USR-2026-0049 · Galactic dynamics
In the SPARC radial-acceleration relation, the parameter-free MOND acceleration scale a₀ is mildly disfavored. The canonical a₀ sits +2.6σ above the data's own per-galaxy median offset (+0.116 dex); the zero-parameter cosmological guesses cH₀/2π and cH₀/6 land at +1.6σ and +2.0σ; a free-fit a₀ is consistent (+0.3σ).
PROVISIONAL
canonical a₀ +2.6σ_median; free-fit +0.3σ_median
re-run & confirmed 2026-07-12 (R0 — founder CI; independence pending)
A zero-free-parameter test of whether the RAR acceleration scale equals a cosmological combination of c and H₀. Canonical a₀ is marginally high (+2.6σ_median); a free-fit a₀ is fine — a marginal, neither a detection nor a kill.
Falsify-box — how to kill this claim
SURVIVED
parameter-free a₀ (cH₀-type) is excluded at >3σ_median, or confirmed at <1σ_median
Verification record — every quoted number, re-run 2026-07-12
| quantity | measured | verdict |
|---|---|---|
| canonical a₀ offset | +2.6σ_median (+0.116 dex) | MATCH |
| cH₀/2π offset | +1.6σ_median (+0.072 dex) | MATCH |
| free-fit a₀ offset | +0.3σ_median (+0.016 dex) — consistent | MATCH |
Provenance
script: rar_a0_zero_param_test.py
script status: PRESENT
datasets: SPARC rotation curves · claim-scripts (downloadable from /data — run it yourself) · sparc-rotation-curves (downloadable from /data — run it yourself)
re-run: 2026-07-12
script status: PRESENT
datasets: SPARC rotation curves · claim-scripts (downloadable from /data — run it yourself) · sparc-rotation-curves (downloadable from /data — run it yourself)
re-run: 2026-07-12
Status, honestly
marginal: parameter-free a₀ offsets are +1.6σ to +2.6σ_median; a free-fit a₀ is consistent. Status here is computed from evidence — the author cannot set it, and neither can we. Independent reproduction would move it; nothing else will.
§ Reproduction
rar_a0_zero_param_test.py
The founder's own run of this script, captured verbatim. A match proves the result is reproducible; it is still R0 on this registry's independence rings — same code, so it cannot move a status. Only an outside run does that.
A · Recorded
founder's machine · 2026-08-02
rows parsed: 3391, kept after vbar2>0 & Vobs>0: 3389
galaxies total: 175, galaxies kept: 175
=== (1) FREE a0 FITS ===
std objective (shape-only): a0 = 8.1609e-11 std = 0.1951 dex rms = 0.1968 dex mean offset = +0.0256 dex
RMS objective (shape+amplitude): a0 = 9.5135e-11 std = 0.1953 dex rms = 0.1953 dex mean offset = +0.0024 dex
a0 scan (objective values):
a0 std(dex) rms(dex) mean(dex)
6.000e-11 0.1957 0.2080 +0.0702
7.000e-11 0.1953 0.2011 +0.0481
8.000e-11 0.1951 0.1972 +0.0285
8.160e-11 0.1951 0.1968 +0.0256
9.000e-11 0.1952 0.1955 +0.0109
1.000e-10 0.1954 0.1954 -0.0052
1.082e-10 0.1956 0.1964 -0.0174
1.133e-10 0.1958 0.1973 -0.0246
1.200e-10 0.1960 0.1989 -0.0336
1.300e-10 0.1964 0.2018 -0.0463
1.500e-10 0.1972 0.2091 -0.0694
=== (2) FIXED-a0 (ZERO-PARAMETER) TESTS ===
N points = 3389
case a0 rms(dex) std(dex) mean(dex) penalty vs free
cH0/(2pi) 1.0824e-10 0.1964 0.1956 -0.0175 +0.565% (+0.00110 dex)
cH0/6 1.1335e-10 0.1973 0.1958 -0.0247 +1.045% (+0.00204 dex)
canonical 1.2000e-10 0.1989 0.1960 -0.0336 +1.840% (+0.00359 dex)
FREE(rms) 9.5135e-11 0.1953 0.1953 +0.0024 +0.000% (+0.00000 dex)
Bootstrap (resample galaxies, 2000 draws): delta-RMS(fixed - free refit)
bootstrap free a0 (rms obj): 9.5449e-11 16-84%: [8.8255e-11, 1.0313e-10]
cH0/(2pi): delta-rms = +0.00105 dex [16-84%: +0.00018, +0.00268] P(worse than free) = 1.000
cH0/6 : delta-rms = +0.00197 dex [16-84%: +0.00061, +0.00406] P(worse than free) = 1.000
canonical: delta-rms = +0.00349 dex [16-84%: +0.00159, +0.00612] P(worse than free) = 1.000
=== (3) PER-GALAXY a0 (knee-leverage galaxies) ===
galaxies with >=8 pts spanning g_bar<5e-11 AND g_bar>2e-10: 34
per-galaxy a0: median = 9.1787e-11 16-84%: [5.5812e-11, 2.0005e-10]
in dex around median: [-0.216, +0.338]
std of log10(a0_gal) = 0.262 dex over 34 galaxies
expected scatter from 10% distance errors alone: 0.041 dex (a0 ∝ 1/D)
expected scatter from 15% distance errors alone: 0.061 dex (a0 ∝ 1/D)
Observed per-galaxy scatter 0.262 dex vs 0.041-0.061 dex distance floor
-> excess scatter (quadrature, vs 15% D err): 0.254 dex
per-galaxy details (sorted by a0):
galaxy a0 rms(dex) Npts D(Mpc)
NGC4217 3.627e-11 0.2746 19 18.00
NGC5371 4.239e-11 0.0933 19 39.70
UGC03580 4.288e-11 0.1965 47 20.70
NGC6195 4.403e-11 0.0374 23 127.80
NGC0801 5.048e-11 0.0784 13 80.70
NGC5055 5.382e-11 0.0397 28 9.90
UGC06614 6.094e-11 0.0776 13 88.70
UGC02916 6.397e-11 0.1039 43 65.40
NGC4157 6.530e-11 0.0597 17 18.00
NGC0289 6.849e-11 0.0636 28 20.80
NGC6946 6.972e-11 0.0383 58 5.52
NGC0891 7.048e-11 0.0896 18 9.91
NGC2955 7.359e-11 0.0503 24 97.90
NGC7331 7.424e-11 0.0578 36 14.70
NGC3198 8.364e-11 0.1303 43 13.80
NGC2683 8.890e-11 0.0557 11 9.81
UGC03546 8.903e-11 0.0946 30 28.70
UGC09133 9.455e-11 0.0730 68 57.10
IC4202 1.090e-10 0.2321 32 100.40
NGC2903 1.128e-10 0.2180 34 6.60
UGC05253 1.199e-10 0.0713 73 22.90
NGC5033 1.237e-10 0.0555 22 15.70
NGC3893 1.280e-10 0.0330 10 18.00
UGC02885 1.335e-10 0.0513 19 80.60
NGC3521 1.397e-10 0.0283 41 7.70
UGC08699 1.647e-10 0.0480 41 39.30
NGC6674 1.657e-10 0.0735 15 51.20
UGC03205 1.871e-10 0.0726 48 50.00
NGC7814 2.051e-10 0.0324 18 14.40
UGC02953 2.150e-10 0.1159 115 16.50
UGC06787 2.449e-10 0.0643 71 21.30
UGC06786 2.914e-10 0.0617 45 29.30
UGC02487 3.028e-10 0.0561 17 69.10
NGC2841 3.460e-10 0.0571 50 14.10
error on per-galaxy median ~ 0.0449 dex
cH0/(2pi): log-offset from per-gal median = +0.0716 dex -> +1.6 sigma_median
cH0/6 : log-offset from per-gal median = +0.0916 dex -> +2.0 sigma_median
canonical: log-offset from per-gal median = +0.1164 dex -> +2.6 sigma_median
FREE(rms): log-offset from per-gal median = +0.0156 dex -> +0.3 sigma_median
B · Yours
not runnable in-browser
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