We present the Burdick Crag Mass (BCM) framework — a substrate wave model driven by supermassive black hole neutrino flux that classifies SPARC galaxies into three distinct substrate interaction states without dark matter. Using the 175-galaxy SPARC rotation curve dataset (Lelli et al. 2016), we identify a stable tripartite classification: Class I (Transport-Dominated, 9/31 massive bracket), Class II (Residual/Hysteresis, 7/31), and Class III (Ground State, 15/31). This classification remains stable under parameter perturbation, indicating a physical boundary in galactic substrate topology rather than a model artifact. The dark matter signal is reinterpreted as the neutrino maintenance budget of the spatial substrate, funded continuously by the central SMBH. A testable prediction is provided for IceCube/KM3NeT neutrino flavor ratio measurements at galactic edges. Version 1. 2 adds: The BCM Structural Override System (Classes IV-VI), extending the original three-class topology to six physically distinct substrate interaction states. New classes confirmed: Class IV (Declining Substrate — outer rim depletion), Class V-A (Ram Pressure — asymmetric lambda field), Class V-B (Substrate Theft — multi-body SMBH competition), Class VI (Barred Substrate Pipe — bar-channeled flux). Validation runs on three galaxies with the override system confirmed: NGC3953 Class VI delta flipped from -31. 3 to +11. 1 km/s (substrate wins) via bar dipole geometry and LINER throttle; NGC7793 Class V-B flipped to substrate win (+2. 2 km/s) via 2D HI Moment-0 morphology and void depletion; NGC2841 Class I control stable at +28. 4 km/s. Environmental depletion suppression gate confirmed for NGC2976 (substrate vacuum, Newton RMS 3. 7 km/s). 2D HI Moment-0 ingestion live for three THINGS galaxies. BCMSubstrateₒverrides. py and Genesis Renderer visualization methodology included. No per-object tuning parameters maintained throughout. Version 2. 1 adds: Complete solar system planetary substrate solver (all 8 planets). Resonance Hamiltonian H (m) = (cₛ - Omega*R/m) ² confirmed for Earth (m=1), Jupiter (m=1), Saturn (m=6), Uranus (m=2), Neptune (m=2). Mercury m=1 prediction documented for BepiColombo magnetometer target. Gap 7 (Uranus-Neptune Twin Paradox) identified and quantified — Lambda regime classifier implemented. Mixing Length Theory convective velocity added to all planetary parameters. Diamond rain convective pump identified as Uranus substrate mechanism. Full codebase open source: https: //github. com/Joy4joy4all/Burdick-Crag-Mass Version 3. 0 adds: Phase diagnostic framework with cosdeltaₚhi (phase alignment between substrate memory field and forcing field) and decouplingᵣatio (amplitude separation between observable and substrate). These two orthogonal axes distinguish coupled regimes (Class I, cosdeltaₚhi ~ 1. 0) from energy-depleted phase-locked states (Class V-B, phase coherent but structurally empty). Resolution mode boundary discovery: NGC2841 Class I resolution sweep (128/256/512 grid) reveals peak substrate expression at 256 grid; at 512, finer modes fragment the inner field — the mode boundary is itself a physical finding. Neptune/Uranus Q6/Q7 prime mode stability hypothesis: Neptune Q=6 (composite, energy radiates outward, explaining 2. 6x excess heat) versus Uranus Q=7 (prime, irreducible, energy contained internally, explaining thermal silence despite stronger B-field). Data-driven lambda: outerₛlope computed from rotation curve outer 20%, replacing fixed lambda=0. 1 with a physically motivated per-galaxy coupling that preserves the no per-object tuning principle. NGC0801 Class IV outerwinner divergence identified. Language precision: "No per-object tuning parameters" replaces "Zero free parameters" throughout — the global parameters (lambda=0. 1 baseline, kappa=2. 0, grid=256, layers=8) are universal, no per-galaxy tuning occurs. Version 4. 0 adds: Stellar tachocline extension with resonance Hamiltonian correction, 13-star combined arms registry, tachocline gate discovery, and publication-quality figures. STELLAR TACHOCLINE EXTENSION: The BCM wave equation is applied at stellar scale using tachocline induction current Jᵢnd = sigma * vconv * B as the substrate source term. A 13-star registry spans all six BCM galactic classes, organized into vanguard (confirmable) and mystery (anomalous) tiers. The resonance Hamiltonian achieves 9/10 eigenmode matches: Sun m=4, Alpha Centauri A m=4, Epsilon Eridani m=3, AB Doradus m=2, HR 1099 m=2, Proxima Centauri m=1, V374 Pegasi m=1, TRAPPIST-1 m=1, and Betelgeuse m=3. RESONANCE HAMILTONIAN FIX: The prior stellar solver used raw Bessel amplitudes at a constant argument (kR = 2pi for all stars), returning m=5 regardless of physical properties. This is replaced with H (m) = (cₛ - Omega*Rₜach/m) ² ported from the planetary solver. The minimum-energy mode is the predicted eigenmode. Match rate improved from 3/10 to 9/10. TACHOCLINE GATE: Fully convective stars (convective depth fraction >= 0. 9) lock to m=1 — no tachocline means dipole-only substrate coupling. Confirmed for Proxima Centauri, V374 Pegasi, and TRAPPIST-1 (3/3). EV Lacertae at the gate boundary (convdepth=0. 9, mₒbs=2 vs mH=1) identifies a mode boundary analogous to the grid 512 resolution boundary at galactic scale. BETELGEUSE: Red supergiant m=3 from giant convective cells confirmed by Hamiltonian minimum. Interpreted as transition from wave-dominated to convection-dominated substrate regime. Great Dimming 2019-2020 reframed as substrate mode event — directed mass ejection at one of three azimuthal nodes. SCALE INVARIANCE: Average lambdaₛtellar / lambdagalactic = 0. 977. Combined arms: 175 SPARC galaxies (122/175 substrate wins, six-class topology), 8 solar system planets (resonance Hamiltonian confirmed), 13 stars (9/10 Hamiltonian match). One equation across twelve orders of magnitude in spatial scale with no scale-specific tuning. CLASS COVERAGE (all six BCM galactic classes now have stellar analogs): Class I Transport 4/4 (Sun, Alpha Cen A, Epsilon Eri, AB Dor). Class II Marginal 1/1 (EV Lac). Class III Ground State 1/1 (Tau Ceti). Class IV Baryonic-Dominated 1/1 (Vega). Class V-A Ram Pressure 3/3 (Proxima, V374 Peg, TRAPPIST-1). Class VI Barred Pipe 1/1 (HR 1099). Class? Anomalous 2/2 (Tabby, Betelgeuse).
Stephen Justin Senior Burdick (Tue,) studied this question.