronomical Society. The Astrophysical Journal Supplement Series, Volume 273, Number 2 Citation Rahul Shah et al 2024 ApJS 273 27 DOI 10.3847/1538-4365/ad5558 DownloadArticle PDFDownloadArticle ePub Authors Figures Tables References Article data Download PDFDownload ePub Article metrics 1930 Total downloads 2020 total citations on Dimensions. Share this article Article information Abstract We investigate the prospect of reconstructing the “cosmic distance ladder” of the Universe using a novel deep learning framework called LADDER—Learning Alg...
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FRCMFD — Evolving Theoretical Document

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Geometry is emergent, not fundamental. Curvature is interpreted as a representation of response gradients. FRCMFD — Evolving Theoretical Architecture FRCMFD — Evolving Theoretical Architecture FRCMFD is an evolving theoretical architecture grounded in a response-based ontology, in which geometry, time, and gravitational behavior are treated as emergent effective descriptions arising from the evolution of a finite-capacity substrate state \( S \). The governing equations are provisional and remain under active development; they are progressively shaped and constrained by empirical data, including—but not limited to—rotation curves, baryonic scaling relations, and cosmic-flow environments. Within this framework, the ontology defines the substrate, and observational data guide the ongoing refinement of the constitutive and dynamical equations that describe how \( S \) behaves. This document represents the locked-in, non-overclaimed framing of the current architecture. ...
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