{"paper":{"title":"Arbitrary-Order Pad\\'e-Closed Anchored Two-Derivative Time Discretizations: $s$ Active Stages, Order $2s$, and $L$-Stability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Zhixin Huo","submitted_at":"2026-07-27T15:57:23Z","abstract_excerpt":"An arbitrary-order family of implicit two-derivative one-step methods is constructed in an anchored active-stage formulation. At each information node the method uses both the vector field and its first total time derivative, enriching the local Hermite data without increasing the number of unknown stage states. With the known initial value retained as an anchor and $s$ unknown active stages, $2s$ Hermite moment conditions yield global order $2s$. The two remaining coefficients in each stage row are fixed by the second-subdiagonal Pad\\'{e} approximant $[s-1/s+1]_{e^z}$. For every ordered real "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.24592","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.24592/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}