{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:52DXACACADFTIWPKCFYZ7AG4BF","short_pith_number":"pith:52DXACAC","canonical_record":{"source":{"id":"1312.0274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-01T21:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"9b9276237c0f6b1917da35e86d0497013e76661ddc027f0ed03a74b81fa480d4","abstract_canon_sha256":"1c50582123f43d389b9ee507c4d4f7b28819ef098b01732e4e637a257aa64a45"},"schema_version":"1.0"},"canonical_sha256":"ee8770080200cb3459ea11719f80dc09789d2e5a038014083efd19a57b3ea9f6","source":{"kind":"arxiv","id":"1312.0274","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0274","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0274v1","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0274","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"52DXACACADFT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"52DXACACADFTIWPK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"52DXACAC","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:52DXACACADFTIWPKCFYZ7AG4BF","target":"record","payload":{"canonical_record":{"source":{"id":"1312.0274","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-01T21:01:09Z","cross_cats_sorted":[],"title_canon_sha256":"9b9276237c0f6b1917da35e86d0497013e76661ddc027f0ed03a74b81fa480d4","abstract_canon_sha256":"1c50582123f43d389b9ee507c4d4f7b28819ef098b01732e4e637a257aa64a45"},"schema_version":"1.0"},"canonical_sha256":"ee8770080200cb3459ea11719f80dc09789d2e5a038014083efd19a57b3ea9f6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:46.220431Z","signature_b64":"fFZT4CFnwiBywtWo6BRTAvBOWO4OGpOzJQN0XgCovNF7yU3O6Mrp2EgpzcysE9t5LglSvve669tWs48Kd9KsCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ee8770080200cb3459ea11719f80dc09789d2e5a038014083efd19a57b3ea9f6","last_reissued_at":"2026-05-18T03:05:46.219768Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:46.219768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.0274","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oCS0RqyiCUNUhdML4r2AnL69xr9hfjgcTv7x6achbLYpuLIvN+O2b5MiXpUf/VHdMniVffK9AMufJzCpJFBXAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:44:28.096444Z"},"content_sha256":"6ef41e63dfa3e9b47ebad96c25b03bc9a173467ff3c4800a8db6e9ab55f7c495","schema_version":"1.0","event_id":"sha256:6ef41e63dfa3e9b47ebad96c25b03bc9a173467ff3c4800a8db6e9ab55f7c495"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:52DXACACADFTIWPKCFYZ7AG4BF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimal Pancyclicity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sean Griffin","submitted_at":"2013-12-01T21:01:09Z","abstract_excerpt":"A pancyclic graph is a simple graph containing a cycle of length $k$ for all $3\\leq k\\leq n$. Let $m(n)$ be the minimum number of edges of all pancyclic graphs on $n$ vertices. Exact values are given for $m(n)$ for $n\\leq 37$, combining calculations from an exhaustive search on graphs with up to 29 vertices with a construction that works for up to 37 vertices. The behavior of $m(n)$ in general is also explored, including a proof of the conjecture that $m(n+1)>m(n)$ for all $n$ in some special cases."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0274","kind":"arxiv","version":1},"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":"2026-05-18T03:05:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+3TCa1xQXuszrwnhAm7CFMNuLz+Ieml9h2cC4uUxwJS9RXaoWnHXbhT7VD+Py4yxh6e9MhFm9cHM5CgSKDsFCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T08:44:28.097114Z"},"content_sha256":"a42a940cda26cf0f00770f4afdeda76675488c9b0f09d59d75d8bf815c7c75f9","schema_version":"1.0","event_id":"sha256:a42a940cda26cf0f00770f4afdeda76675488c9b0f09d59d75d8bf815c7c75f9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/52DXACACADFTIWPKCFYZ7AG4BF/bundle.json","state_url":"https://pith.science/pith/52DXACACADFTIWPKCFYZ7AG4BF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/52DXACACADFTIWPKCFYZ7AG4BF/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":"2026-05-26T08:44:28Z","links":{"resolver":"https://pith.science/pith/52DXACACADFTIWPKCFYZ7AG4BF","bundle":"https://pith.science/pith/52DXACACADFTIWPKCFYZ7AG4BF/bundle.json","state":"https://pith.science/pith/52DXACACADFTIWPKCFYZ7AG4BF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/52DXACACADFTIWPKCFYZ7AG4BF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:52DXACACADFTIWPKCFYZ7AG4BF","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":"1c50582123f43d389b9ee507c4d4f7b28819ef098b01732e4e637a257aa64a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-01T21:01:09Z","title_canon_sha256":"9b9276237c0f6b1917da35e86d0497013e76661ddc027f0ed03a74b81fa480d4"},"schema_version":"1.0","source":{"id":"1312.0274","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.0274","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"arxiv_version","alias_value":"1312.0274v1","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0274","created_at":"2026-05-18T03:05:46Z"},{"alias_kind":"pith_short_12","alias_value":"52DXACACADFT","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"52DXACACADFTIWPK","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"52DXACAC","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:a42a940cda26cf0f00770f4afdeda76675488c9b0f09d59d75d8bf815c7c75f9","target":"graph","created_at":"2026-05-18T03:05:46Z","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":"A pancyclic graph is a simple graph containing a cycle of length $k$ for all $3\\leq k\\leq n$. Let $m(n)$ be the minimum number of edges of all pancyclic graphs on $n$ vertices. Exact values are given for $m(n)$ for $n\\leq 37$, combining calculations from an exhaustive search on graphs with up to 29 vertices with a construction that works for up to 37 vertices. The behavior of $m(n)$ in general is also explored, including a proof of the conjecture that $m(n+1)>m(n)$ for all $n$ in some special cases.","authors_text":"Sean Griffin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-01T21:01:09Z","title":"Minimal Pancyclicity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0274","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":"sha256:6ef41e63dfa3e9b47ebad96c25b03bc9a173467ff3c4800a8db6e9ab55f7c495","target":"record","created_at":"2026-05-18T03:05:46Z","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":"1c50582123f43d389b9ee507c4d4f7b28819ef098b01732e4e637a257aa64a45","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-01T21:01:09Z","title_canon_sha256":"9b9276237c0f6b1917da35e86d0497013e76661ddc027f0ed03a74b81fa480d4"},"schema_version":"1.0","source":{"id":"1312.0274","kind":"arxiv","version":1}},"canonical_sha256":"ee8770080200cb3459ea11719f80dc09789d2e5a038014083efd19a57b3ea9f6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ee8770080200cb3459ea11719f80dc09789d2e5a038014083efd19a57b3ea9f6","first_computed_at":"2026-05-18T03:05:46.219768Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:46.219768Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fFZT4CFnwiBywtWo6BRTAvBOWO4OGpOzJQN0XgCovNF7yU3O6Mrp2EgpzcysE9t5LglSvve669tWs48Kd9KsCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:46.220431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.0274","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ef41e63dfa3e9b47ebad96c25b03bc9a173467ff3c4800a8db6e9ab55f7c495","sha256:a42a940cda26cf0f00770f4afdeda76675488c9b0f09d59d75d8bf815c7c75f9"],"state_sha256":"e040a6fe8bc4cf83c564f4412dfdf34707c5d859cb99f12df2293622223ec466"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GI/JMI/Bc3Q2nPODMTXBD+Ln6vCJvtWjg37Zt/SFN3ry0LybV0PTyMqrxusEHpX9PBYyEhnVk+CidToCSqI3Ag==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T08:44:28.100692Z","bundle_sha256":"ed6748e2d69acd157a4570961c614b6a74a2e79c8014ced04d19496b1b21a5e3"}}