Summary

This PR publishes the Wave 3 performance pass across diffusion, diffusion-geometry, spectral, Hodge, and DEC paths.

What changed

• added bench_diffgeo, Wave 3 perf note scaffolding, and IGNEOUS_PERF_NOTES_DIR support for the perf scripts
• reused 1-form operators inside the 2-form diffusion-geometry path and rewrote the generic k-form weak derivative around denser block assembly
• parallelized the generic form up-Laplacian assembly and removed an inner tiny solve with closed-form adjugate arithmetic
• cached the normalized kernel operator for repeated eigensolve matvecs
• fused and parallelized post-kNN diffusion-build passes while preserving the accepted sparse build path
• reused gamma assembly in HodgeWorkspace
• replaced circular workspace preparation with exact matrix formulas for Gamma(x, phi) and the scalar weak Laplacian
• matrixized Hodge curl-energy assembly over cached Markov and gamma data
• added a dense generalized spectrum fast path with Cholesky whitening and exact fallback
• parallelized stable DEC face-incidence construction while preserving per-vertex face order
• recorded kept and rejected experiments in notes/perf/20260306-wave3/

CI smoke impact vs main

The PR smoke workflow on GitHub compares this branch against main on GitHub runners with parallel backend and 4 threads. Those are the right numbers to use for branch-vs-main review.

Headline wins from the current smoke report:

• bench_pipeline_hodge_main: 1.763 s -> 372.939 ms (-78.85%)
• bench_hodge_phase_circular: 1.082 s -> 13.206 ms (-98.78%)
• bench_hodge_phase_curl_energy: 294.807 ms -> 39.683 ms (-86.54%)
• bench_hodge_phase_weak_derivative: 27.624 ms -> 4.518 ms (-83.64%)
• bench_pipeline_diffusion_main/20: 67.129 ms -> 27.147 ms (-59.56%)
• bench_pipeline_diffusion_main/100: 70.464 ms -> 30.595 ms (-56.58%)
• bench_pipeline_spectral_main: 110.190 ms -> 50.714 ms (-53.98%)
• bench_diffusion_build/2000: 54.226 ms -> 20.929 ms (-61.40%)
• bench_weak_derivative/2000/16: 2.727 ms -> 121.210 us (-95.55%)
• bench_curl_energy/2000/16: 10.989 ms -> 1.613 ms (-85.32%)
• bench_eigenbasis/2000/16: 23.269 ms -> 14.480 ms (-37.77%)
• bench_geometry_structure_ms/1000x1000: 89.510 ms -> 74.975 ms (-16.24%)

Local campaign deltas

Some larger numbers in the Wave 3 notes are measured against the campaign's earlier local Release baselines rather than directly against main. Those numbers capture the cumulative effect of the full optimization campaign on the local perf machine.

Examples from the kept Wave 3 artifacts:

• bench_diffgeo_pipeline/4000/64/32/32: 4169.532 ms -> 145.730 ms
• bench_pipeline_hodge_main: 3275.117 ms -> 149.293 ms
• bench_pipeline_spectral_main: 216.192 ms -> 16.783 ms
• igneous-diffusion-geometry --n-points 1000 --output-dir <tempdir>: real 1.40 -> 0.07

Validation

• ctest --test-dir build --output-on-failure -j8
• 14/14 passing
• targeted diffgeo, hodge, spectral, and DEC tests were run for each kept pass and logged in notes/perf/20260306-wave3/journal.md

Notes

• the detailed campaign log, artifacts, and rejected experiments are in notes/perf/20260306-wave3/
• the main remaining shared hotspot is still the large-basis diffusion eigenbasis solve