{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HKC4YFA6CDQFFVLUBGS4VDCG6P","short_pith_number":"pith:HKC4YFA6","canonical_record":{"source":{"id":"1310.0199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-01T09:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"1f91b1e7af12eec7a8ae994483c2cd8b1b12e32e5c2cbbea218fc9de09aa76c1","abstract_canon_sha256":"e3645499a5779d783ec1d36c9b5f6ff26a349c4c8bad1b7a08267431ad3f1964"},"schema_version":"1.0"},"canonical_sha256":"3a85cc141e10e052d57409a5ca8c46f3f31db8b30d0f6056f59611d2b81ff12a","source":{"kind":"arxiv","id":"1310.0199","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0199","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0199v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0199","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"HKC4YFA6CDQF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HKC4YFA6CDQFFVLU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HKC4YFA6","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HKC4YFA6CDQFFVLUBGS4VDCG6P","target":"record","payload":{"canonical_record":{"source":{"id":"1310.0199","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-01T09:15:29Z","cross_cats_sorted":[],"title_canon_sha256":"1f91b1e7af12eec7a8ae994483c2cd8b1b12e32e5c2cbbea218fc9de09aa76c1","abstract_canon_sha256":"e3645499a5779d783ec1d36c9b5f6ff26a349c4c8bad1b7a08267431ad3f1964"},"schema_version":"1.0"},"canonical_sha256":"3a85cc141e10e052d57409a5ca8c46f3f31db8b30d0f6056f59611d2b81ff12a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:11:45.179412Z","signature_b64":"7ilDMj2Eh5MYjn0JXxmXo22jYMiiryIg4aog36+OhT+9yC46ZOiP/hPT85PnA2sJGSU0vhJZQa28HSRFjqiwAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a85cc141e10e052d57409a5ca8c46f3f31db8b30d0f6056f59611d2b81ff12a","last_reissued_at":"2026-05-18T03:11:45.178709Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:11:45.178709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.0199","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":"2026-05-18T03:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ub/LPuVxwdtFI+xreekeFVLdCwnqMDBqT1wbX+479mrEvmwbsbqHRZ4JhUaBopRrPnNLinOcz3Yp6sNbT/+sDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:17:10.282481Z"},"content_sha256":"417ee3c88e76414a496aa06c9a5f200286164069a3f8d2cb6600aae95dce4e7d","schema_version":"1.0","event_id":"sha256:417ee3c88e76414a496aa06c9a5f200286164069a3f8d2cb6600aae95dce4e7d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HKC4YFA6CDQFFVLUBGS4VDCG6P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Cycles in Projective Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ashley Klahr, David Heywood, Elaina Aceves, Oscar Vega","submitted_at":"2013-10-01T09:15:29Z","abstract_excerpt":"We prove that every possible $k$-cycle can be embedded into $PG(n,q)$, for all $n\\geq 3$ and $q$ a power of a prime."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0199","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":"2026-05-18T03:11:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nVIAsGzk75zeb9xQ3N5lXA2dW6f7Rr5RwaGguLLHcnbfzAwLwqY6pJvDXB/Iz7QL06sgt/j5rD3oE15XaLrVAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T15:17:10.283222Z"},"content_sha256":"2b22644a6611852614b8fa2033b686dac2bdbe9b56fc1e0fa1a8126a55c6d43c","schema_version":"1.0","event_id":"sha256:2b22644a6611852614b8fa2033b686dac2bdbe9b56fc1e0fa1a8126a55c6d43c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P/bundle.json","state_url":"https://pith.science/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P/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":"2026-06-11T15:17:10Z","links":{"resolver":"https://pith.science/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P","bundle":"https://pith.science/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P/bundle.json","state":"https://pith.science/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKC4YFA6CDQFFVLUBGS4VDCG6P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HKC4YFA6CDQFFVLUBGS4VDCG6P","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":"e3645499a5779d783ec1d36c9b5f6ff26a349c4c8bad1b7a08267431ad3f1964","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-01T09:15:29Z","title_canon_sha256":"1f91b1e7af12eec7a8ae994483c2cd8b1b12e32e5c2cbbea218fc9de09aa76c1"},"schema_version":"1.0","source":{"id":"1310.0199","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.0199","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"arxiv_version","alias_value":"1310.0199v1","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.0199","created_at":"2026-05-18T03:11:45Z"},{"alias_kind":"pith_short_12","alias_value":"HKC4YFA6CDQF","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HKC4YFA6CDQFFVLU","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HKC4YFA6","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:2b22644a6611852614b8fa2033b686dac2bdbe9b56fc1e0fa1a8126a55c6d43c","target":"graph","created_at":"2026-05-18T03:11:45Z","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 prove that every possible $k$-cycle can be embedded into $PG(n,q)$, for all $n\\geq 3$ and $q$ a power of a prime.","authors_text":"Ashley Klahr, David Heywood, Elaina Aceves, Oscar Vega","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-01T09:15:29Z","title":"Cycles in Projective Spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.0199","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":"sha256:417ee3c88e76414a496aa06c9a5f200286164069a3f8d2cb6600aae95dce4e7d","target":"record","created_at":"2026-05-18T03:11:45Z","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":"e3645499a5779d783ec1d36c9b5f6ff26a349c4c8bad1b7a08267431ad3f1964","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-10-01T09:15:29Z","title_canon_sha256":"1f91b1e7af12eec7a8ae994483c2cd8b1b12e32e5c2cbbea218fc9de09aa76c1"},"schema_version":"1.0","source":{"id":"1310.0199","kind":"arxiv","version":1}},"canonical_sha256":"3a85cc141e10e052d57409a5ca8c46f3f31db8b30d0f6056f59611d2b81ff12a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a85cc141e10e052d57409a5ca8c46f3f31db8b30d0f6056f59611d2b81ff12a","first_computed_at":"2026-05-18T03:11:45.178709Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:11:45.178709Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7ilDMj2Eh5MYjn0JXxmXo22jYMiiryIg4aog36+OhT+9yC46ZOiP/hPT85PnA2sJGSU0vhJZQa28HSRFjqiwAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:11:45.179412Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.0199","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:417ee3c88e76414a496aa06c9a5f200286164069a3f8d2cb6600aae95dce4e7d","sha256:2b22644a6611852614b8fa2033b686dac2bdbe9b56fc1e0fa1a8126a55c6d43c"],"state_sha256":"f5248a00ce9beeed7a721150743d87c638efbd6a54bae7f9852c279b4f6c02cc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7P+hSLt2hfNExYgZSpoS781fYV4SgUsmHXCn+OO1jgDyoYPklbISXG7Erg9LActyqP3yM9MZcj/bGX+qz6AsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T15:17:10.287290Z","bundle_sha256":"1427fc73141d49a11ebe05192d117a73d44e3ce79bbfe08febeb038dbf62e89f"}}