feat(cam-clear): verified concave engagement and island union bound #136
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Delete branch "patman/island-engagement"
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Island lane I-c. First-principles re-derivation of concave arc_engagement (law of cosines, boundary values pinned) with dense proptests vs the exact StockState oracle — retires the "mirror symmetry, untested" caveat that was flagged the riskiest math in the lane. Plus island_union_engagement multi-feature upper bound. IMPORTANT REVIEW NOTE: this commit is DOC-ONLY on the existing arc_engagement code — function bodies verified byte-identical to main across the whole chain (an earlier recon claim that it changed convex behavior was adjudicated false via function-body hashes). Opus review PASS.
Derive the concave arc_engagement branch from first principles (material inside the arc, tool outside; engaged sub-arc via law of cosines) and verify it numerically against exact StockState::engagement over a (delta, r, rho_e) grid -- the branch was previously mirror-symmetry derived and never exercised. Add island_union_engagement, the exact per-feature-distance union bound (design SS3(a)/SS4 ID-7/ID-8) over an island-bearing feature set, with an upper-bound cross-check against StockState. NOTE FOR REVIEW: this commit rewrites the documented contract of `arc_engagement` -- including the convex/concave routing rule that main's existing certified `plan_rings` path already relies on ("convex vs concave is the feature's material side, routed by `is_convex_envelope_arc` from the arc's sweep sign"; an outer wall reads concave, an island wall convex). That is a documentation change only. `arc_engagement` and `is_convex_envelope_arc` are byte-identical to main throughout this whole stack -- verified, no commit in the lane touches either body -- so nothing here alters existing non-island behavior. Read the doc rewrite as pinning the existing routing empirically (the design's P3, resolved by the 2026-07-26 addendum: route by winding, never by a hand-applied island label), not as correcting it. Reviewers who want the empirical basis should read `concave_arc_engagement_matches_stockstate` and `concave_arc_engagement_pinned_disk_is_certified_bound`, which are the first direct exercise the concave branch has ever had. Co-authored-by: patman-assist <patrick-ai@kgroo.co>