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

CANONICAL / SUPERSESSION NOTICE (v4.0) 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intermediate formulations of Wilhoite Scaling Theory (WST) — also referred to as Geometric Scaling Fields (GSF) — are superseded by the canonical formulation released as Version 4.0. Earlier documents, including exploratory derivations, prototype equations, and intermediate parameterizations from Versions 1.x–3.x, 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) v4.0.” This canonical specification is defined by: the frozen set of v4.0 canonical field equations, the associated covariant scalar–metric action formulation, and the v4.0 full-regime reproducibility package included in this record. Together, these materials define the complete and reproducible v4.0 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, and 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 v4.0 Parameter Structure Earlier exploratory implementations of WST introduced expanded parameter sets in order to investigate phenomenological flexibility across astrophysical regimes. In Version 4.0, the theory is reformulated as a dimensionally closed, phenomenological gravitational framework with a minimal global parameter set controlling the geometric response. The canonical formulation consists of: Core geometric response parameters These parameters define the nonlocal gravitational response kernel: rc, prr_c, \; p_rrc,pr where rcr_crc is the characteristic spatial response scale prp_rpr is the spatial decay exponent of the response kernel Coherence parameters ρ∗, mc\rho_*, \; m_cρ∗,mc which determine how local baryonic structure modulates the response field. Cosmological response parameters A0, A1, zt, mz, pzA_0, \; A_1, \; z_t, \; m_z, \; p_zA0,A1,zt,mz,pz which control the redshift-dependent amplitude of the geometric response. Large-scale growth parameters μ0, kq, pk, γs\mu_0, \; k_q, \; p_k, \; \gamma_sμ0,kq,pk,γs which describe the scale-dependent modification of gravitational growth. Background embedding parameter Ωeff\Omega_{\text{eff}}Ωeff which specifies the effective matter-like density governing background expansion in the WST cosmological embedding. Together these parameters define the minimal phenomenological parameterization used for full-regime testing in v4.0. Canonical v4.0 Scope Version 4.0 replaces earlier parameter-expanded or transitional implementations with a unified phenomenological formulation capable of producing predictions across multiple observational regimes. The v4.0 framework simultaneously defines: galaxy-scale gravitational dynamics, cluster-scale lensing morphology, large-scale structure growth, weak gravitational lensing, and late-time cosmological expansion. The theory is defined by a single response potential sourced by baryonic structure, from which all observable gravitational effects are derived. No additional dark-matter particle sector is introduced. Reproducibility Package (v3.2) The v3..2 reproducibility package provides numerical pipelines sufficient to reproduce tests across the following regimes: Galaxy dynamics SPARC rotation curve sample. Galaxy clusters Statistical and morphological gravitational lensing diagnostics including: Bullet Cluster Abell 2744 Abell 370 Cluster analyses focus on lensing morphology, coherence structure, and scale-response behavior, rather than full pixel-level mass reconstruction. Structure growth Linear growth-rate measurements: fσ8f\sigma_8fσ8 Late-time cosmology Distance constraints from: cosmic chronometers baryon acoustic oscillations (BAO) Solar-system consistency Weak-field limits and PPN-level consistency checks. Data Availability The SPARC galaxy database is not redistributed within this record and must be obtained from the original authors. SPARC reference: Lelli, F., McGaugh, S. S., & Schombert, J. M. (2016).SPARC: Mass Models for 175 Disk Galaxies with Spitzer Photometry and Accurate Rotation Curves.Astronomical Journal, 152, 157.doi:10.3847/0004-6256/152/6/157 Cluster κ-maps and survey products are also not redistributed and must be obtained from their respective public data archives. Positioning Wilhoite Scaling Theory is presented as a phenomenologically grounded alternative to dark-matter-based gravitational models, emphasizing geometric structure generated by baryonic distributions rather than additional particle components. The materials provided here are intended for: independent reproduction, critical evaluation, and further theoretical development. Status Version 4.0 represents the current canonical specification of Wilhoite Scaling Theory. Earlier versions remain archived for historical provenance but should not be interpreted as the current formulation of the theory. Future revisions will be issued only in response to: falsification, new observational constraints, or demonstrated internal inconsistency.