{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:HKLAHCZH6DX2GCYYE7PPHZ7LI7","short_pith_number":"pith:HKLAHCZH","canonical_record":{"source":{"id":"1510.04689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T19:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"897d819af69834a43996eabcfafb7822341e314cd7eb4d3d9251a2ea0dd8eaab","abstract_canon_sha256":"b1a56a0611d4927947e3d32581eb2fad6e36c8901fdee278cd82982f59b8cb14"},"schema_version":"1.0"},"canonical_sha256":"3a96038b27f0efa30b1827def3e7eb47db9b109be5f9f5cd6d8857a14ed23529","source":{"kind":"arxiv","id":"1510.04689","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04689","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04689v1","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04689","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"HKLAHCZH6DX2","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HKLAHCZH6DX2GCYY","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HKLAHCZH","created_at":"2026-05-18T12:29:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:HKLAHCZH6DX2GCYYE7PPHZ7LI7","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04689","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T19:59:31Z","cross_cats_sorted":[],"title_canon_sha256":"897d819af69834a43996eabcfafb7822341e314cd7eb4d3d9251a2ea0dd8eaab","abstract_canon_sha256":"b1a56a0611d4927947e3d32581eb2fad6e36c8901fdee278cd82982f59b8cb14"},"schema_version":"1.0"},"canonical_sha256":"3a96038b27f0efa30b1827def3e7eb47db9b109be5f9f5cd6d8857a14ed23529","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:30:01.938580Z","signature_b64":"cLSdifsy4co45fw8NFQ+hwv83Gu0AmLxUfDE8gGO4RzbPUtbGBn4AivyhhRb2tkzBMntm91tB9qpIVdbWde5DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3a96038b27f0efa30b1827def3e7eb47db9b109be5f9f5cd6d8857a14ed23529","last_reissued_at":"2026-05-18T01:30:01.937936Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:30:01.937936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04689","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":"2026-05-18T01:30:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iCfhxXRMbdlFTKZmtMUOIJrfFaOU0j+ND4vkuHN0Cdj0XI65fkEMMWTTtfneT4bFhbgPhx2D8wcSScOC6rk2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:01:00.805471Z"},"content_sha256":"c84101c4143de6a4b1e2a7ed5de7265e8807682753db9020eeee168b2fdd38c5","schema_version":"1.0","event_id":"sha256:c84101c4143de6a4b1e2a7ed5de7265e8807682753db9020eeee168b2fdd38c5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:HKLAHCZH6DX2GCYYE7PPHZ7LI7","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Tur\\'an numbers of extensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Liana Yepremyan, Sergey Norin","submitted_at":"2015-10-15T19:59:31Z","abstract_excerpt":"The extension of an $r$-uniform hypergraph $G$ is obtained from it by adding for every pair of vertices of $G$, which is not covered by an edge in $G$, an extra edge containing this pair and $r-2$ new vertices. Keevash and Sidorenko~ have previously determined Tur\\'an densities of two families of hypergraph extensions. We determine the Tur\\'an numbers for these families, using classical stability techniques and new tools introduced in our earlier paper."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04689","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":"2026-05-18T01:30:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ea7Ft1eRG+MmTKCienZ17skj4syWmd4+WJot2ziZVCb72U9P0/HxRgXjLfJt9gmKWwce8AOPlorob4eKFAlKAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:01:00.806127Z"},"content_sha256":"494307aa35e9199fd95e780ec60ccf683bf0c51c58fc0049299a21d8c900d983","schema_version":"1.0","event_id":"sha256:494307aa35e9199fd95e780ec60ccf683bf0c51c58fc0049299a21d8c900d983"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7/bundle.json","state_url":"https://pith.science/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7/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":"2026-05-25T21:01:00Z","links":{"resolver":"https://pith.science/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7","bundle":"https://pith.science/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7/bundle.json","state":"https://pith.science/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HKLAHCZH6DX2GCYYE7PPHZ7LI7/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HKLAHCZH6DX2GCYYE7PPHZ7LI7","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":"b1a56a0611d4927947e3d32581eb2fad6e36c8901fdee278cd82982f59b8cb14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T19:59:31Z","title_canon_sha256":"897d819af69834a43996eabcfafb7822341e314cd7eb4d3d9251a2ea0dd8eaab"},"schema_version":"1.0","source":{"id":"1510.04689","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04689","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04689v1","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04689","created_at":"2026-05-18T01:30:01Z"},{"alias_kind":"pith_short_12","alias_value":"HKLAHCZH6DX2","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HKLAHCZH6DX2GCYY","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HKLAHCZH","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:494307aa35e9199fd95e780ec60ccf683bf0c51c58fc0049299a21d8c900d983","target":"graph","created_at":"2026-05-18T01:30:01Z","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 extension of an $r$-uniform hypergraph $G$ is obtained from it by adding for every pair of vertices of $G$, which is not covered by an edge in $G$, an extra edge containing this pair and $r-2$ new vertices. Keevash and Sidorenko~ have previously determined Tur\\'an densities of two families of hypergraph extensions. We determine the Tur\\'an numbers for these families, using classical stability techniques and new tools introduced in our earlier paper.","authors_text":"Liana Yepremyan, Sergey Norin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T19:59:31Z","title":"Tur\\'an numbers of extensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04689","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:c84101c4143de6a4b1e2a7ed5de7265e8807682753db9020eeee168b2fdd38c5","target":"record","created_at":"2026-05-18T01:30:01Z","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":"b1a56a0611d4927947e3d32581eb2fad6e36c8901fdee278cd82982f59b8cb14","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-15T19:59:31Z","title_canon_sha256":"897d819af69834a43996eabcfafb7822341e314cd7eb4d3d9251a2ea0dd8eaab"},"schema_version":"1.0","source":{"id":"1510.04689","kind":"arxiv","version":1}},"canonical_sha256":"3a96038b27f0efa30b1827def3e7eb47db9b109be5f9f5cd6d8857a14ed23529","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a96038b27f0efa30b1827def3e7eb47db9b109be5f9f5cd6d8857a14ed23529","first_computed_at":"2026-05-18T01:30:01.937936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:01.937936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cLSdifsy4co45fw8NFQ+hwv83Gu0AmLxUfDE8gGO4RzbPUtbGBn4AivyhhRb2tkzBMntm91tB9qpIVdbWde5DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:01.938580Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04689","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c84101c4143de6a4b1e2a7ed5de7265e8807682753db9020eeee168b2fdd38c5","sha256:494307aa35e9199fd95e780ec60ccf683bf0c51c58fc0049299a21d8c900d983"],"state_sha256":"fa5bed436ed1ac8f1127fc601cde844a89f32730598968a387320360954194da"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ApO7vhcpTJTd19fn0LgjPvjC5HvcfDpi63kAniMsfT1ASbqM0lX/hCeJtBUgpZLJVPPHSX+6V581NaG5H1zgBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:01:00.809282Z","bundle_sha256":"c17fc8c94828703131570d8099c07ef8bd9164f9d36f715d7a99df462dae3d3d"}}