PlateOverlapAnalyzer.Capture(parts, OverlapMaterialCache) reuses each clean
program's converted entities and prepared material across requests, and
Analyze(snapshot, previous) reuses pair results whose two parts kept the
same source, exact pose and relative order, renumbering them. A recheck
after moving one part only clips that part's neighbors again.
On 501 real PEP plates: full check median 1 ms / max 6.4 s; incremental
recheck after one move median 0.1 ms / max 38 ms. Incremental results
matched uncached full analysis exactly across 2505 edits.
