{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:7UOKYJXTU5PTNZYWRNTVTV5Z7D","short_pith_number":"pith:7UOKYJXT","canonical_record":{"source":{"id":"1811.04902","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-12T18:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"b8b1cd93d6115f6118a91c27ddb2410edc327b0512277204b38366c7429139b4","abstract_canon_sha256":"0068ef1b6e33928ca57d8b6b5feffcf0e1c5e38b02c48f29d5504bda0e79acfd"},"schema_version":"1.0"},"canonical_sha256":"fd1cac26f3a75f36e7168b6759d7b9f8d49143d8b78ea560d274c293d424de49","source":{"kind":"arxiv","id":"1811.04902","version":6},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04902","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04902v6","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04902","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"7UOKYJXTU5PT","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7UOKYJXTU5PTNZYW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7UOKYJXT","created_at":"2026-05-18T12:32:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:7UOKYJXTU5PTNZYWRNTVTV5Z7D","target":"record","payload":{"canonical_record":{"source":{"id":"1811.04902","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-12T18:41:49Z","cross_cats_sorted":[],"title_canon_sha256":"b8b1cd93d6115f6118a91c27ddb2410edc327b0512277204b38366c7429139b4","abstract_canon_sha256":"0068ef1b6e33928ca57d8b6b5feffcf0e1c5e38b02c48f29d5504bda0e79acfd"},"schema_version":"1.0"},"canonical_sha256":"fd1cac26f3a75f36e7168b6759d7b9f8d49143d8b78ea560d274c293d424de49","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:55.705166Z","signature_b64":"5yYTSnwQiDl47JFTXFfka58s0TIPTNLGm/ImkBhbt5xnQX5cmaHXm1guV7APWJVDOLcY++o124EKbrvK3kiSCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd1cac26f3a75f36e7168b6759d7b9f8d49143d8b78ea560d274c293d424de49","last_reissued_at":"2026-05-17T23:40:55.704545Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:55.704545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.04902","source_version":6,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gHWAEChZCWrTMoUo92/iXT4U15g1ycpQLg/d7bBVbzrXsPjEilISgwfiLcoLX+klXVvuuuZwRe83nbLawKAWAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:25:35.013183Z"},"content_sha256":"4898c4614980a32f93e77dd1209c51868f800b24ae90d48ba2318b037f755e5d","schema_version":"1.0","event_id":"sha256:4898c4614980a32f93e77dd1209c51868f800b24ae90d48ba2318b037f755e5d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:7UOKYJXTU5PTNZYWRNTVTV5Z7D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Erd\\H{o}s-Ko-Rado property of trees of depth two","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carl Feghali","submitted_at":"2018-11-12T18:41:49Z","abstract_excerpt":"A family of sets is intersecting if any two sets in the family intersect. Given a graph $G$ and an integer $r\\geq 1$, let $\\mathcal{I}^{(r)}(G)$ denote the family of independent sets of size $r$ of $G$. For a vertex $v$ of $G$, let $\\mathcal{I}^{(r)}_v(G)$ denote the family of independent sets of size $r$ that contain $v$. This family is called an $r$-star. Then $G$ is said to be $r$-EKR if no intersecting subfamily of $ \\mathcal{I}^{(r)}(G)$ is bigger than the largest $r$-star. Let $k, n, r \\geq 1$, and let $T(n, k)$ be the tree of depth two in which the root has degree $n$ and every neighbou"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04902","kind":"arxiv","version":6},"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":"2026-05-17T23:40:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"O9tQo0OA1FsG3UyktOi14yBJQi7N5B/CfOfyru4idakFwno9FbSBPm6D1ClhZPcPmkVzYO7hVeLve2xTOcXEDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:25:35.013560Z"},"content_sha256":"6f997d400ac463a2de19c53ec72a8e1ed81995ed209bc63bf2374bf1933aa764","schema_version":"1.0","event_id":"sha256:6f997d400ac463a2de19c53ec72a8e1ed81995ed209bc63bf2374bf1933aa764"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D/bundle.json","state_url":"https://pith.science/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D/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":"2026-06-01T19:25:35Z","links":{"resolver":"https://pith.science/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D","bundle":"https://pith.science/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D/bundle.json","state":"https://pith.science/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7UOKYJXTU5PTNZYWRNTVTV5Z7D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:7UOKYJXTU5PTNZYWRNTVTV5Z7D","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":"0068ef1b6e33928ca57d8b6b5feffcf0e1c5e38b02c48f29d5504bda0e79acfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-12T18:41:49Z","title_canon_sha256":"b8b1cd93d6115f6118a91c27ddb2410edc327b0512277204b38366c7429139b4"},"schema_version":"1.0","source":{"id":"1811.04902","kind":"arxiv","version":6}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.04902","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"arxiv_version","alias_value":"1811.04902v6","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.04902","created_at":"2026-05-17T23:40:55Z"},{"alias_kind":"pith_short_12","alias_value":"7UOKYJXTU5PT","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_16","alias_value":"7UOKYJXTU5PTNZYW","created_at":"2026-05-18T12:32:11Z"},{"alias_kind":"pith_short_8","alias_value":"7UOKYJXT","created_at":"2026-05-18T12:32:11Z"}],"graph_snapshots":[{"event_id":"sha256:6f997d400ac463a2de19c53ec72a8e1ed81995ed209bc63bf2374bf1933aa764","target":"graph","created_at":"2026-05-17T23:40:55Z","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":"A family of sets is intersecting if any two sets in the family intersect. Given a graph $G$ and an integer $r\\geq 1$, let $\\mathcal{I}^{(r)}(G)$ denote the family of independent sets of size $r$ of $G$. For a vertex $v$ of $G$, let $\\mathcal{I}^{(r)}_v(G)$ denote the family of independent sets of size $r$ that contain $v$. This family is called an $r$-star. Then $G$ is said to be $r$-EKR if no intersecting subfamily of $ \\mathcal{I}^{(r)}(G)$ is bigger than the largest $r$-star. Let $k, n, r \\geq 1$, and let $T(n, k)$ be the tree of depth two in which the root has degree $n$ and every neighbou","authors_text":"Carl Feghali","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-12T18:41:49Z","title":"The Erd\\H{o}s-Ko-Rado property of trees of depth two"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.04902","kind":"arxiv","version":6},"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":"sha256:4898c4614980a32f93e77dd1209c51868f800b24ae90d48ba2318b037f755e5d","target":"record","created_at":"2026-05-17T23:40:55Z","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":"0068ef1b6e33928ca57d8b6b5feffcf0e1c5e38b02c48f29d5504bda0e79acfd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-11-12T18:41:49Z","title_canon_sha256":"b8b1cd93d6115f6118a91c27ddb2410edc327b0512277204b38366c7429139b4"},"schema_version":"1.0","source":{"id":"1811.04902","kind":"arxiv","version":6}},"canonical_sha256":"fd1cac26f3a75f36e7168b6759d7b9f8d49143d8b78ea560d274c293d424de49","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd1cac26f3a75f36e7168b6759d7b9f8d49143d8b78ea560d274c293d424de49","first_computed_at":"2026-05-17T23:40:55.704545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:55.704545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5yYTSnwQiDl47JFTXFfka58s0TIPTNLGm/ImkBhbt5xnQX5cmaHXm1guV7APWJVDOLcY++o124EKbrvK3kiSCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:55.705166Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.04902","source_kind":"arxiv","source_version":6}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4898c4614980a32f93e77dd1209c51868f800b24ae90d48ba2318b037f755e5d","sha256:6f997d400ac463a2de19c53ec72a8e1ed81995ed209bc63bf2374bf1933aa764"],"state_sha256":"e4d7fb4fa10f30a393c816024cc0c29429ce2362c2f1435d8c422e2adf1c9b26"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LbrBo76URkEk+8JnOQQMhfwqJypMG6O7fCPhVmTF3PbJhAlmn5x59wHbnS65pqtMqhBvNbkCuM8wr/bb0MyyCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:25:35.015737Z","bundle_sha256":"407f268eceb0fa23abe75670f86ca6b7ca0a2a5000601786827126df1008e2c8"}}