rtx-cfd: indexed polygon SDF — bit-identical queries, the fluid's measured hot function cut

The 2026-08-30 fluid profile (symbolized samples, rigid AND coupled
phases of the FSI3 default) attributed the fluid step to the function:
polygon_signed_distance 51% rigid / 35% coupled — the embedded mask
rebuild and its ghost reconstruction walk every edge of the ~150-vertex
interface polygon for every cell-centre and face query, every step.
(Also measured, refuting the parked consolidation: Level::new — the MG
hierarchy build — is 0.5-0.7% in BOTH phases; caching it would buy
nothing. The MG smoother at 34-40% is the honest remaining fluid cost.)

PolygonSdf (solvers/incompressible/polygon_sdf.rs): a binned edge
index whose query is BIT-IDENTICAL to polygon_signed_distance by
construction — per-edge distances use the same float ops, the ring
search provably visits a superset of the argmin (convex-projection
lower bound sqrt(d_out^2 + ((r-1)b)^2)), and parity XORs the same ray
tests over exactly the straddling edges (y-binned). Equality is
ASSERTED, not assumed: tests compare to_bits against the brute force
over ~40k adversarial points (flag-like walks, random polygons with
degenerate zero-length edges, horizontal-edge/vertex-y rays). Wired
into EmbeddedBody::polygon and the FSI harness's shared geometry
(rebuilt per set_geometry, ~microseconds for 150 edges).

Verification — the bar for a bit-exact change is digit identity, and
it holds: FSI2 and FSI3 committed defaults reproduce EVERY printed
digit of the banded-LU baseline logs (uy 3.7732±3.7920 / 6.0229±
25.2190 mm, conservation 8.26e-12 / 1.49e-12, rigid drags 121.4 /
426.9); rtx-cfd full suite 0 failures; rtx-fsi lib/piston/transfer/
FSI1 green. The study pins need no re-run: the trajectories are
unchanged by construction and confirmed by measurement.

Wall clock: FSI2 rigid 323 -> 167 s (1.93x), whole default 400 -> 225 s;
FSI3 rigid 420 -> 250 s (1.68x), whole default 539 -> 343 s. Cumulative
with the banded LU this session: FSI3 default 944 -> 343 s (2.75x),
FSI2 524 -> 225 s (2.33x).

Co-Authored-By: Claude Fable 5 <[email protected]>
Claude-Session: https://claude.ai/code/session_01X2GmJXeQ2njUecEKiJZ1G2

crates/specialized/rtx-cfd/src/solvers/incompressible/mod.rs

@@ -26,6 +26,7 @@ pub mod piso;
 pub mod piso_gpu;
 /// Five-point Poisson problems and the multigrid-preconditioned CG solver
 pub mod poisson;
+pub mod polygon_sdf;
 /// SIMPLE algorithm implementation
 pub mod simple;
 /// GPU-accelerated SIMPLE algorithm implementation
@@ -49,6 +50,7 @@ pub use piso::{PisoParameters, PisoResult, PisoSolver};
 #[cfg(feature = "cuda")]
 pub use piso_gpu::PisoGpuSolver;
 pub use poisson::{MultigridParameters, PoissonProblem, PoissonSolution, PoissonSolverKind};
+pub use polygon_sdf::PolygonSdf;
 pub use simple::{ConvectionScheme, SimpleParameters, SimpleResult, SimpleSolver};
 #[cfg(feature = "cuda")]
 pub use simple_gpu::SimpleGpuSolver;