Wilhoite Scaling Theory: A Scalable Geometric Explanation of Galaxy Dynamics and Cosmology

CANONICAL / SUPERSESSION NOTICE (v4.1) All earlier exploratory, parameter-expanded, or intermediate formulations of Wilhoite Scaling Theory (WST)—also referred to as Geometric Scaling Fields (GSF)—are superseded by the canonical formulation released as Version 4.1. Earlier documents, including exploratory derivations, prototype equations, and intermediate parameterizations from Versions 1.x–4.0, are retained solely for historical provenance. These materials document the developmental evolution of the framework but do not represent the current authoritative specification of the theory. The authoritative formulation is: “Canonical Equations of Wilhoite Scaling Theory (WST / Geometric Scaling Fields) v4.1.” This canonical specification is defined by: the frozen set of v4.1 canonical field equations the associated covariant scalar–metric action formulation the v4.1 full-regime reproducibility package included in this record Together, these materials define the complete and reproducible v4.1 formulation of the theory. Theory Overview Wilhoite Scaling Theory (WST), also referred to as Geometric Scaling Fields (GSF), is a baryon-only geometric framework for gravitational phenomena. Rather than invoking non-baryonic particle dark matter, WST proposes that baryonic structure generates a scale-dependent geometric response in the gravitational sector. This response modifies effective gravitational behavior in low-acceleration regimes while remaining continuous with Newtonian and relativistic limits. The resulting geometric response produces effective gravitational phenomena consistent with: galaxy rotation curves cluster-scale gravitational lensing morphology large-scale structure growth late-time cosmological distance observables The theory is formulated as a nonlocal geometric response sourced by baryonic structure, encoded through a scale-dependent response kernel and associated scalar–metric coupling. Canonical v4.1 Parameter Structure Earlier exploratory implementations introduced expanded parameter sets to explore phenomenological flexibility across regimes. In Version 4.1, the theory is reformulated as a dimensionally closed framework with a minimal global parameter set controlling the geometric response. Core geometric response parameters rc, pr rc: characteristic spatial response scale pr: spatial decay exponent Coherence parameters ρ*, mc These govern how local baryonic structure modulates the response field. Cosmological response parameters A0, A1, zt, mz, pz These control the redshift evolution of the geometric response. Large-scale growth parameters μ0, kq, pk, γs These describe scale-dependent growth modification. Background embedding parameter Ωeff This defines the effective matter-like density governing background expansion. Effective galaxy-regime collapse (new in v4.1) Version 4.1 establishes that the galaxy-scale response admits a collapsed three-parameter representation: σ_scale, Ac, As corresponding to: radial response scale compactness amplitude morphology amplitude This is a derived manifold of the canonical parameter space, not an additional parameterization. It provides an equivalent low-dimensional representation of the galaxy operator with no per-galaxy theoretical fit parameters. Canonical v4.1 Scope The v4.1 framework defines a unified response across: galaxy dynamics cluster lensing morphology large-scale structure growth weak lensing late-time cosmology All observables are derived from a single baryon-sourced response potential. No dark matter particle sector is introduced. Reproducibility Package (v3.2 lineage, extended in v4.1) The v3.2 pipeline (retained as the validated computational baseline and extended in v4.1) supports reproducibility across: Galaxy dynamics SPARC rotation curve sample Galaxy clusters Version 4.1 extends validation to a 29-cluster sample, including both merging and relaxed systems. Cluster sample (N = 29): a1423, a209, a2261, a2744, a383, a611, abells1063, bullet, clj1226, macs0025, macs0329, macs0416, macs0429, macs0647, macs0717, macs0744, macs1115, macs1149, macs1206, macs1311, macs1423, macs1720, macs1931, macs2129, ms2137, rxj1347, rxj1532, rxj2129, rxj2248 Cluster analyses are performed in two complementary regimes: (1) 2D morphological response Convergence (κ) comparison Peak offsets Multi-band scale decomposition Coherence / asymmetry structure (2) 1D scale-spectrum formulation (new in v4.1) Clusters are additionally represented through a reduced observable: λ_pred ↔ λ_obs This compresses cluster structure into: characteristic scale (λ) band power distribution pairwise separation statistics entropy / coherence metrics This enables: cross-cluster comparison in a unified space regime classification (relaxed vs merging) reduced-dimensional validation of the response law Structure growth Linear growth rate fσ8 Late-time cosmology Cosmic chronometers BAO Solar-system consistency Weak-field / PPN constraints Data Availability SPARC data must be obtained from: Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016)Astronomical Journal, 152, 157doi:10.3847/0004-6256/152/6/157 Cluster lensing maps must be obtained from their respective public archives. Positioning WST is presented as a phenomenological alternative to dark-matter-based gravity, in which gravitational structure arises from baryonic geometry rather than unseen particles. Version 4.1 strengthens this position by demonstrating: a low-dimensional galaxy response (3 parameters) a structured multi-cluster validation (29 systems) a new reduced cluster observable (1D scale-spectrum) Status Version 4.1 is the current canonical specification of Wilhoite Scaling Theory. Earlier versions are retained for provenance but are superseded. Future revisions will be issued only in response to: falsification new observational constraints demonstrated internal inconsistency