Open: the site's label is OPEN (; page last edited 12 January 2026), and the site marks the problem as not resolvable by a finite computation. The standing derived from the claim pages is open, claim none. Three of the four claim pages concern the second question: Steinerberger's base-3 observation, a pending partial claim answering the second question in the affirmative, which the site's commentary credits to him while the site labels the whole problem OPEN and declares no parts, so that the credit is context and not acceptance, Shiu's criterion and infinitude theorem, a pending partial claim giving the same answer with the exact criterion (the commentary credits the observation, not this paper), and van Doorn's generalization to periodic numerators, a pending partial claim from a dated note with a conditional Lean proof by the prover Aristotle. The fourth, Wu and Yan's conditional density theorem, an accepted conditional claim, gives the second question only under an open independence conjecture and derives nothing; no claim settles or pends on the first. For the first, no proof, disproof, preprint or proof claim that $(a_n,L_n)=1$ infinitely often was found in the search whose scope the Current assessment records: Shiu's paper states it as a conjecture, and Wu and Yan's theorem is conditional and concerns the other half. This is a bounded negative finding, not a certificate of openness.