{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:O7KATSH5LFA2DP4FXLWRHOSG7N","short_pith_number":"pith:O7KATSH5","canonical_record":{"source":{"id":"1711.07734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-21T11:53:47Z","cross_cats_sorted":[],"title_canon_sha256":"d26df91e7c00009e962121f2e2961f4514ecc87f3b954027b07d40b458c933eb","abstract_canon_sha256":"c651eb922d0e8fc32409bca21cd650abdd38861c3d6f7b5a117071943d0015b3"},"schema_version":"1.0"},"canonical_sha256":"77d409c8fd5941a1bf85baed13ba46fb7ee508ba1f466264b0750944cc30f83d","source":{"kind":"arxiv","id":"1711.07734","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07734","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07734v1","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07734","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"pith_short_12","alias_value":"O7KATSH5LFA2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7KATSH5LFA2DP4F","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7KATSH5","created_at":"2026-05-18T12:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:O7KATSH5LFA2DP4FXLWRHOSG7N","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07734","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-21T11:53:47Z","cross_cats_sorted":[],"title_canon_sha256":"d26df91e7c00009e962121f2e2961f4514ecc87f3b954027b07d40b458c933eb","abstract_canon_sha256":"c651eb922d0e8fc32409bca21cd650abdd38861c3d6f7b5a117071943d0015b3"},"schema_version":"1.0"},"canonical_sha256":"77d409c8fd5941a1bf85baed13ba46fb7ee508ba1f466264b0750944cc30f83d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:56.615952Z","signature_b64":"UKzXg6tFv0mxWOoSteIg/4N2ONH1pi98YEh5eBOBh/lVXuEGWTIcySeFFdigjhpip76acx1WazGqXyb5CgesDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77d409c8fd5941a1bf85baed13ba46fb7ee508ba1f466264b0750944cc30f83d","last_reissued_at":"2026-05-18T00:29:56.615331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:56.615331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07734","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":"2026-05-18T00:29:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nbD8PTG/KQFFeuTnFNbxP/IwT8lHLHgH1m4Mru+BKZkGUnKNUQsVqVvv7n00tP8nx0TvQ2WFnVhBfKzjpK4tCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:54:11.346920Z"},"content_sha256":"6ff01af36d99dc94fd64c12ddfb229f8dd05267fac23148ac8f80a2d2cd15464","schema_version":"1.0","event_id":"sha256:6ff01af36d99dc94fd64c12ddfb229f8dd05267fac23148ac8f80a2d2cd15464"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:O7KATSH5LFA2DP4FXLWRHOSG7N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Turan number of 2P_7","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yongtang Shi, Yongxin Lan, Zhongmei Qin","submitted_at":"2017-11-21T11:53:47Z","abstract_excerpt":"The Tur\\'an number of a graph $H$, denoted by $ex(n,H)$, is the maximum number of edges in any graph on $n$ vertices which does not contain $H$ as a subgraph. Let $P_{k}$ denote the path on $k$ vertices and let $mP_{k}$ denote $m$ disjoint copies of $P_{k}$. Bushaw and Kettle [Tur\\'{a}n numbers of multiple paths and equibipartite forests, Combin. Probab. Comput. 20(2011) 837--853] determined the exact value of $ex(n,kP_\\ell)$ for large values of $n$. Yuan and Zhang [The Tur\\'{a}n number of disjoint copies of paths, Discrete Math. 340(2)(2017) 132--139] completely determined the value of $ex(n,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07734","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":"2026-05-18T00:29:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"chGEuuwy2HfitRw+iFoFvU3gwzJczSG1lnDDNbQoibRcuirfBddDT98kUsKsva7Ivj/2SXAnmdcpekyxqn7UBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T13:54:11.347265Z"},"content_sha256":"774b0136f5b4196dad455f240324817707c4f62db5a96ba67093b8bb92cfa77c","schema_version":"1.0","event_id":"sha256:774b0136f5b4196dad455f240324817707c4f62db5a96ba67093b8bb92cfa77c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7KATSH5LFA2DP4FXLWRHOSG7N/bundle.json","state_url":"https://pith.science/pith/O7KATSH5LFA2DP4FXLWRHOSG7N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7KATSH5LFA2DP4FXLWRHOSG7N/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":"2026-06-03T13:54:11Z","links":{"resolver":"https://pith.science/pith/O7KATSH5LFA2DP4FXLWRHOSG7N","bundle":"https://pith.science/pith/O7KATSH5LFA2DP4FXLWRHOSG7N/bundle.json","state":"https://pith.science/pith/O7KATSH5LFA2DP4FXLWRHOSG7N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7KATSH5LFA2DP4FXLWRHOSG7N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:O7KATSH5LFA2DP4FXLWRHOSG7N","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":"c651eb922d0e8fc32409bca21cd650abdd38861c3d6f7b5a117071943d0015b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-21T11:53:47Z","title_canon_sha256":"d26df91e7c00009e962121f2e2961f4514ecc87f3b954027b07d40b458c933eb"},"schema_version":"1.0","source":{"id":"1711.07734","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07734","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07734v1","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07734","created_at":"2026-05-18T00:29:56Z"},{"alias_kind":"pith_short_12","alias_value":"O7KATSH5LFA2","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"O7KATSH5LFA2DP4F","created_at":"2026-05-18T12:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"O7KATSH5","created_at":"2026-05-18T12:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:774b0136f5b4196dad455f240324817707c4f62db5a96ba67093b8bb92cfa77c","target":"graph","created_at":"2026-05-18T00:29:56Z","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":"The Tur\\'an number of a graph $H$, denoted by $ex(n,H)$, is the maximum number of edges in any graph on $n$ vertices which does not contain $H$ as a subgraph. Let $P_{k}$ denote the path on $k$ vertices and let $mP_{k}$ denote $m$ disjoint copies of $P_{k}$. Bushaw and Kettle [Tur\\'{a}n numbers of multiple paths and equibipartite forests, Combin. Probab. Comput. 20(2011) 837--853] determined the exact value of $ex(n,kP_\\ell)$ for large values of $n$. Yuan and Zhang [The Tur\\'{a}n number of disjoint copies of paths, Discrete Math. 340(2)(2017) 132--139] completely determined the value of $ex(n,","authors_text":"Yongtang Shi, Yongxin Lan, Zhongmei Qin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-21T11:53:47Z","title":"The Turan number of 2P_7"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07734","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":"sha256:6ff01af36d99dc94fd64c12ddfb229f8dd05267fac23148ac8f80a2d2cd15464","target":"record","created_at":"2026-05-18T00:29:56Z","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":"c651eb922d0e8fc32409bca21cd650abdd38861c3d6f7b5a117071943d0015b3","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-11-21T11:53:47Z","title_canon_sha256":"d26df91e7c00009e962121f2e2961f4514ecc87f3b954027b07d40b458c933eb"},"schema_version":"1.0","source":{"id":"1711.07734","kind":"arxiv","version":1}},"canonical_sha256":"77d409c8fd5941a1bf85baed13ba46fb7ee508ba1f466264b0750944cc30f83d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77d409c8fd5941a1bf85baed13ba46fb7ee508ba1f466264b0750944cc30f83d","first_computed_at":"2026-05-18T00:29:56.615331Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:29:56.615331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UKzXg6tFv0mxWOoSteIg/4N2ONH1pi98YEh5eBOBh/lVXuEGWTIcySeFFdigjhpip76acx1WazGqXyb5CgesDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:29:56.615952Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07734","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ff01af36d99dc94fd64c12ddfb229f8dd05267fac23148ac8f80a2d2cd15464","sha256:774b0136f5b4196dad455f240324817707c4f62db5a96ba67093b8bb92cfa77c"],"state_sha256":"529767ab816554ca445e98de58f03b7d108b336a26ec1cd82c69122382d21c39"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ensaN6a5bZdpn3XcYwXsPPFrfB/VrhT1bcIrC2H7UN1Pguk1cUlGY1SYKBWfDKxvELJqwr05wUkESb0EPKblAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T13:54:11.349237Z","bundle_sha256":"cb32f3f6ff6a8012c027dc93b28a2a7b81b5967de2db96a88b43a379d1d756b4"}}