{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5QFTN73U4UQB5PQ44IPK6NHTUK","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":"a23d725e0924f970da3f3ec68855b23393c7994155cf1c5d367808a7cc7b7fdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-07-03T11:05:02Z","title_canon_sha256":"be22f9fb3912f5a280073b54bb1e77a2d6a7ce0d00e83b511b8ace8593b51ab0"},"schema_version":"1.0","source":{"id":"1507.00871","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.00871","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"arxiv_version","alias_value":"1507.00871v2","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.00871","created_at":"2026-05-18T00:50:13Z"},{"alias_kind":"pith_short_12","alias_value":"5QFTN73U4UQB","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_16","alias_value":"5QFTN73U4UQB5PQ4","created_at":"2026-05-18T12:29:05Z"},{"alias_kind":"pith_short_8","alias_value":"5QFTN73U","created_at":"2026-05-18T12:29:05Z"}],"graph_snapshots":[{"event_id":"sha256:bbe669ff06d9ff760c9a8dad6e224f0d110ac217f5e83b73f5834bdbe9a3c1ce","target":"graph","created_at":"2026-05-18T00:50:13Z","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 are motivated by a problem about running: If a race was completed in an average pace of P minutes per mile, is there necessarily some mile of the race that was run in exactly P minutes? The answer is no. We explain why, and describe the history of this celebrated problem, known as the Universal Chord Theorem. We also clarify and streamline the proof of a more powerful result by Heinz Hopf from 1937.","authors_text":"Diana Davis, Keith Burns, Orit Davidovich","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-07-03T11:05:02Z","title":"Average pace and horizontal chords"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.00871","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:fd5c72817419e9bdbd9d077c6f528f550f1491df2f2b722c743b665427bc403f","target":"record","created_at":"2026-05-18T00:50:13Z","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":"a23d725e0924f970da3f3ec68855b23393c7994155cf1c5d367808a7cc7b7fdd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.HO","submitted_at":"2015-07-03T11:05:02Z","title_canon_sha256":"be22f9fb3912f5a280073b54bb1e77a2d6a7ce0d00e83b511b8ace8593b51ab0"},"schema_version":"1.0","source":{"id":"1507.00871","kind":"arxiv","version":2}},"canonical_sha256":"ec0b36ff74e5201ebe1ce21eaf34f3a28ae2edd232faf5e0a7364753d840a223","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ec0b36ff74e5201ebe1ce21eaf34f3a28ae2edd232faf5e0a7364753d840a223","first_computed_at":"2026-05-18T00:50:13.824753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:50:13.824753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1UWgMiwODtbViccttxTRvtojBYv43LLSZ8Rla7gkuVXvu+O/yTDnYZa5dKNp0zSRCRbUHnUkJ1m9Dgc9Ph4cBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:50:13.825464Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.00871","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd5c72817419e9bdbd9d077c6f528f550f1491df2f2b722c743b665427bc403f","sha256:bbe669ff06d9ff760c9a8dad6e224f0d110ac217f5e83b73f5834bdbe9a3c1ce"],"state_sha256":"5a86018546b6cc786b725de9ce7ebf53319249283eeb75cce23307eb43b4390e"}