{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:A3XMRH4U6YLQEFWZY62JEIXGO7","short_pith_number":"pith:A3XMRH4U","canonical_record":{"source":{"id":"1508.07289","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T17:43:58Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dbb374f4d0f162e1a73856919a165a408691ae28233cac51567966e65fe00fcf","abstract_canon_sha256":"fe51b2885c2955fedef287081c0133710d7a0e737c72fb7f340f8410b67bcdd9"},"schema_version":"1.0"},"canonical_sha256":"06eec89f94f6170216d9c7b49222e677e755907362b87cead02b8c135a9fba07","source":{"kind":"arxiv","id":"1508.07289","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07289","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07289v3","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07289","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"A3XMRH4U6YLQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A3XMRH4U6YLQEFWZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A3XMRH4U","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:A3XMRH4U6YLQEFWZY62JEIXGO7","target":"record","payload":{"canonical_record":{"source":{"id":"1508.07289","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T17:43:58Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dbb374f4d0f162e1a73856919a165a408691ae28233cac51567966e65fe00fcf","abstract_canon_sha256":"fe51b2885c2955fedef287081c0133710d7a0e737c72fb7f340f8410b67bcdd9"},"schema_version":"1.0"},"canonical_sha256":"06eec89f94f6170216d9c7b49222e677e755907362b87cead02b8c135a9fba07","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:31:29.133918Z","signature_b64":"FCHY5qO7twSXYJfij0ozm15OrK/kRnM9H78bWqkd9PlV5Xhv3RIQJsyf5Na5x+mFtSQNqSAIyY3CmZTZLkLqDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"06eec89f94f6170216d9c7b49222e677e755907362b87cead02b8c135a9fba07","last_reissued_at":"2026-05-18T00:31:29.133347Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:31:29.133347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.07289","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"XYBCLpwE41+bFrpnQUgQ/5VChwf/v4Vid0iBd5mpYx1b6Qsbgn9S4VMrwiXvjFp6a+ICS42RS3iPY7L9za8cDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:09:03.759755Z"},"content_sha256":"f1be53e4593231768ab2cac62381399bfbacc51142890fb95a31240a51bc1766","schema_version":"1.0","event_id":"sha256:f1be53e4593231768ab2cac62381399bfbacc51142890fb95a31240a51bc1766"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:A3XMRH4U6YLQEFWZY62JEIXGO7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Problems on Track Runners","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth","submitted_at":"2015-08-28T17:43:58Z","abstract_excerpt":"Consider the circle $C$ of length 1 and a circular arc $A$ of length $\\ell\\in (0,1)$.\n  It is shown that there exists $k=k(\\ell) \\in \\mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds so that at any time $t \\geq 0$, at least one of the $k$ runners is not in $A$.\n  On the other hand, we show the following:\n  Assume that $k$ runners $1,2,\\ldots,k$, with constant rationally independent (thus distinct) speeds $\\xi_1,\\xi_2,\\ldots,\\xi_k$, run clockwise along a circle of length $1$, starting from arbitrary points. For every circular arc $A\\subs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07289","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:31:29Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M+ldZkmkQReJr5XNc7NcRuy8czaqvugNHEKf6r3DfPVhlds8jBeO0KmYpLsfNZPNgQBk+YuvuQuYNzkUUx43CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:09:03.760112Z"},"content_sha256":"b85d20fa19379f22aef3f187977b09a50ccb17c4e1109a7236be0f77de98668b","schema_version":"1.0","event_id":"sha256:b85d20fa19379f22aef3f187977b09a50ccb17c4e1109a7236be0f77de98668b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/A3XMRH4U6YLQEFWZY62JEIXGO7/bundle.json","state_url":"https://pith.science/pith/A3XMRH4U6YLQEFWZY62JEIXGO7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/A3XMRH4U6YLQEFWZY62JEIXGO7/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T11:09:03Z","links":{"resolver":"https://pith.science/pith/A3XMRH4U6YLQEFWZY62JEIXGO7","bundle":"https://pith.science/pith/A3XMRH4U6YLQEFWZY62JEIXGO7/bundle.json","state":"https://pith.science/pith/A3XMRH4U6YLQEFWZY62JEIXGO7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/A3XMRH4U6YLQEFWZY62JEIXGO7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:A3XMRH4U6YLQEFWZY62JEIXGO7","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":"fe51b2885c2955fedef287081c0133710d7a0e737c72fb7f340f8410b67bcdd9","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T17:43:58Z","title_canon_sha256":"dbb374f4d0f162e1a73856919a165a408691ae28233cac51567966e65fe00fcf"},"schema_version":"1.0","source":{"id":"1508.07289","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.07289","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"arxiv_version","alias_value":"1508.07289v3","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.07289","created_at":"2026-05-18T00:31:29Z"},{"alias_kind":"pith_short_12","alias_value":"A3XMRH4U6YLQ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"A3XMRH4U6YLQEFWZ","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"A3XMRH4U","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:b85d20fa19379f22aef3f187977b09a50ccb17c4e1109a7236be0f77de98668b","target":"graph","created_at":"2026-05-18T00:31:29Z","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":"Consider the circle $C$ of length 1 and a circular arc $A$ of length $\\ell\\in (0,1)$.\n  It is shown that there exists $k=k(\\ell) \\in \\mathbb{N}$, and a schedule for $k$ runners along the circle with $k$ constant but distinct positive speeds so that at any time $t \\geq 0$, at least one of the $k$ runners is not in $A$.\n  On the other hand, we show the following:\n  Assume that $k$ runners $1,2,\\ldots,k$, with constant rationally independent (thus distinct) speeds $\\xi_1,\\xi_2,\\ldots,\\xi_k$, run clockwise along a circle of length $1$, starting from arbitrary points. For every circular arc $A\\subs","authors_text":"Adrian Dumitrescu, Csaba D. T\\'oth","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T17:43:58Z","title":"Problems on Track Runners"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07289","kind":"arxiv","version":3},"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:f1be53e4593231768ab2cac62381399bfbacc51142890fb95a31240a51bc1766","target":"record","created_at":"2026-05-18T00:31:29Z","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":"fe51b2885c2955fedef287081c0133710d7a0e737c72fb7f340f8410b67bcdd9","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-28T17:43:58Z","title_canon_sha256":"dbb374f4d0f162e1a73856919a165a408691ae28233cac51567966e65fe00fcf"},"schema_version":"1.0","source":{"id":"1508.07289","kind":"arxiv","version":3}},"canonical_sha256":"06eec89f94f6170216d9c7b49222e677e755907362b87cead02b8c135a9fba07","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"06eec89f94f6170216d9c7b49222e677e755907362b87cead02b8c135a9fba07","first_computed_at":"2026-05-18T00:31:29.133347Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:31:29.133347Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FCHY5qO7twSXYJfij0ozm15OrK/kRnM9H78bWqkd9PlV5Xhv3RIQJsyf5Na5x+mFtSQNqSAIyY3CmZTZLkLqDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:31:29.133918Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.07289","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f1be53e4593231768ab2cac62381399bfbacc51142890fb95a31240a51bc1766","sha256:b85d20fa19379f22aef3f187977b09a50ccb17c4e1109a7236be0f77de98668b"],"state_sha256":"bbb30146cdd8494083d6f824b26f3452a072f3075bd7f899d680462af6126121"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HyEHf6FyY2Ph0VtR9BgxDZ/bWr/rjg1cAkjeQiYJgSinSEPvaxysEyebWZVxqS7b2ou7MCN8EN4prO6xnHsXCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:09:03.762722Z","bundle_sha256":"b5aaeeeb683b262844be66d95d45fe684108015f0b46116298fe208a2c408273"}}