{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:LL5PXA235K7DHYEN2I4HEU4E4P","short_pith_number":"pith:LL5PXA23","canonical_record":{"source":{"id":"1612.08856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T11:32:32Z","cross_cats_sorted":[],"title_canon_sha256":"70b3bdec9a7e301dd8f1605e72b06d516d6e26321eab0417def6f666df134798","abstract_canon_sha256":"55979f2ae35535acde082bea06e64f65426cf7095ee7818c38596bddd8bbee6f"},"schema_version":"1.0"},"canonical_sha256":"5afafb835beabe33e08dd238725384e3f9d74a4248c6e9dcb04a891857eab771","source":{"kind":"arxiv","id":"1612.08856","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08856","created_at":"2026-05-18T00:53:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08856v1","created_at":"2026-05-18T00:53:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08856","created_at":"2026-05-18T00:53:47Z"},{"alias_kind":"pith_short_12","alias_value":"LL5PXA235K7D","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LL5PXA235K7DHYEN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LL5PXA23","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:LL5PXA235K7DHYEN2I4HEU4E4P","target":"record","payload":{"canonical_record":{"source":{"id":"1612.08856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T11:32:32Z","cross_cats_sorted":[],"title_canon_sha256":"70b3bdec9a7e301dd8f1605e72b06d516d6e26321eab0417def6f666df134798","abstract_canon_sha256":"55979f2ae35535acde082bea06e64f65426cf7095ee7818c38596bddd8bbee6f"},"schema_version":"1.0"},"canonical_sha256":"5afafb835beabe33e08dd238725384e3f9d74a4248c6e9dcb04a891857eab771","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:47.001503Z","signature_b64":"ga7OMwnBpliwRP7kO0tvzckjkL0vuP0cSwxFjymqkzTFuFNbHYB41NkYCaqTAcCvDWYvaqK9yBdiSpnTHjiwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5afafb835beabe33e08dd238725384e3f9d74a4248c6e9dcb04a891857eab771","last_reissued_at":"2026-05-18T00:53:47.001105Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:47.001105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.08856","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":"2026-05-18T00:53:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juKOroFT2/7SLfKl00lohwFlNr9q3b6V5U59pTc3ZyAW0xc62s4OVxbrn/XW0oHkPx7MamGDZywUONA0CyUcBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:08:51.551111Z"},"content_sha256":"7a85b93d453d237e5a7b213ceae45c779271749d4b307ef937109dffa0135e12","schema_version":"1.0","event_id":"sha256:7a85b93d453d237e5a7b213ceae45c779271749d4b307ef937109dffa0135e12"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:LL5PXA235K7DHYEN2I4HEU4E4P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Turan numbers of complete 3-uniform Berge-hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"L. Maherani, M. Shahsiah","submitted_at":"2016-12-28T11:32:32Z","abstract_excerpt":"Given a family $\\mathcal{F}$ of $r$-graphs, the Tur\\'{a}n number of $\\mathcal{F}$ for a given positive integer $N$, denoted by $ex(N,\\mathcal{F})$, is the maximum number of edges of an $r$-graph on $N$ vertices that does not contain any member of $\\mathcal{F}$ as a subgraph.  For given $r\\geq 3$, a  complete $r$-uniform Berge-hypergraph, denoted by { ${K}_n^{(r)}$}, is an $r$-uniform hypergraph of order $n$  with the core sequence $v_{1}, v_{2}, \\ldots ,v_{n}$ as the vertices and  distinct edges $e_{ij},$ $1\\leq i<j\\leq n,$ where every $e_{ij}$ contains both   $v_{i}$ and $v_{j}$. Let $\\mathca"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08856","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":"2026-05-18T00:53:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaiPZK6tW/1GuglkazwY3RXwNvfqu4LtWVYfj3yKvmhtbr8ryUDNwnhkmM9rhHXpCj4bUwjt6ntQ7oHLDJ3PCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:08:51.551469Z"},"content_sha256":"a8eced8f9be24cfd89d72ac74ffd3e6882b828d5edb31d376222044248ffa1a9","schema_version":"1.0","event_id":"sha256:a8eced8f9be24cfd89d72ac74ffd3e6882b828d5edb31d376222044248ffa1a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL5PXA235K7DHYEN2I4HEU4E4P/bundle.json","state_url":"https://pith.science/pith/LL5PXA235K7DHYEN2I4HEU4E4P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL5PXA235K7DHYEN2I4HEU4E4P/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":"2026-06-23T18:08:51Z","links":{"resolver":"https://pith.science/pith/LL5PXA235K7DHYEN2I4HEU4E4P","bundle":"https://pith.science/pith/LL5PXA235K7DHYEN2I4HEU4E4P/bundle.json","state":"https://pith.science/pith/LL5PXA235K7DHYEN2I4HEU4E4P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL5PXA235K7DHYEN2I4HEU4E4P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:LL5PXA235K7DHYEN2I4HEU4E4P","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":"55979f2ae35535acde082bea06e64f65426cf7095ee7818c38596bddd8bbee6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T11:32:32Z","title_canon_sha256":"70b3bdec9a7e301dd8f1605e72b06d516d6e26321eab0417def6f666df134798"},"schema_version":"1.0","source":{"id":"1612.08856","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.08856","created_at":"2026-05-18T00:53:47Z"},{"alias_kind":"arxiv_version","alias_value":"1612.08856v1","created_at":"2026-05-18T00:53:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08856","created_at":"2026-05-18T00:53:47Z"},{"alias_kind":"pith_short_12","alias_value":"LL5PXA235K7D","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"LL5PXA235K7DHYEN","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"LL5PXA23","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:a8eced8f9be24cfd89d72ac74ffd3e6882b828d5edb31d376222044248ffa1a9","target":"graph","created_at":"2026-05-18T00:53:47Z","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":"Given a family $\\mathcal{F}$ of $r$-graphs, the Tur\\'{a}n number of $\\mathcal{F}$ for a given positive integer $N$, denoted by $ex(N,\\mathcal{F})$, is the maximum number of edges of an $r$-graph on $N$ vertices that does not contain any member of $\\mathcal{F}$ as a subgraph.  For given $r\\geq 3$, a  complete $r$-uniform Berge-hypergraph, denoted by { ${K}_n^{(r)}$}, is an $r$-uniform hypergraph of order $n$  with the core sequence $v_{1}, v_{2}, \\ldots ,v_{n}$ as the vertices and  distinct edges $e_{ij},$ $1\\leq i<j\\leq n,$ where every $e_{ij}$ contains both   $v_{i}$ and $v_{j}$. Let $\\mathca","authors_text":"L. Maherani, M. Shahsiah","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T11:32:32Z","title":"Turan numbers of complete 3-uniform Berge-hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08856","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":"sha256:7a85b93d453d237e5a7b213ceae45c779271749d4b307ef937109dffa0135e12","target":"record","created_at":"2026-05-18T00:53:47Z","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":"55979f2ae35535acde082bea06e64f65426cf7095ee7818c38596bddd8bbee6f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-28T11:32:32Z","title_canon_sha256":"70b3bdec9a7e301dd8f1605e72b06d516d6e26321eab0417def6f666df134798"},"schema_version":"1.0","source":{"id":"1612.08856","kind":"arxiv","version":1}},"canonical_sha256":"5afafb835beabe33e08dd238725384e3f9d74a4248c6e9dcb04a891857eab771","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5afafb835beabe33e08dd238725384e3f9d74a4248c6e9dcb04a891857eab771","first_computed_at":"2026-05-18T00:53:47.001105Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:47.001105Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ga7OMwnBpliwRP7kO0tvzckjkL0vuP0cSwxFjymqkzTFuFNbHYB41NkYCaqTAcCvDWYvaqK9yBdiSpnTHjiwCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:47.001503Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.08856","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7a85b93d453d237e5a7b213ceae45c779271749d4b307ef937109dffa0135e12","sha256:a8eced8f9be24cfd89d72ac74ffd3e6882b828d5edb31d376222044248ffa1a9"],"state_sha256":"8de906d153c639766abd40e0eeb46ef7eff545baaf3a9fa3fe65ff95c737a99f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"l4z6qylfVGtlu2NcfcQAxcWeuDA9d774eslP0UhcBVCSD3tdj9Ynn8+p8U4Hy7mw5sJX0mq2BkqU0KRxRiSGDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:08:51.553377Z","bundle_sha256":"56bb689a28fb40a59fa6896b22ab1f10559d8b4f6ff6e52bab3de912648f58ff"}}