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An arc lead-in meeting a straight window edge tangentially has a double root at its joint. Rounding split it into two contacts a few 1e-8 apart, or dropped it so the exact ray fallback reported the joint as an uncertain contact. Either refused a valid entry, so N26-27U's windows lost most of their entries and the plate never planned. Treat a contact within 1e-6 of a joint its boundary passes through as the joint, and let the exact line fallback skip ray hits at contacts already recorded. The pinned-hole test now expects the other hole's nearest entry rather than the fallback both runs used to share. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>