Zero-Parameter Baryonic Retrodiction from Scalar Geometry: The ARK V5.4 Inverse Solver and Environmental Entropy Extensions

Important note: Due to significant issues in application of theory within the code as written, the code nor the paper itself represent a final product application of theory. I found that contamination of an idea for deriving baryon played into a circular dependency for estimation that Claude solved by instituting a hyperparameter clamp, which caused 2/3 of the results that converged to expected values to become near perfect matches without the theory doing much heavy lifting at all. Additionally, one of the initiating scalars that was attempted to be used was the entropy scalar, which what's does not provide us with enough data to properly determine the remaining scalar values. It's not correct application of theory. Due to roughly 1/3 of results converging, I am leaving this uploaded for the moment while I refine proper application. I can only confidently say that there was  29% convergence, not 95%.

One of the more difficult aspects of using AI as a primary tool is how quickly and easily that AI landscape changes, And how quickly a previously reliable process becomes unreliable.

-12 March 2026

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  Description: This repository contains the manuscript, Python solver codebase, and empirical results for the ARK V5.4 inverse solver. This framework presents a zero-free-parameter method for retrodicting baryonic velocity contributions from observed galactic rotation curves by applying a single, unified scalar field equation derived from 1D radial scalar geometry.

  Where standard dark matter halo profiles require hundreds of fitted parameters to model large datasets, the V5.4 solver achieves a global root-mean-square (RMS) residual of 34.8 km/s and a 95.4% convergence rate across 175 galaxies from the SPARC database using solely observable baryonic inputs.

  This publication documents two critical extensions:

  • V5.4ε (Environmental Entropy): Introduces a minimum environmental entropy flux term, achieving 100% convergence. This macro-scale application mirrors the open-system thermodynamic requirements previously identified in subatomic modeling (e.g., neutron decay stability in Papers XXIV and XXV), suggesting a fundamental, scale-invariant feature of the field equation.

  • V5.4ε-full (Diagnostic): An explicitly circular diagnostic tool that optimizes the entropy term per galaxy to map residual structure. The analysis reveals a strong correlation (r = 0.86) with the baryonic-to-observed velocity ratio, indicating that the remaining residual ceiling is primarily constrained by the accuracy of standard mass-to-light (M/L) photometric assumptions rather than framework physics.

  Repository Contents:

  • Manuscript (PDF): Paper XXVI: Zero-Parameter Baryonic Retrodiction from Scalar Geometry.

  • Python Solvers (.py): Standalone scripts implementing the unified field equation for the core V5.4 solver, the V5.4ε extension, and the V5.4ε-full diagnostic tool. (Requires numpy and scipy).

  • Empirical Results (.json & plots): Complete per-galaxy calculations, convergence statuses, optimized ε values, and residual visualizations for all 175 SPARC galaxies.

  (Note: To run the provided Python solvers locally, users must download the canonical rotation curve dataset at https://zenodo.org/records/16284118 and update the local directory path within the code).