Phase 2 shipped the Kerr deriv() and the adaptive RK45 integration loop in
the shader (black_hole.wgsl:260, 320-390), but the CPU mirror in physics.rs
only covered the single-step Kerr derivative (kerr_bending_accel), not the
loop. That left the AGENTS.md 'CPU <-> shader mirror' contract broken for
Phase 2: the spin-dependent capture radius, the adaptive step control, and
the budget = accepted-steps-only / dt_min forced-accept semantics existed
only on the GPU, with nothing testable on the CPU side.
Add a faithful CPU mirror and the loop-level tests that close the gap:
- rk45_step(): Dormand-Prince step mirroring black_hole.wgsl:260-285, using
kerr_bending_accel so it is also the Phase 1 step at chi=0.
- is_captured_rk45(): the full adaptive loop mirroring black_hole.wgsl:320-390
— same seeding (total_path / steps), same reject/retry at dt_min (the
forced-accept floor that prevents infinite retry), same accept-then-refine,
and the spin-dependent capture radius r+(chi) via kerr_horizon.
Tests (tests/physics_test.rs):
- spin=0 RK45 loop captures below bcrit and escapes above (degeneracy).
- spin=0.9 still captures a b~2.0 ray (horizon shrinks but not past b<bcrit).
- capture set does not grow as spin increases across a bcrit-straddling sweep.
- rk45_step error shrinks monotonically with dt (the property the adaptive
loop's reject/accept decision depends on).
Note: probing the error scaling showed it falls between 2nd and 4th order in
dt, not a clean 5th, because of the per-stage normalize() projection the
shader (and now the mirror) applies. The loop only relies on monotonicity, so
this is correct-as-shipped; documented in a doc-comment on rk45_step so a
future reader is not misled by the '45' in the name.
cargo test: 17 passed (3 Phase 1 inline + 14 integration, up from 12).
xfy
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