========================================================================== SPARC ROTATION-CURVE TEST: RS causal-response model, zero per-galaxy knobs ========================================================================== phi = 1.618033988750 derived: alpha = 0.381966 C_xi = 0.291796 A = 1.095492 p = 0.952254 Upsilon* = phi seams: tau0 = 7.299682e-15 s N_tau = 142.4 N_r = 126.3 -> r0 = 17.614 kpc a0 = 1.9371e-10 m/s^2 baseline: MOND simple mu, a0 = 1.23e-10 m/s^2 (same masks, same errors) per-galaxy chi^2/N over the Q=1 subsample (99 galaxies, 1854 masked points): galaxy type N RS chi2/N MOND chi2/N D631-7 dwarf 16 1.125 2.318 DDO064 dwarf 13 0.114 0.864 DDO161 dwarf 30 0.448 4.803 ESO079-G014 spiral 13 0.447 8.579 ESO116-G012 spiral 14 0.570 3.112 ESO563-G021 massive 28 1.591 8.924 F563-1 spiral 10 2.104 0.512 F563-V2 spiral 7 2.200 0.211 F568-1 spiral 10 2.977 0.213 F568-3 spiral 16 0.303 2.597 F568-V1 spiral 13 2.499 0.126 F571-8 spiral 11 8.337 15.323 F574-1 spiral 13 0.325 2.652 F579-V1 spiral 13 0.679 2.469 F583-1 spiral 20 1.219 0.652 F583-4 dwarf 11 0.115 4.173 IC4202 massive 17 3.369 22.077 NGC0024 spiral 27 0.548 0.401 NGC0100 spiral 20 0.804 5.386 NGC0801 massive 10 11.997 32.712 NGC0891 massive 18 11.006 44.303 NGC1003 spiral 36 1.521 6.662 NGC1090 spiral 23 6.175 21.690 NGC2403 spiral 70 1.784 7.475 NGC2841 massive 50 1.226 3.166 NGC2903 massive 32 4.711 25.868 NGC2955 massive 17 10.054 20.270 NGC2998 massive 11 5.120 14.106 NGC3109 dwarf 24 1.676 0.269 NGC3198 spiral 40 2.349 12.738 NGC3521 massive 26 3.451 29.576 NGC3741 dwarf 21 1.595 0.297 NGC3893 spiral 10 3.777 16.414 NGC3917 spiral 17 1.016 9.367 NGC3953 massive 8 3.567 24.077 NGC3972 spiral 10 0.783 7.252 NGC3992 massive 9 1.096 11.627 NGC4088 spiral 12 22.214 49.175 NGC4100 spiral 19 0.893 12.724 NGC4157 massive 17 11.164 28.570 NGC4183 spiral 23 0.340 6.811 NGC4217 spiral 18 14.347 44.819 NGC4559 spiral 32 4.948 17.038 NGC5005 massive 13 3.383 14.603 NGC5033 massive 21 3.374 13.297 NGC5055 massive 27 14.756 40.862 NGC5371 massive 18 12.767 44.830 NGC5585 spiral 21 2.246 7.581 NGC5907 massive 19 2.978 16.481 NGC5985 massive 15 4.291 0.484 NGC6195 massive 20 8.086 30.442 NGC6503 spiral 31 1.516 9.118 NGC6674 massive 14 0.798 8.184 NGC6946 spiral 24 9.413 31.431 NGC7331 massive 36 8.537 38.822 NGC7793 spiral 31 1.556 7.754 NGC7814 massive 17 0.446 8.616 UGC00128 spiral 21 1.590 3.370 UGC00191 spiral 9 0.151 2.153 UGC00731 dwarf 12 2.270 0.587 UGC01230 spiral 10 0.460 3.091 UGC01281 dwarf 20 0.341 1.085 UGC02487 massive 17 1.342 3.450 UGC02885 massive 17 1.921 11.414 UGC03205 massive 18 0.619 8.309 UGC03546 massive 26 3.421 22.471 UGC04278 spiral 23 0.500 2.081 UGC04325 spiral 8 1.149 0.617 UGC04499 dwarf 9 0.321 4.069 UGC05005 spiral 8 0.502 5.499 UGC05414 dwarf 6 0.439 4.116 UGC05721 spiral 22 1.907 0.379 UGC05750 dwarf 8 0.036 4.551 UGC06399 spiral 9 0.199 2.292 UGC06446 spiral 17 1.125 0.438 UGC06614 massive 13 6.503 19.567 UGC06667 spiral 8 5.012 0.378 UGC06786 massive 41 0.360 6.361 UGC06917 spiral 11 0.168 4.814 UGC06930 spiral 10 0.261 6.445 UGC06983 spiral 17 0.347 2.431 UGC07125 dwarf 13 1.946 13.495 UGC07151 dwarf 11 0.343 4.290 UGC07323 spiral 9 1.733 9.338 UGC07399 spiral 10 4.335 0.525 UGC07524 spiral 27 0.144 3.378 UGC07603 dwarf 12 0.747 0.844 UGC07608 dwarf 7 1.630 0.029 UGC08286 spiral 17 1.174 0.509 UGC08490 spiral 30 1.184 0.475 UGC08550 dwarf 11 0.483 0.719 UGC09133 massive 62 3.940 17.634 UGC10310 dwarf 7 0.038 2.927 UGC11455 massive 34 5.016 28.510 UGC11820 spiral 7 0.277 2.123 UGC11914 massive 37 0.268 10.830 UGC12632 dwarf 14 0.231 2.112 UGC12732 spiral 16 0.604 1.654 UGCA442 dwarf 8 1.098 0.400 ========================================================================== AGGREGATE (Q=1) ========================================================================== median chi^2/N RS causal-response: 1.5163 MOND: 5.4987 mean chi^2/N RS causal-response: 2.8976 MOND: 10.3501 fraction of galaxies with RS chi^2/N < 2: 0.6263 galaxies with chi^2/N > 5: RS 17 MOND 51 RAR scatter (log10 a_obs - log10 a_model, 1854 points): 0.1976 dex BTFR (99 galaxies): slope = 4.0009, scatter = 0.2297 dex preregistered gate: PASS iff mean chi^2/N < 2.0 AND f(chi^2/N<2) > 0.7 FAIL iff mean chi^2/N > 2.0 OR f(chi^2/N<2) < 0.5 VERDICT: FAIL (mean = 2.898, f_good = 0.626) chart data: NGC3198 (Q=1, Rd = 3.14 kpc) r_kpc vobs verr vbar v_RS v_MOND masked 0.32 24.4 35.9 80.5 68.4 86.7 False 0.64 43.3 16.3 93.7 82.7 103.7 False 0.96 45.5 16.1 100.5 90.9 113.7 False 1.28 58.5 15.4 105.2 96.9 121.3 True 1.61 68.8 7.6 107.1 100.5 126.1 True 1.93 76.9 10.3 105.8 101.3 127.4 True 2.24 82.0 8.1 110.7 106.6 134.3 True 2.57 86.9 7.6 113.1 110.0 138.8 True 2.89 97.6 3.0 113.2 111.5 141.0 True 3.21 100.0 5.3 119.3 117.8 148.6 True 3.54 107.0 7.5 128.8 126.7 159.3 True 3.85 113.0 7.3 138.1 135.5 169.5 True 4.17 117.0 5.2 146.9 144.1 179.5 True 4.50 119.0 5.7 153.3 150.7 187.0 True 4.82 127.0 5.4 159.6 157.3 194.4 True 5.15 132.0 4.3 164.7 163.0 200.7 True 5.46 134.0 2.4 169.5 168.5 206.6 True 5.78 137.0 0.9 173.8 173.5 212.0 True 6.10 140.0 2.8 177.6 178.3 216.9 True 6.43 142.0 0.9 180.7 182.5 221.3 True 6.74 144.0 1.2 181.4 184.6 223.2 True 7.06 146.0 1.6 179.7 184.8 223.0 True 8.04 147.0 3.0 173.4 184.1 221.0 True 9.04 148.0 3.0 167.6 183.3 219.3 True 10.04 152.0 2.0 164.7 184.7 220.1 True 11.04 155.0 2.0 163.4 187.2 222.2 True 12.05 156.0 2.0 161.8 189.2 223.8 True 14.05 157.0 2.0 154.2 187.9 222.3 True 16.07 153.0 2.0 142.4 181.3 216.2 True 18.13 153.0 2.0 134.0 177.1 212.8 True 20.05 154.0 2.0 128.9 175.2 211.7 True 22.12 153.0 2.0 123.4 172.6 210.2 True 24.03 150.0 2.0 118.3 169.5 208.4 True 26.10 149.0 2.0 113.9 167.0 207.1 True 28.16 148.0 2.0 110.3 165.2 206.6 True 30.08 146.0 2.0 106.8 162.9 205.6 True 32.14 147.0 2.0 103.3 160.4 204.5 True 34.06 148.0 2.0 100.7 158.8 204.1 True 36.12 148.0 2.0 98.6 157.7 204.2 True 38.19 149.0 2.0 96.7 156.7 204.5 True 40.10 150.0 2.0 95.2 155.8 204.8 True 42.17 150.0 3.0 94.0 155.5 205.6 True 44.08 149.0 3.0 91.8 153.7 205.0 True