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the Q/D conditions together with B(p) are sufficient to guarantee order p.","weakest_assumption":"The Q- and D-space residual conditions remain linearly independent and the two structured linear systems at each recursive step remain solvable for the chosen stage count; this is invoked when the authors state that the Butcher coefficients are obtained from the two linear systems (abstract and §3-4)."}},"verdict_id":"bc09107e-a7cd-46b6-988f-97d5e1aa5a20"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:046555ac17b425cb044e7102b27769ca8e13b6015c503d00195853a5f784b34d","target":"record","created_at":"2026-05-20T00:03:35Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"2a84312a414541211905507e3f056935936770ce587ba254f6110f374e3e66a6","cross_cats_sorted":["cs.NA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.NA","submitted_at":"2026-05-16T13:43:57Z","title_canon_sha256":"3dae47c10513ca7b75122c5fd34c682a5b0473f0f4118990ac3811a7c9175355"},"schema_version":"1.0","source":{"id":"2605.16995","kind":"arxiv","version":1}},"canonical_sha256":"172c52c03b5835434d916e781f458c28c1adfdb856e7e417c9b813b8c21ff9c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"172c52c03b5835434d916e781f458c28c1adfdb856e7e417c9b813b8c21ff9c7","first_computed_at":"2026-05-20T00:03:35.030479Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:03:35.030479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x8DaOPqlb6WATG+V+BeF+zQfPPdonj5bQIS2o3gfDppog8pxHBINgJMgTVDr+AjllpRrchCVfNRk8jcxQ3prDQ==","signature_status":"signed_v1","signed_at":"2026-05-20T00:03:35.031295Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16995","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:046555ac17b425cb044e7102b27769ca8e13b6015c503d00195853a5f784b34d","sha256:1932c527c2a12a5a463aa1300f4e7026d404634aae17c687fa2ac5604400cc63"],"state_sha256":"eb97234150b7b0b5e6a37f432daab5bf0ab609225de10d15af501f6ce3f57eb7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lwe9XfbUIpK87Au3QCyDmI5ygSHGfuClt8pZHZVyMXJtLWbhzF7NrHkqkCD9Dep2l9og8Siypnr8alcprPk2BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T20:43:41.466619Z","bundle_sha256":"9f732e74d8a54b80733307df43fad5a032f4a88b239f45b47667c6dc9ca45711"}}