{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:B34PYBLXDSWCAX4OUUJOIDYO65","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":"3e56d92f0e311cb614404ad176d587c6dbcbff4b134238b22e441d024de08a2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-15T12:50:06Z","title_canon_sha256":"856560164922738065a6d696d00bcc527f5ebe1ecf15c9f7526fac1073107b9e"},"schema_version":"1.0","source":{"id":"1904.07006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.07006","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"arxiv_version","alias_value":"1904.07006v1","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.07006","created_at":"2026-05-17T23:48:35Z"},{"alias_kind":"pith_short_12","alias_value":"B34PYBLXDSWC","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_16","alias_value":"B34PYBLXDSWCAX4O","created_at":"2026-05-18T12:33:12Z"},{"alias_kind":"pith_short_8","alias_value":"B34PYBLX","created_at":"2026-05-18T12:33:12Z"}],"graph_snapshots":[{"event_id":"sha256:71a11e24775cf50b7d9d23a6217be525743deece0be2852d113c1a4929a03955","target":"graph","created_at":"2026-05-17T23:48:35Z","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":"We use Taylor's formula with Lagrange remainder to prove that functions with bounded second derivative are rectifiable in the case when polygonal paths are defined by interval subdivisions which are equally spaced. We discuss potential benefits for such an approach in introductory calculus courses.","authors_text":"Patrik Nystedt","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-15T12:50:06Z","title":"Arc length of function graphs via Taylor's formula"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.07006","kind":"arxiv","version":1},"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":"sha256:69bfd41019913e93545756712d406284bb9905197befcc99cff2ec0b1ed3d765","target":"record","created_at":"2026-05-17T23:48:35Z","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":"3e56d92f0e311cb614404ad176d587c6dbcbff4b134238b22e441d024de08a2c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2019-04-15T12:50:06Z","title_canon_sha256":"856560164922738065a6d696d00bcc527f5ebe1ecf15c9f7526fac1073107b9e"},"schema_version":"1.0","source":{"id":"1904.07006","kind":"arxiv","version":1}},"canonical_sha256":"0ef8fc05771cac205f8ea512e40f0ef7531716cede65028dc67ce7c4a7154768","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0ef8fc05771cac205f8ea512e40f0ef7531716cede65028dc67ce7c4a7154768","first_computed_at":"2026-05-17T23:48:35.498418Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:48:35.498418Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"639Doivn9XvtOiH86T6D7k9RN2BI5Y1wHcXJzD7BsQzHkD6I8Tcmue6CiC+yd56m5t+OxguxO2T+HXKiqkggBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:48:35.498961Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.07006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:69bfd41019913e93545756712d406284bb9905197befcc99cff2ec0b1ed3d765","sha256:71a11e24775cf50b7d9d23a6217be525743deece0be2852d113c1a4929a03955"],"state_sha256":"ade5a55dbeaf51f7e4558e98df9a56a3bfe0dce4e2e1f569af13d86416513143"}