{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:L5DWYCBKUIA3C5635T5YJXSXAO","short_pith_number":"pith:L5DWYCBK","canonical_record":{"source":{"id":"1609.08983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T16:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"f1648636b288c26fff00f64c516ffed73eb41f86f7ff202721ffe4aae3590236","abstract_canon_sha256":"af0cc603254516732dc42b9051f0d25aecac6cfc683c3e13fb5d6ffe91190694"},"schema_version":"1.0"},"canonical_sha256":"5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab","source":{"kind":"arxiv","id":"1609.08983","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08983","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08983v1","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08983","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"L5DWYCBKUIA3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L5DWYCBKUIA3C563","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L5DWYCBK","created_at":"2026-05-18T12:30:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:L5DWYCBKUIA3C5635T5YJXSXAO","target":"record","payload":{"canonical_record":{"source":{"id":"1609.08983","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T16:06:40Z","cross_cats_sorted":[],"title_canon_sha256":"f1648636b288c26fff00f64c516ffed73eb41f86f7ff202721ffe4aae3590236","abstract_canon_sha256":"af0cc603254516732dc42b9051f0d25aecac6cfc683c3e13fb5d6ffe91190694"},"schema_version":"1.0"},"canonical_sha256":"5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:41.452627Z","signature_b64":"o8GYmi9vaVOT3q794LnVCRsngPYr3bZAzF4w4yywmC/vJl4F3riOo23UuWCDfoJsw9pSlmeQ0ZlV3NDPYQNhCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab","last_reissued_at":"2026-05-18T01:03:41.452248Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:41.452248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1609.08983","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":"2026-05-18T01:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZGtXimJ1ODiWWmBlAoH+TN8RLUuUmrf6fnYW0BWvsDSv+yjr2f34EjoTKHkn5v84zLej9aBxNl42vGVxxQi7BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:39:24.135675Z"},"content_sha256":"91d177a25ffa4e43a904afad968ac5bc629b8132595db4874f65ba32e9630356","schema_version":"1.0","event_id":"sha256:91d177a25ffa4e43a904afad968ac5bc629b8132595db4874f65ba32e9630356"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:L5DWYCBKUIA3C5635T5YJXSXAO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Turan numbers of extensions of some sparse hypergraphs via Lagrangians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Biao Wu, Tao Jiang, Yuejian Peng","submitted_at":"2016-09-28T16:06:40Z","abstract_excerpt":"Given a positive integer $n$ and an $r$-uniform hypergraph (or $r$-graph for short) $F$, the Turan number $ex(n,F)$ of $F$ is the maximum number of edges in an $r$-graph on $n$ vertices that does not contain $F$ as a subgraph. The extension $H^F $ of $F$ is obtained as follows: For each pair of vertices $v_i,v_j$ in $F$ not contained in an edge of $F$, we add a set $B_{ij}$ of $r-2$ new vertices and the edge $\\{v_i,v_j\\} \\cup B_{ij}$, where the $B_{ij}$ 's are pairwise disjoint over all such pairs $\\{i,j\\}$. Let $K^r_p$ denote the complete $r$-graph on $p$ vertices. For all sufficiently large "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08983","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":"2026-05-18T01:03:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z5K/l9VJIimf6hudRxCnP8vwop+B8bwui9cwLWbbn0FsSmPPeU8zYQVfMXPLQ+A18OqyzfEVinUbH/ubngSHDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T00:39:24.136022Z"},"content_sha256":"86c91be33c928a47baa775566670ba07c7210a895eed1ffbdd693bf1da8b193c","schema_version":"1.0","event_id":"sha256:86c91be33c928a47baa775566670ba07c7210a895eed1ffbdd693bf1da8b193c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5DWYCBKUIA3C5635T5YJXSXAO/bundle.json","state_url":"https://pith.science/pith/L5DWYCBKUIA3C5635T5YJXSXAO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5DWYCBKUIA3C5635T5YJXSXAO/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":"2026-06-03T00:39:24Z","links":{"resolver":"https://pith.science/pith/L5DWYCBKUIA3C5635T5YJXSXAO","bundle":"https://pith.science/pith/L5DWYCBKUIA3C5635T5YJXSXAO/bundle.json","state":"https://pith.science/pith/L5DWYCBKUIA3C5635T5YJXSXAO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5DWYCBKUIA3C5635T5YJXSXAO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:L5DWYCBKUIA3C5635T5YJXSXAO","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":"af0cc603254516732dc42b9051f0d25aecac6cfc683c3e13fb5d6ffe91190694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T16:06:40Z","title_canon_sha256":"f1648636b288c26fff00f64c516ffed73eb41f86f7ff202721ffe4aae3590236"},"schema_version":"1.0","source":{"id":"1609.08983","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1609.08983","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"arxiv_version","alias_value":"1609.08983v1","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.08983","created_at":"2026-05-18T01:03:41Z"},{"alias_kind":"pith_short_12","alias_value":"L5DWYCBKUIA3","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"L5DWYCBKUIA3C563","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"L5DWYCBK","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:86c91be33c928a47baa775566670ba07c7210a895eed1ffbdd693bf1da8b193c","target":"graph","created_at":"2026-05-18T01:03:41Z","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 positive integer $n$ and an $r$-uniform hypergraph (or $r$-graph for short) $F$, the Turan number $ex(n,F)$ of $F$ is the maximum number of edges in an $r$-graph on $n$ vertices that does not contain $F$ as a subgraph. The extension $H^F $ of $F$ is obtained as follows: For each pair of vertices $v_i,v_j$ in $F$ not contained in an edge of $F$, we add a set $B_{ij}$ of $r-2$ new vertices and the edge $\\{v_i,v_j\\} \\cup B_{ij}$, where the $B_{ij}$ 's are pairwise disjoint over all such pairs $\\{i,j\\}$. Let $K^r_p$ denote the complete $r$-graph on $p$ vertices. For all sufficiently large ","authors_text":"Biao Wu, Tao Jiang, Yuejian Peng","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T16:06:40Z","title":"Turan numbers of extensions of some sparse hypergraphs via Lagrangians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08983","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":"sha256:91d177a25ffa4e43a904afad968ac5bc629b8132595db4874f65ba32e9630356","target":"record","created_at":"2026-05-18T01:03:41Z","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":"af0cc603254516732dc42b9051f0d25aecac6cfc683c3e13fb5d6ffe91190694","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-28T16:06:40Z","title_canon_sha256":"f1648636b288c26fff00f64c516ffed73eb41f86f7ff202721ffe4aae3590236"},"schema_version":"1.0","source":{"id":"1609.08983","kind":"arxiv","version":1}},"canonical_sha256":"5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f476c082aa201b177dbecfb84de57038d8a0b6e013cd83173d2e3ab427be1ab","first_computed_at":"2026-05-18T01:03:41.452248Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:03:41.452248Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o8GYmi9vaVOT3q794LnVCRsngPYr3bZAzF4w4yywmC/vJl4F3riOo23UuWCDfoJsw9pSlmeQ0ZlV3NDPYQNhCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:03:41.452627Z","signed_message":"canonical_sha256_bytes"},"source_id":"1609.08983","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91d177a25ffa4e43a904afad968ac5bc629b8132595db4874f65ba32e9630356","sha256:86c91be33c928a47baa775566670ba07c7210a895eed1ffbdd693bf1da8b193c"],"state_sha256":"7e4fd293b8429a7035340eeb5ddb2fb00bbf7fcc6247cb6263050268579ae086"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fvLv1HszmVjt7HWLM1dS98s5b1klGGcV56UWtMt1l6wtO7J50p2lNYO4z9z0kF89SlD0OWVppixcBc3Q9vfGAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T00:39:24.138010Z","bundle_sha256":"9e22b0f43d05fc3e9331b93a74a305a10be8d71aab728f9c8a2d493c7e0d63e6"}}