{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VJU67KFAW4CVN2ET4JW5KFDOML","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":"3350adc92ef1174637764dc67588ac8b009aa06d97fb64c30ca7dd4075f82ee1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-12T23:50:00Z","title_canon_sha256":"fe963e9f3d752f99eaca1c9962899a47361869377b4e6ea7eb13193e636b3885"},"schema_version":"1.0","source":{"id":"1305.2646","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.2646","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"arxiv_version","alias_value":"1305.2646v1","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.2646","created_at":"2026-05-18T03:25:57Z"},{"alias_kind":"pith_short_12","alias_value":"VJU67KFAW4CV","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VJU67KFAW4CVN2ET","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VJU67KFA","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:f766e1f30cfbf4433f1926421b6e7dc493dd3a2d43afb74f33ac3b806542c684","target":"graph","created_at":"2026-05-18T03:25:57Z","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 define and study embeddings of cycles in finite affine and projective planes. We show that for all $k$, $3\\le k\\le q^2$, a $k$-cycle can be embedded in any affine plane of order $q$. We also prove a similar result for finite projective planes: for all $k$, $3\\le k\\le q^2+q+1$, a $k$-cycle can be embedded in any projective plane of order $q$.","authors_text":"Felix Lazebnik, Keith E. Mellinger, Oscar Vega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-12T23:50:00Z","title":"Embedding cycles in finite planes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.2646","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":"sha256:7d277d7b430f4f526bb3290f1eab5d725940347bb805f841caa48f4a89a941da","target":"record","created_at":"2026-05-18T03:25:57Z","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":"3350adc92ef1174637764dc67588ac8b009aa06d97fb64c30ca7dd4075f82ee1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-05-12T23:50:00Z","title_canon_sha256":"fe963e9f3d752f99eaca1c9962899a47361869377b4e6ea7eb13193e636b3885"},"schema_version":"1.0","source":{"id":"1305.2646","kind":"arxiv","version":1}},"canonical_sha256":"aa69efa8a0b70556e893e26dd5146e62f90f1d456dfb0a9c1dda649b4491a3a3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa69efa8a0b70556e893e26dd5146e62f90f1d456dfb0a9c1dda649b4491a3a3","first_computed_at":"2026-05-18T03:25:57.276988Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:57.276988Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"qLhb/3u2m2JRw7oLZbVNIJAWL//h7MVFx0NaBS4UQ19M8Zfa5up1nlHtrwZWrePlzCkrgKOsB2cCZRdYlbrDCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:57.277650Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.2646","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d277d7b430f4f526bb3290f1eab5d725940347bb805f841caa48f4a89a941da","sha256:f766e1f30cfbf4433f1926421b6e7dc493dd3a2d43afb74f33ac3b806542c684"],"state_sha256":"a12de1565922ec90a1ecea92f636f1d32b57cd53db6ba15b5de00206da1e8773"}