Call for Blind Test Data: Testing Inclination Degeneracy Solution

In orbital mechanics it is mathematically impossible to extract the true orbital velocity [math]\beta[/math] and the inclination angle [math]i[/math] from [math]K \propto \beta \sin(i)[/math] exclusively using a 1D spectroscopic curve as input. Resolving this requires independent 3D spatial data (astrometry) or transit observations.

However, within a relational approach, this limitation can be bypassed (apparently) by isolating a second-order systemic scalar invariant,
[math]Z_{sys} = \frac{1}{\sqrt{1-\frac{R_{s}}{r}}} \frac{1}{\sqrt{1-\beta^{2}}}[/math]. This invariant is strictly proportional to the absolute kinetic ([math]\beta^2[/math]) and potential terms, but independent of the observer's line of sight [math]i[/math].

By applying a dynamic 5-parameter inversion (Differential Evolution + MCMC) based strictly on these relational invariants, I recently succeeded in blindly extracting the complete 3D spatial geometry of the S0-2 star using nothing but 1D Keck radial velocity data. The extracted inclination matched the independent GRAVITY 3D-interferometer to within the instrumental noise limits.

Now, for complete methodological purity, I need to isolate myself from the data (it is the only way to convince the skeptic within me).

I am now calling for a strictly blind test. Please participate and help me test these remarkable (but still questionable) results.

CRITICAL DATA REQUIREMENTS:

For the [math]Z_{sys}[/math] invariant shift to mathematically exceed the noise floor of modern spectrographs, the system must be highly relativistic.

1. Kinematic Scale: Peak orbital velocities must exceed ~1000 km/s ([math]\beta > 0.003[/math]). Standard exoplanets will not work because the second-order [math]\beta^2[/math] shift is orders of magnitude smaller than instrumental noise limits. Ideal candidates are tight compact binaries (WD/NS/BH) or other extreme S-stars.

2. Unprocessed Relativistic Data: The dataset must be raw or minimally processed: [Time (MJD), Radial Velocity (km/s) or Redshift (Z), Measurement Error]. Crucially, the data MUST NOT be pre-corrected for Transverse Doppler or Gravitational Redshift (though standard Barycentric/LSR background velocity correction is fine).

3. Optional (for computational efficiency): Providing the Period ([math]P[/math]) and Epoch of Periapsis ([math]T_{peri}[/math]) is helpful to bound the MCMC sampler, but entirely optional if the data covers at least one full orbit.

DATASET EXAMPLE:

MJD,RV_km_s,sigma_km_s,Instrument
51718.50000,1192,100,NIRSPEC
52427.50000,-491,39,NIRC2
52428.50000,-494,39,NIRC2
52739.23275,-1571,59,VLT
52769.18325,-1512,40,VLT
52798.50000,-1608,34,NIRC2
52799.50000,-1536,36,NIRC2
52803.15150,-1428,51,VLT
53179.00000,-1157,47,NIRC2
53200.90875,-1055,46,VLT
53201.63925,-1056,37,VLT
53236.33800,-1039,39,VLT
53428.45950,-1001,77,VLT
53448.18300,-960,37,VLT
53449.27875,-910,54,VLT
53520.50000,-983,37,NIRC2
53554.50000,-847,18,OSIRIS
53904.50000,-721,25,OSIRIS
53916.50000,-671,25,OSIRIS
53917.50000,-692,26,OSIRIS
54300.29167,-485,22,OSIRIS
...

Please drop the raw CSV data or a link below and I'll respond with results of my attempt to recover the orbital parametrization of the anonymised system. Do not provide the system name or accepted parameters. Let the pure numerical framework speak for itself.

Here are my results for the S2 star, extracted strictly from the input stream (MJD, RV_km_s):


=== DYNAMIC PRECESSION RECOVERY ===
Eccentricity (e): 0.88498 (GRAVITY Ref: 0.88466)
Base Arg of Periapsis (ω0): 66.26° (GRAVITY Ref: 66.13°)
Internal Precession: 0.207° / orbit
---------------------------------------------------
Global Kin. Proj. (β): 0.006448
Extracted Inclination (i): 135.68° (GRAVITY Ref: ~134°)
Background Drift (v_z0): -20.56 km/s
Fit Quality (χ²): 166.87


Any suggestions, critiques, or participation are welcome.

Edited 2 hours ago2 hr by Anton Rize