BK-IOD cannot be selected: it is reachable only as a fallback after every Gauss root has failed

The Bernstein-Khushalani 5-parameter linear initial orbit determination is in the package and works, but there is no way to ask for it. orbitfit accepts iod="gauss" or iod="auto", and under auto the BK seed is tried only when every Gauss root has already failed to seed a converged fit (orbitfit.py:1206-1216). For a survey of distant objects that is the wrong order, and the code's own comment at that line says so:

BK-IOD shines on distant short arcs -- exactly where Gauss's three-point geometry is ill-conditioned.

Two things block selecting it, and neither is in the fitter:

1. It is never registered. iod.py registers only gauss (line 201). run_bk_iod is called directly inside do_fit's fallback rather than through the registry, so get_iod("bk") does not exist.
2. _orbitfit hardcodes the accepted names: if iod.lower() in ["gauss", "auto"] (orbitfit.py:1570), with anything else routed to do_other_fit, which raises. iod_methods() already exists in iod.py and is already imported into orbitfit.py at line 87, unused for this.

So a registered method still cannot be reached from the public entry point. The same line is why PR #554 has to append "herget" to that list: every new method needs an edit in a file other than the one it registers in.

What it costs, measured on a real survey

110 trans-Neptunian objects recovered by a shift-and-stack search of DECam Deep Ecliptic Exploration Project (DEEP) data, fields DEEP001-006, by P. H. Bernardinelli, who supplied both the detections and his own orbit fits. 493 detection pairs, median heliocentric distance 42 AU, magnitudes 22.3-26.3, all with MPC designations. Each object has 8-12 observations, taken in pairs about four hours apart, across 3 nights spanning roughly 770 days with the nights 300-400 days apart. Fits are gravity-only with supplied per-observation uncertainties (median 0.13 arcsec).

Because _build_sequence splits on 90-day gaps, seq[0] is a single night -- four observations, four hours -- for every object, and do_fit screens each IOD candidate against it. The Cartesian engine is asked for six free parameters there, ndof = 2.

43 of the 57 Cartesian failures reach flag 0 under the BK engine and 3 are lost. The 57 failures are 49 at flag 3 and 8 at flag 4. The recovered fits are sound rather than merely converged: reduced chi-square p10/median/p90 of 0.18 / 0.48 / 1.44 across all BK flag-0 fits, and heliocentric distances of 35-77 AU with a median of 42.8.

The BK path succeeds because it solves five parameters with gdot pinned by the bound-orbit energy prior, which is tractable against four observations of a distant object where six free parameters are not.

Suggested change

Register a bk_iod(observations, seq) wrapper mirroring gauss_iod's contract -- run_bk_iod on seq[0] at the middle observation's epoch, matching the convention the existing fallback already uses -- and replace the hardcoded list with a registry lookup, iod.lower() == "auto" or iod.lower() in iod_methods(). run_bk_iod and MU_SUN are already importable from layup.routines and layup.constants. do_other_fit's error survives for genuinely unknown names. Tests can extend tests/layup/test_bk_iod.py and test_iod_auto.py.

Deliberately not proposed here

Whether auto should try BK-IOD first for distant objects, rather than only after Gauss has failed. This dataset argues for it, but it is one population of trans-Neptunian objects and Gauss-first is presumably right for the main belt. That is a measurement and a behaviour change, not plumbing, and it should be decided separately from making the method reachable at all.

Drafted with Claude Opus 5.

Start in iod.py with gauss_iod, the registration logic, and iod_methods(), then trace _orbitfit and do_fit in orbitfit.py, especially lines 1206-1216 and 1570. Run the existing tests in tests/layup/test_bk_iod.py and test_iod_auto.py before extending coverage. Done means BK can be selected through the public orbitfit entry point while unknown IOD names still fail as before.