A boat is reaching down onto me while I'm close-hauled — does close-hauled beat reaching?

No. “Close-hauled beats reaching” was dropped from racing decades ago and decides nothing today. On the same tack and overlapped, Rule 11 gives right of way to the leeward boat and the windward boat keeps clear — windward being the boat on the side the wind comes from. Point of sail never enters into it: swap the two boats over and it is the close-hauled boat that must move.

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Next on this shelf — The Upwind Beat