{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4XTIUOIBFEFG4QD6SYOTLTLJEZ","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"b65d48e7653e58240059aebddbc7cc6f816dc7dc7d5abcd5e231465334a0ffba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-09T09:28:46Z","title_canon_sha256":"0a51af1247a7e5c283d0e9cf84ad173c5d63642c1d805662381452650465bfdf"},"schema_version":"1.0","source":{"id":"1305.2041","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2041","created_at":"2026-05-18T03:24:53Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2041v2","created_at":"2026-05-18T03:24:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2041","created_at":"2026-05-18T03:24:53Z"},{"alias_kind":"pith_short_12","alias_value":"4XTIUOIBFEFG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4XTIUOIBFEFG4QD6","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4XTIUOIB","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:6cb6b274beab34bcb4bdb16a2225f243dfbc3bbe2f7bc40fbf518ae84fdb9564","target":"graph","created_at":"2026-05-18T03:24:53Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of polynomial basis functions that results in a collocation scheme with two important features: the condition number of the linear system is independent of the number of collocation points; and the underlying boundary conditions are imposed exactly. Moreover, the new basis leads to exact inverse of the pseudospectral differentiation matrix (PSDM) of the highes","authors_text":"Li-Lian Wang, Michael Daniel Samson, Xiaodan Zhao","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-09T09:28:46Z","title":"A well-conditioned collocation method using pseudospectral integration matrix"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2041","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:26dc1e5fb30b44274bfc11bd39533cb3eeb3c67437185b0e121de018c4c5c38f","target":"record","created_at":"2026-05-18T03:24:53Z","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":"b65d48e7653e58240059aebddbc7cc6f816dc7dc7d5abcd5e231465334a0ffba","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2013-05-09T09:28:46Z","title_canon_sha256":"0a51af1247a7e5c283d0e9cf84ad173c5d63642c1d805662381452650465bfdf"},"schema_version":"1.0","source":{"id":"1305.2041","kind":"arxiv","version":2}},"canonical_sha256":"e5e68a3901290a6e407e961d35cd69264a111f3d4724abadec7a7443ee2fb137","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e5e68a3901290a6e407e961d35cd69264a111f3d4724abadec7a7443ee2fb137","first_computed_at":"2026-05-18T03:24:53.623926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:24:53.623926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SW5C1RIkqhxX1u78wBF0MBywhkU9eIDKmG2NrWDYW8hKchQNgcYCRdBov/VZJ2KLO9yC8E04FJ77xUFr0lELCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:24:53.624692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2041","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26dc1e5fb30b44274bfc11bd39533cb3eeb3c67437185b0e121de018c4c5c38f","sha256:6cb6b274beab34bcb4bdb16a2225f243dfbc3bbe2f7bc40fbf518ae84fdb9564"],"state_sha256":"4134014a8a4be08a5f00e0afe6f910dce35ae71c20d03a3a9beb3a296d412243"}