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 ~ vₘax³. 9, independently recovering the baryonic Tully-Fisher relation (L ~ v⁴; Tully & Fisher 1977) from the same frozen parameters — this scaling was not an input. All 29 galaxies remain sub-Eddington (max L_ν/LEdd 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 Tₘuₙu, null pump proof (sigma to zero without SMBH injection, 5 of 5 essential), boundary dynamics with sigmacrit saturation clamp, three perturbation regimes, Pi = sigmaₑdge over sigmacrit 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: BCMᵥ26TullyFisherAmplitudeScalingAblation (Test 2 revision 6) and BCMᵥ26TullyFisherExponentStability (Test 4), both completed 2026-04-21 and referenced by timestamp in the paper. All theoretical concepts, experimental design, and originating insights belong solely to Stephen Justin Burdick Sr. AI systems (Claude, ChatGPT, Gemini) were used strictly as computational processing tools at the direction of the Foreman. Emerald Entities LLC — GIBUSH Systems.
Stephen Justin Senior Burdick (Tue,) studied this question.