Burdick Crag Mass: A Substrate Wave Model for Galactic Rotation Curves Without Dark Matter — v7 with Anchor Partition Regime Map, ROOT_REENTRY Anatomy, and Macro-Torsion Operator - Tully-Fisher Exponent Stability

Version 7.0: Paper A of the Burdick Crag Mass (BCM) framework. All results from v6 are retained. Version 7.0 adds the Anchor Partition Regime Map, ROOT_REENTRY galaxy anatomy, and a structurally regime-safe Macro-Torsion operator tested against the complete SPARC175 sample. Core BCM performance (retained from v6): BCM beats Newtonian baryonic fits on 130 of 175 SPARC galaxies (74.3%) and beats MOND on 172 of 175 (98.3%). Mean reduced chi-squared: BCM 63.1, Newton 157.6, MOND 1122.6. Four frozen global parameters plus one amplitude coefficient per galaxy. Tully-Fisher exponent alpha = 3.42 (95% CI [3.03, 3.88]), with bracket-stratified breakdown at the massive velocity bracket (alpha = -0.29, CI fully below classical) identifying a scale-dependent substrate coupling transition. Version 7.0 additions: The Anchor Partition Ratio (APR) is applied to all 175 SPARC galaxies as a direct decomposition of observed rotation curves against Newtonian baryonic predictions, requiring no BCM solver execution. APR = (Vobs squared minus V_newton squared) divided by Vobs squared, computed point-by-point from published SPARC data. Across 175 galaxies, the APR median is 0.693 and 152 of 175 galaxies (86.9%) sit on the substrate-dominant side of the decomposition. Six empirical APR regimes are identified: MASS_FLOOR (23 galaxies, Newton explains the curve), DWARF_INTERMEDIATE (18 galaxies), SUBSTRATE_PLATEAU (62 galaxies, vmax 50-150 km/s, APR_outer median 0.77, BCM wins 91.9%), MIXED_TRANSITION (29 galaxies), SUPPRESSION_VALLEY (37 galaxies, vmax 150-300 km/s, APR_outer median 0.47, Newton wins 75.7%), and ROOT_REENTRY (6 galaxies, vmax above 300 km/s, APR_outer median 0.60, BCM underfit). The regime assignment is determined by vmax and APR_outer without solver execution. Joining the regime labels with archived BCM solver records confirms the regime map predicts BCM performance: SUBSTRATE_PLATEAU recovers 91.9% BCM wins and SUPPRESSION_VALLEY recovers 75.7% Newton wins. A sharp APR discontinuity is confirmed at 125 km/s: mean APR_outer below 125 km/s is 0.6179 versus 0.4248 above, a delta of +0.193. This boundary aligns independently with the Tully-Fisher exponent transition reported in v6 (peak bracket alpha at mid-velocity before collapse at massive bracket), constituting two independent measurements identifying the same substrate transition in the SPARC data. The six ROOT_REENTRY galaxies (ESO563-G021, NGC2841, NGC5985, UGC02487, UGC02885, UGC02953) carry APR_outer between 0.52 and 0.76, indicating substantial outer-disk substrate signal. However, the current BCM solver underperforms Newton on these systems (mean BCM outer RMS 94.0 versus Newton outer RMS 78.7). Anatomical analysis of each galaxy confirms the substrate signal is outer-disk concentrated in 5 of 6 systems, and the solver failure is largest in the outer radial zone. UGC02487 (vmax = 383 km/s) is the sole ROOT_REENTRY BCM win and is identified as the primary calibration target. A Macro-Torsion operator is proposed to address the ROOT_REENTRY outer-disk underfit: T = eta times Theta(vmax minus 300 km/s) times the absolute value of (partial v_phi over partial r minus v_phi over r). The Heaviside function at v_crit = 300 km/s gates the operator: it fires only for ROOT_REENTRY systems and produces zero effect on all other regimes. Tested against all six APR regimes, the operator shows 53% RMS sensitivity for ROOT_REENTRY and exactly 0.000% sensitivity for every other regime across the full eta sweep, confirming structural isolation. The operator reduces ROOT_REENTRY mean outer RMS from 113.5 to 58.4 at first-probe parameters. It is not yet integrated into the BCM solver; it is presented as a confirmed directional extension with a falsifiable prediction: the six ROOT_REENTRY galaxies should show improved outer-disk residuals when the solver is extended with this term. A companion Volume Dilatant operator was tested and rejected as formulated: it degraded control regime performance catastrophically (SUPPRESSION_VALLEY outer RMS increased 305%) due to per-galaxy normalization that removed mass discrimination. A physically anchored reformulation is reserved for a future version. All theoretical concepts, dimensional ontology, experimental design, and originating insights belong solely to Stephen Justin Burdick Sr. Computational processing was performed at SJB's direction using AI tools. Emerald Entities LLC — GIBUSH Systems. Version 3.0: A substrate-based phenomenological alternative to cold dark matter in which the dark matter signal is modeled as the energy maintenance budget of a pre-existing 2D spatial substrate. Using four global parameters (lambda=0.1, kappa=2.0, grid=256, layers=8) and zero per-galaxy tuning, we classify 175 SPARC rotation curve galaxies into six physically distinct substrate interaction states. On 29 representative galaxies, BCM achieves a mean reduced chi-squared of 42.1 compared to NFW's 92.1 (two fitted parameters per galaxy) and MOND's 1630.4. The framework generates falsifiable predictions for IceCube/KM3NeT neutrino flavor gradients, Betelgeuse tachocline recovery, and binary mass transfer rates. All code and data: https://github.com/Joy4joy4all/Burdick-Crag-Mass Version 4.0: Preprint presenting a substrate wave model for galactic rotation curves using four frozen global parameters and zero per-galaxy tuning. Reduced chi-squared comparison against NFW and MOND on 29 SPARC galaxies: BCM wins 13/29 (mean χ²=42.1 vs NFW 92.1), dominates massive bracket 7/12 (avg χ²=62.7 vs NFW 241.8). MOND wins 0/29. The substrate maintenance luminosity scales as L_ν ~ v_max^3.9, independently recovering the baryonic Tully-Fisher relation (L ~ v^4; Tully & Fisher 1977) from the same frozen parameters — this scaling was not an input. All 29 galaxies remain sub-Eddington (max L_ν/L_Edd < 6×10⁻⁴). Predicted neutrino flux exceeds IceCube point-source sensitivity by 2-5 orders of magnitude for galaxies within 20 Mpc. All code and data publicly available on GitHub. Included, v1.0 and v2.0 drafts Version 5.0: Adds Einstein coupling (stress-energy tensor T_μν derived from physical velocity excess, Newtonian limit 4/5 PASS, conservation 10⁻²⁰, substrate enclosed mass 10⁷-10¹² M☉), null pump proof (σ→0.000000 without SMBH injection, 5/5 ESSENTIAL), and boundary dynamics (three substrate regimes: diffusive healing 0.99987, coherence failure 0.742, boundary nonlinear 38×; σ_crit saturation limit discovered; Alpha Centauri 8/8 stable; Π = σ_edge/σ_crit control parameter). Covers v1-v24 results. Full chi-squared comparison (13/29 BCM wins, mean χ²=42.1 vs NFW 92.1), neutrino flux prediction (L_ν ~ v^3.9 Tully-Fisher recovery), and falsifiable predictions including $225 benchtop device. Version 6.0: Paper A of the Burdick Crag Mass (BCM) framework, version 6.0. This update presents results from the complete 175-galaxy SPARC rotation curve sample, replacing the 29-galaxy representative analysis in v5. Headline results: BCM beats Newtonian baryonic fits on 130 of 175 galaxies (74.3%). BCM beats MOND on 172 of 175 galaxies (98.3%). Mean reduced chi-squared: Newton 157.6, MOND 1122.6, BCM 63.1. Median reduced chi-squared: Newton 51.6, MOND 343.9, BCM 17.7. Parameter count: BCM uses four frozen global parameters (lambda=0.1, kappa_BH=2.0, grid=256, layers=8) plus one amplitude coefficient per galaxy. An ablation study confirms the per-galaxy amplitude carries real physical information: a single global amplitude fit (1 parameter total) performs 13.8x worse than per-galaxy fitting, and an unscaled fit (0 parameters) fails catastrophically. BCM's parameter count (1 per galaxy) sits between NFW dark matter halos (2 per galaxy) and MOND (1 global). Tully-Fisher exponent stability: Full-sample alpha = 3.42 with 95% confidence interval [3.03, 3.88], consistent with classical baryonic Tully-Fisher. Bracket-stratified bootstrap (1000 resamples) reveals substantial scale-dependence: the relation breaks down at the massive bracket (v_max > 200 km/s, alpha = -0.29, CI fully below classical). This scale-dependent transition motivates a theoretical extension in a forthcoming companion paper. Paper A's claims do not depend on that extension. Content retained from v5: six-class substrate taxonomy, Einstein coupling with stress-energy tensor T_mu_nu, null pump proof (sigma to zero without SMBH injection, 5 of 5 essential), boundary dynamics with sigma_crit saturation clamp, three perturbation regimes, Pi = sigma_edge over sigma_crit control parameter, binary stellar dynamics on Alpha Centauri, HR 1099, and Spica, and falsifiable predictions for IceCube/KM3NeT flavor gradients, Betelgeuse tachocline recovery (2030-2031), and a 225 dollar benchtop device. Production run: 175 galaxies at grid=256 with 25000 integration steps per galaxy, 148.6 minutes wall time on a single NVIDIA GPU. Source data: BCM_v26_Tully_Fisher_Amplitude_Scaling_Ablation (Test 2 revision 6) and BCM_v26_Tully_Fisher_Exponent_Stability (Test 4), both completed 2026-04-21 and referenced by timestamp in the paper.