99 galaxies. Zero per-galaxy knobs. One verdict, reported verbatim.
Dark-matter fits give every galaxy its own halo, two or three dials each. This script fits nothing per galaxy: the paper-v07 causal-response kernel runs with global constants (some derived from φ = (1+√5)/2, some RS-motivated, plus declared calibration seams), and is scored against the public SPARC sample (175 disk galaxies; the 99 highest-quality Q=1 curves enter the aggregate). A MOND baseline runs through the identical masks and error model, so the comparison has no home-field advantage. The preregistered pass/fail gate prints its verdict at the end, whatever it says.
What is derived, what is a seam
Derived from φ: the dynamical exponent α = 1 − 1/φ and the mass-to-light ratio
Υ★ = φ. HAS RS BASIS (RS-motivated forms matching the paper fit to ~2%, not
forced): the gas coupling Cξ = 2φ−4 and the profile constants
A = 1 + αlock/2 and p = 1 − αlock/4, where
αlock = α/2 = (1 − 1/φ)/2 (Lean
GravityParameters.A_amplitude, p_steepness). Declared calibration seams, named in
the script header and carried in Lean only as literal definitions: the tick
τ₀ = 7.2997×10−15 s and the rungs Nτ = 142.4,
Nr = 126.3 (the Fibonacci 142/126 reading is conjecture). Nothing varies per galaxy.
Gate says FAIL. Median says 3.6× better.
The preregistered gate fails on the mean, dragged by 17 outliers. The median, 1.52 vs MOND's 5.50 on identical masks and errors, is the strongest zero-per-galaxy result we know of. Both numbers are on this page because both are true.
MOND on the same footing
Simple-μ MOND with the standard a₀ = 1.23×10−10 m/s² runs through the same masks, the same error model, the same Υ★. It scores median 5.50, mean 10.35, with 51 galaxies over χ²/N = 5 against RS's 17. The point of the baseline is that any scoring bias hits both models equally.
NGC 3198, straight from the run
The classic flat-rotation-curve galaxy. Newtonian gravity on the visible baryons (thin line) falls away beyond 10 kpc; the observed curve (squares) stays flat to 44 kpc. The RS kernel (gold) lifts the baryonic prediction with no per-galaxy input; MOND (dashed) overshoots this galaxy. Numbers are copied from the reference output's chart-data block, so you can diff every point.
Aggregate over the Q=1 sample
| Metric (99 galaxies, 1854 masked points) | RS causal-response | MOND (simple μ) |
|---|---|---|
| median χ²/N | 1.516 | 5.499 |
| mean χ²/N | 2.898 | 10.350 |
| galaxies with χ²/N > 5 | 17 | 51 |
| RAR scatter (dex) | 0.198 | – |
| BTFR slope / scatter | 4.001 / 0.230 dex | – |
The baryonic Tully–Fisher slope lands at 4.001 with zero tuning; the deep-MOND prediction is exactly 4. The radial-acceleration-relation scatter of 0.198 dex is computed from all masked Q=1 points.
Run it yourself
One file plus the public SPARC data. Download both, unzip the data next to the script, run. About two seconds. The per-galaxy table, the aggregates, the gate verdict, and the NGC 3198 chart block should match the reference output exactly.
$ unzip -q sparc_data.zip && python3 sparc_rotation_test.py SPARC ROTATION-CURVE TEST: RS causal-response model, zero per-galaxy knobs derived: alpha = 0.381966 C_xi = 0.291796 A = 1.095492 p = 0.952254 seams: tau0 = 7.299682e-15 s N_tau = 142.4 N_r = 126.3 median chi^2/N RS causal-response: 1.5163 MOND: 5.4987 RAR scatter (log10 a_obs - log10 a_model, 1854 points): 0.1976 dex BTFR (99 galaxies): slope = 4.0009, scatter = 0.2297 dex VERDICT: FAIL (mean = 2.898, f_good = 0.626)
HYPOTHESIS with a preregistered falsifier, and the falsifier currently reads FAIL:
the gate demands mean χ²/N < 2.0 and the measured mean is 2.898 (17 outlier galaxies; the median
is 1.52). We report that verbatim rather than switching to the statistic that passes. On the Lean anchoring:
the global constants come from Lean's GravityParameters.lean, and the SPARC score artifacts are
certified in Lean (MassToLightPhiLockedSPARCRerunScoreCard.lean, matching these numbers to 6+
decimals), but the paper-v07 kernel form this lab runs is the paper's, not yet a Lean capstone; Lean's ILG
w_t is a different, time-only kernel. The rungs Nτ = 142.4,
Nr = 126.3 and τ₀ are declared calibration seams, Lean literal defs, not derivations
(the Fibonacci 142/126 reading is conjecture); Cξ, A, and p are HAS RS BASIS (~2% match to the
paper fit); Υ★ = φ is an RS policy choice where SPARC convention would use
~0.5 at 3.6μm. All χ² values, for every theory, depend on the fixed error model (paper Sec. 4.3);
with raw SPARC errors alone nothing fits, RS or MOND or halo fits alike. What IS solid: zero per-galaxy
parameters, an identical-pipeline MOND baseline, and every number on this page reproducible from the two
downloads above.