{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ESSOM7T226NUDQ32ARPIZTCYQN","short_pith_number":"pith:ESSOM7T2","canonical_record":{"source":{"id":"1902.07134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T04:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"ce2afc8ceddc292f846cabc73284b7ef5b058014b95540c81a50354bd4b43cd9","abstract_canon_sha256":"4e61cd5dfdff2b37473ce0f96cb750eaba2f8c2da69ab07cd64f2239391f597c"},"schema_version":"1.0"},"canonical_sha256":"24a4e67e7ad79b41c37a045e8ccc588354b83be2a79ad59f7f3132c6d69a90c3","source":{"kind":"arxiv","id":"1902.07134","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ESSOM7T226NUDQ32ARPIZTCYQN","target":"record","payload":{"canonical_record":{"source":{"id":"1902.07134","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-02-17T04:58:55Z","cross_cats_sorted":[],"title_canon_sha256":"ce2afc8ceddc292f846cabc73284b7ef5b058014b95540c81a50354bd4b43cd9","abstract_canon_sha256":"4e61cd5dfdff2b37473ce0f96cb750eaba2f8c2da69ab07cd64f2239391f597c"},"schema_version":"1.0"},"canonical_sha256":"24a4e67e7ad79b41c37a045e8ccc588354b83be2a79ad59f7f3132c6d69a90c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:52:50.766236Z","signature_b64":"AFritsMqdR+dJeil3Xatx3rxxutG8grgdLO+ekPAhEuCN6ULU4xzzM3W7kbnayM9MSqGI1tw2OVRjAMJmc/3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24a4e67e7ad79b41c37a045e8ccc588354b83be2a79ad59f7f3132c6d69a90c3","last_reissued_at":"2026-05-17T23:52:50.765503Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:52:50.765503Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1902.07134","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gdkCEEsAq2FlsGUT3tofyVMEkfOz9c250suho7O/Y/UNOTG5rSEfxSkD0t/LE7sYzVh0SuHb01LWLh7Z25gLBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:29:42.298876Z"},"content_sha256":"0bee8d9ef05fc9a2063ba32e1ad1340db868e32ef604bc37a389b2ace4b54fa7","schema_version":"1.0","event_id":"sha256:0bee8d9ef05fc9a2063ba32e1ad1340db868e32ef604bc37a389b2ace4b54fa7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ESSOM7T226NUDQ32ARPIZTCYQN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangian densities of short 3-uniform linear paths and Tur\\'an numbers of their extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Biao Wu, Yuejian Peng","submitted_at":"2019-02-17T04:58:55Z","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{("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.07134","kind":"arxiv","version":2},"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":"2026-05-17T23:52:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E6iOu/ZCS0YlaVXSIDk72ZI6vPn2muUPnYrrpgIwd1I229QaSLG75ukGZIOHamgSawlnt4gUUCcyrs9EL2VjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T14:29:42.299224Z"},"content_sha256":"67eda0a207d07e8bb60b0c2ee4f0c1b52e3407322434c8f545c92fbf21eaf2b7","schema_version":"1.0","event_id":"sha256:67eda0a207d07e8bb60b0c2ee4f0c1b52e3407322434c8f545c92fbf21eaf2b7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ESSOM7T226NUDQ32ARPIZTCYQN/bundle.json","state_url":"https://pith.science/pith/ESSOM7T226NUDQ32ARPIZTCYQN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ESSOM7T226NUDQ32ARPIZTCYQN/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":"2026-06-02T14:29:42Z","links":{"resolver":"https://pith.science/pith/ESSOM7T226NUDQ32ARPIZTCYQN","bundle":"https://pith.science/pith/ESSOM7T226NUDQ32ARPIZTCYQN/bundle.json","state":"https://pith.science/pith/ESSOM7T226NUDQ32ARPIZTCYQN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ESSOM7T226NUDQ32ARPIZTCYQN/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BGkr/cSVFhrp807PIMBRAQjti0fzJXoX/8ql6I5oNYoFFTrEk8e6b9dZp6DYRx8ca/VIxlhItpK0lSbJTnVOBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T14:29:42.301182Z","bundle_sha256":"7dcb53b6e1cfb38467978b232de05f675d21f9952d170473a48aae788b665b8e"}}