Add BK 5-parameter linear IOD (run_bk_iod) + complementary-IOD sweep

[matthewholman]

This branch was developed with Claude Code, on top of an initial
implementation I had started.

Adds a universal-BK 5-parameter linear initial orbit determination
(run_bk_iod) as the layup-side analog of liborbfit's prelim_fit,
plus an engine-sweep tool that quantifies how BK-IOD compares to
Gauss on the diagnostic-scan dataset.

What

A single closed-form weighted least-squares solve over (α, β, γ, α̇, β̇) with γ̇ pinned to 0. Per-observation model (small-angle
no-gravity, gnomonic tangent-plane projection, light-time corrected):

t_i    = (jd_i − (r_obs_i · n̂₀) / c) − epoch
X_i    = r_obs_i · â,    Y_i    = r_obs_i · b̂
x_obs  = (ρ̂_i · â) / (ρ̂_i · n̂₀)
y_obs  = (ρ̂_i · b̂) / (ρ̂_i · n̂₀)

x_obs = α + α̇·t_i − γ·X_i
y_obs = β + β̇·t_i − γ·Y_i

γ̇'s covariance is filled from the bound-orbit energy prior
(σ_γ̇² from bk_basis::sigma_gdot_sq). 6×6 BK covariance is
transformed to Cartesian via the analytic dcart_dbk chain rule.
Returned as a standard FitResult with method="bk_iod".

Headline result: BK-IOD and Gauss are complementary

Running tools/bk_iod_sweep.py on the diagnostic-scan dataset (98
cases, σ_obs = 0.1″, BK LM applied after each IOD as the seed):

Outcome	Count
Gauss→LM converges, BK→LM also converges	64
Only BK→LM converges	8
Only Gauss→LM converges	18
Both fail	8 (all 0.04-day arcs, 3 obs — data limit)

So a pipeline that tries Gauss and falls back to BK covers
90/98 cases, vs Gauss alone (82) or BK alone (72).

Across the 64 cases where both pipelines converge:

• Drift ratio (BK_LM / Gauss_LM): median 0.26, mean 0.56 (BK
  seeds give ~4× tighter LM convergence on the typical case)
• Iter ratio (BK_LM / Gauss_LM): median 0.68, mean 0.85 (BK
  seeds need ~32% fewer LM iterations)

Per-population breakdown (BK win = both converge and BK closer to truth):

Population              n   G->LM ok  B->LM ok  BK win  G win  BK only  G only
centaur_15AU           14         12        12      11      1        0       0
centaur_25AU           14         12        12      10      1        1       1
classical_42AU         14         11        13       8      3        2       0
mainbelt_2.5AU         14         12         6       4      1        1       7
mainbelt_3.5AU         14         13         5       4      1        0       8
scattered_70AU         14         10        12       7      2        3       1
sednoid_80AU           14         12        12      10      1        1       1
TOTAL                  98         82        72      54     10        8      18

Pattern: BK-IOD dominates Gauss for distant objects (centaur,
classical, scattered, sednoid: 46 BK wins vs 8 Gauss wins). Gauss
wins for mainbelt where BK-IOD's small-γ·ze assumption breaks.

Documented regime of validity

bk_iod.cpp carries an explicit "REGIME OF VALIDITY" block in its
docstring with an empirical sweet-spot table across arc lengths.
BK-IOD is sub-percent on heliocentric distance for TNOs at well-
chosen arcs (5-30 days for 40-80 AU objects), but fails outside its
regime — mainbelt at >1 day gives catastrophic answers. The model
omits the perspective factor 1/(1 − γ·ze); that's a feature of
linear IODs (same as prelim_fit), not a bug, and is intended use
is to seed the BK LM, not produce a final orbit.

Tests

tests/layup/test_bk_iod.py covers (10 tests, all passing):

• Smoke: empty / few-obs guards return without crashing.
• test_bk_iod_distant_objects: BK-IOD recovers truth to within
  a few percent of r_helio on 4 representative distant cases
  (sweet-spot tolerances per the regime table).
• test_bk_iod_seeds_lm_to_truth: the actual intended use —
  BK-IOD's output, fed into run_bk_native_fit, converges to
  within 1% of truth on all 4 cases, even when the IOD itself is
  several percent off. LM convergence basins are wider than
  BK-IOD's bias.

New files

src/lib/orbit_fit/bk_iod.cpp   ~190 lines, inlined into namespace orbit_fit
src/lib/orbit_fit/orbit_fit.cpp  one-line include
src/main.cpp                  bk_iod_bindings registration
tests/layup/test_bk_iod.py    10 tests
tools/bk_iod_sweep.py         engine-sweep harness, produces the table above

Dependencies

Stacks on feat/bk-everywhere (PR #326 — provides the bk_basis
primitives, the BK LM driver that BK-IOD seeds, and the dispatch
infrastructure). Once #326 lands, this PR collapses to its 3 new
commits.

Review Checklist for Source Code Changes

• Does pip install still work?
• Have you written a unit test for any new functions? — tests/layup/test_bk_iod.py, 10 tests
• Do all the units tests run successfully? — full suite green
• Does Layup run successfully on a test set of input files/databases? — full diagnostic-scan sweep ran cleanly
• Have you used black on the files you have updated?