{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ESSOM7T226NUDQ32ARPIZTCYQN","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":"4e61cd5dfdff2b37473ce0f96cb750eaba2f8c2da69ab07cd64f2239391f597c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T04:58:55Z","title_canon_sha256":"ce2afc8ceddc292f846cabc73284b7ef5b058014b95540c81a50354bd4b43cd9"},"schema_version":"1.0","source":{"id":"1902.07134","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1902.07134","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"arxiv_version","alias_value":"1902.07134v2","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1902.07134","created_at":"2026-05-17T23:52:50Z"},{"alias_kind":"pith_short_12","alias_value":"ESSOM7T226NU","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_16","alias_value":"ESSOM7T226NUDQ32","created_at":"2026-05-18T12:33:15Z"},{"alias_kind":"pith_short_8","alias_value":"ESSOM7T2","created_at":"2026-05-18T12:33:15Z"}],"graph_snapshots":[{"event_id":"sha256:67eda0a207d07e8bb60b0c2ee4f0c1b52e3407322434c8f545c92fbf21eaf2b7","target":"graph","created_at":"2026-05-17T23:52:50Z","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":"For a fixed positive integer $n$ and an $r$-uniform hypergraph $H$, the Tur\\'an number $ex(n,H)$ is the maximum number of edges in an $H$-free $r$-uniform hypergraph on $n$ vertices, and the Lagrangian density of $H$ is defined as $\\pi_{\\lambda}(H)=\\sup \\{r! \\lambda(G) : G \\;\\text{is an}\\; H\\text{-free} \\;r\\text{-uniform hypergraph}\\}$, where $\\lambda(G)$ is the Lagrangian of $G$. For an $r$-uniform hypergraph $H$ on $t$ vertices, it is clear that $\\pi_{\\lambda}(H)\\ge r!\\lambda{(K_{t-1}^r)}$. We say that an $r$-uniform hypergraph $H$ on $t$ vertices is perfect if $\\pi_{\\lambda}(H)= r!\\lambda{(","authors_text":"Biao Wu, Yuejian Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T04:58:55Z","title":"Lagrangian densities of short 3-uniform linear paths and Tur\\'an numbers of their extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07134","kind":"arxiv","version":2},"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":"sha256:0bee8d9ef05fc9a2063ba32e1ad1340db868e32ef604bc37a389b2ace4b54fa7","target":"record","created_at":"2026-05-17T23:52:50Z","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":"4e61cd5dfdff2b37473ce0f96cb750eaba2f8c2da69ab07cd64f2239391f597c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T04:58:55Z","title_canon_sha256":"ce2afc8ceddc292f846cabc73284b7ef5b058014b95540c81a50354bd4b43cd9"},"schema_version":"1.0","source":{"id":"1902.07134","kind":"arxiv","version":2}},"canonical_sha256":"24a4e67e7ad79b41c37a045e8ccc588354b83be2a79ad59f7f3132c6d69a90c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24a4e67e7ad79b41c37a045e8ccc588354b83be2a79ad59f7f3132c6d69a90c3","first_computed_at":"2026-05-17T23:52:50.765503Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:52:50.765503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AFritsMqdR+dJeil3Xatx3rxxutG8grgdLO+ekPAhEuCN6ULU4xzzM3W7kbnayM9MSqGI1tw2OVRjAMJmc/3Ag==","signature_status":"signed_v1","signed_at":"2026-05-17T23:52:50.766236Z","signed_message":"canonical_sha256_bytes"},"source_id":"1902.07134","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0bee8d9ef05fc9a2063ba32e1ad1340db868e32ef604bc37a389b2ace4b54fa7","sha256:67eda0a207d07e8bb60b0c2ee4f0c1b52e3407322434c8f545c92fbf21eaf2b7"],"state_sha256":"4d65af5875fb619f1f3c8209d4df2da840a7f3516a7fc4df5ebe14b513969a83"}