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rigour: heuristic (agreement-checked) rigour details: 'Computed twice at different working precisions, keeping only the- digits both computations support. That bounds the error from working precision- and nothing else: two runs of the same method agree even when the method is wrong.'+ digits both computations support. Since 2026-08-17 each value is also *proven+ to bracket a zero*: the function is evaluated in ball arithmetic at both ends+ of the interval the written digits denote, and the two results have strictly opposite+ signs, so a zero lies between them by the intermediate value theorem. All entries+ pass. What this does not establish is the index -- that this is the nth zero rather+ than a neighbour -- which needs a count of the zeros below it, and arb''s counting+ is not exposed here.' Display properties: number-header: $n$<sup>th</sup> local extremum of $\text{Ai}(x)$
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