Open on the site: the label is OPEN (no last-edited date shown; accessed), and the site marks the problem as not resolvable by a finite computation. The standing derived from the claim pages is open, claim none: the one claim page, Nayak's note on the intersecting case, is a pending partial claim that the pairs of intersecting intervals with an integer sum are exactly four small pairs, and no claim settles or pends on the full statement. The site's proof-claim tab is empty; the other note announced in the discussion (Zeraoulia, recorded in the Current assessment) offers a reduction and an obstruction for the singleton case, not a proof of finiteness, so it has no page. No proof of finiteness, no infinite family of pairs and no proof claim for the exact statement (or for the singleton case) was found in the search whose scope the Current assessment records; the located results concern one interval approaching $1$, not two intervals summing to an integer. This is a bounded negative finding, not a certificate of openness.