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

CANONICAL / SUPERSESSION NOTICE (v5.0) All earlier exploratory formulations of Wilhoite Scaling Theory (WST), also referred to as Geometric Scaling Fields (GSF), are superseded by the canonical Version 5.0 specification. The authoritative v5.0 formulation consists of: - the frozen WST / GSF scalar-response field equations- the associated covariant scalar–metric action and Lagrangian density- the auxiliary-field form required for reproducible calculation- the fixed allocation constants and carrier ladder- the non-cluster first-principles reproducibility protocol- the empirical test-results addendum included in this record Earlier versions, including v1.x through v4.2, are retained for provenance but are not authoritative. Version 5.0 supersedes prior cluster-amplitude and phenomenological formulations by separating the theory into: (1) a promoted non-cluster first-principles core candidate (2) a cluster-lensing diagnostic frontier not yet included in the promoted first-principles claim --- THEORY OVERVIEW Wilhoite Scaling Theory (WST / Geometric Scaling Fields) is a baryon-only geometric framework for gravitational phenomena. Rather than introducing non-baryonic dark matter or dark energy sectors, WST proposes that baryonic structure sources a scale-dependent geometric response field. This response modifies effective gravitational behavior across regimes while remaining continuous with Newtonian and relativistic limiting behavior. In the v5.0 formulation, all promoted observables are derived from a single baryon-sourced response potential and its fixed readout rules. The central physical claim is: Baryonic systems generate overlapping scale-allocation fields. The universe enforces coexistence among these fields through a finite geometric response. Observable gravitational effects arise from gradients, curvature, and readouts of this baryon-sourced response rather than from unseen mass components. No dark matter particle sector is introduced. No dark energy fluid sector is introduced in the promoted core. --- CANONICAL v5.0 FIELD CONTENT The promoted v5.0 theory is built from: - a spacetime metric g_{\mu\nu}- a baryonic stress-energy source T^{(b)}_{\mu\nu}- a scalar geometric response field \Phi- an auxiliary allocation field used to express the nonlocal response locally- fixed allocation constants derived from the coexistence fraction C = 1/5 The frozen core constants are: C = 1/5 x_init = 1/2 C(1-C) = 0.16 P_soft = 1 - C(1-C) = 0.84 B_env = 1 + C(1-C) = 1.16 The carrier ladder is fixed as: v_channel = c / 6000 sat_v0 = c / 2400 g0 = c / 1200 These constants define the promoted numerical spine of the theory. --- ACTION AND LAGRANGIAN STATUS Version 5.0 introduces the canonical action-level formulation. The promoted record includes: - the proposed covariant scalar–metric action- the baryon-source coupling term- the response-field kinetic term- the finite-allocation potential- the auxiliary-field representation of the nonlocal response- the Euler–Lagrange field equation- the static weak-field solver recipe- the regime readout rules required to reproduce the empirical tests The action is intended to make WST reproducible as a physical field theory rather than as a collection of empirical response fits. The v5.0 action should be treated as the canonical mathematical statement of the current theory. --- PROMOTED NON-CLUSTER CORE The v5.0 promoted claim applies to the non-cluster core only. Included regimes are: - galaxy rotation / SPARC-scale dynamics- CMB response and projection readouts- late-time expansion / H0 branch structure- BAO / SN consistency tests- solar-system and ring-scale local allocation analogs, where used as supporting evidence Clusters are explicitly excluded from the promoted first-principles claim in v5.0. This exclusion is not a rejection of WST cluster behavior. It reflects the current status of the native cluster source-field problem: the frozen lensing readout is promising, but the raw baryonic/gas/source-map construction is not yet closed. --- REGIME READOUTS The v5.0 non-cluster core uses fixed readout rules. SPARC / galaxy dynamics: - direct carrier readout- identity-scale baryonic response- no dark halo component- no non-baryonic matter sector CMB: - geometric projection readout- fixed sqrt(2)-type projection structure- no dark-sector source term in the promoted response law Expansion / H0: - local-soft branch tied to the carrier ladder- lower/tension branch tied to the solar-squared carrier ratio- no dark-energy fluid in the promoted core BAO / SN: - fixed no-dark-energy expansion response- fixed ruler/readout structure- no H0 scan or ruler scan in the promoted first-principles claim Solar / rings / local systems: - treated as supporting evidence for allocation-shell behavior- not used as the sole foundation of the theory --- EMPIRICAL TEST-RESULTS ADDENDUM The v5.0 record includes a test-results addendum. The addendum summarizes: - SPARC / galaxy rotation tests- CMB frozen replay tests- CMB transfer and projection tests- SN / BAO / H0 branch tests- solar and ring-scale support tests- cluster diagnostic tests and their exclusion boundary The empirical addendum is part of the v5.0 record, but the promoted first-principles claim is limited to regimes whose source/readout rules are frozen and reproducible without dark matter, dark energy, halo fitting, or post-hoc amplitude tuning. --- CLUSTER STATUS IN v5.0 Cluster lensing is not included in the promoted first-principles core of v5.0. Earlier v4.x records included a 29-cluster phenomenological validation using regime-aware amplitude laws, including quantities such as: - A1_obs- Q_coh- baryonic connectivity class- decoupled / transitional / coupled cluster regimes Those results are retained for provenance and as motivation, but they are not the authoritative v5.0 formulation. The current v5.0 cluster status is: - frozen WST cluster lensing readout: promising diagnostic support- native source-to-map cluster generation: unresolved- raw baryon/gas/source-field construction: open problem- cluster regime: excluded from promoted first-principles claim Therefore, v5.0 should not be described as a completed first-principles cluster-lensing theory. Clusters remain an active frontier for future WST versions. --- KEY v5.0 CLAIM The central v5.0 claim is: WST / GSF has a derived non-cluster first-principles core candidate based on a baryon-sourced geometric response field, fixed allocation constants, a fixed carrier ladder, and regime readouts that do not require dark matter or dark energy sectors. The theory is not presented as fully complete across all astrophysical regimes. The strongest current formulation is: WST v5.0 is a first-principles non-cluster core candidate with an explicit action/Lagrangian formulation and an empirical test-results ledger. --- INTERPRETATION In WST v5.0, gravitational phenomenology is interpreted as a consequence of baryonic geometric organization. Matter does not merely sit inside a pre-existing gravitational field. Instead, baryonic organization sources a scale-allocation response, and observed gravitational behavior emerges from the coexistence constraints among overlapping response fields. The theory therefore shifts the explanatory burden from unseen matter components to baryon-sourced geometric response. In this interpretation: - galaxy rotation reflects direct carrier response- CMB structure reflects geometric projection readout- late-time expansion reflects carrier/allocation branch structure- BAO/SN behavior reflects fixed no-dark-energy expansion readout- solar/ring systems provide local analogs of allocation-shell behavior- clusters require a still-unfinished baryonic source-field construction --- REPRODUCIBILITY This record includes enough information to reproduce the promoted v5.0 non-cluster core without relying on hidden code choices. The reproducibility package includes: - canonical constants- action and Lagrangian specification- Euler–Lagrange equation- auxiliary-field form- static weak-field solver recipe- regime readout definitions- parameter-count ledger- test-results addendum- guardrail table- falsification criteria- cluster exclusion boundary A valid reproduction of the promoted v5.0 core must preserve the following guardrails: - no dark matter particle sector- no dark energy fluid sector- no NFW halo fitting- no dark halo mass component- no post-hoc amplitude fitting in promoted claims- no H0 scan in the promoted expansion branch- no BAO ruler scan in the promoted BAO branch- no per-regime hidden tuning- clusters excluded unless explicitly labeled diagnostic --- DATA SOURCES SPARC galaxy data: Lelli, McGaugh, Schombert (2016), AJ 152, 157 CMB data: Planck 2018 public likelihood and spectra products where applicable Supernova data: Pantheon+ / SH0ES-style SN Ia compilations where applicable BAO data: Public BAO consensus and survey products where applicable Cluster lensing maps: Public HST / CLASH / HFF / RELICS-style archives are used only for diagnostic cluster work and are not part of the promoted v5.0 first-principles claim. --- POSITIONING WST v5.0 is presented as a baryon-only geometric alternative to dark-matter and dark-energy phenomenology. The promoted claim is not that every regime is solved. The promoted claim is that a fixed non-cluster first-principles spine now exists: - one baryon-sourced response field- one allocation constant C = 1/5- one carrier ladder- fixed regime readouts- no dark matter- no dark energy- explicit action/Lagrangian formulation- reproducible empirical test ledger Clusters remain outside the promoted claim until the native baryonic source-field construction is solved. --- STATUS Version 5.0 is the current canonical specification of Wilhoite Scaling Theory / Geometric Scaling Fields. It supersedes all previous exploratory versions. The current s