{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:N47WJNFQGEHIPBKWF4IDLTBOS3","short_pith_number":"pith:N47WJNFQ","canonical_record":{"source":{"id":"1109.4472","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-21T04:25:59Z","cross_cats_sorted":[],"title_canon_sha256":"20c9685b0601396a5ad09099979b484bb1fee913825b80ce880302754474266a","abstract_canon_sha256":"45d6778de701809deb62ec67333052f5f56a472ba0900ceceeb0f8da42032d9a"},"schema_version":"1.0"},"canonical_sha256":"6f3f64b4b0310e8785562f1035cc2e96c0a0423756c194fa14e19ecc7f1f0dc9","source":{"kind":"arxiv","id":"1109.4472","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4472","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4472v2","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4472","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"N47WJNFQGEHI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N47WJNFQGEHIPBKW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N47WJNFQ","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:N47WJNFQGEHIPBKWF4IDLTBOS3","target":"record","payload":{"canonical_record":{"source":{"id":"1109.4472","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-21T04:25:59Z","cross_cats_sorted":[],"title_canon_sha256":"20c9685b0601396a5ad09099979b484bb1fee913825b80ce880302754474266a","abstract_canon_sha256":"45d6778de701809deb62ec67333052f5f56a472ba0900ceceeb0f8da42032d9a"},"schema_version":"1.0"},"canonical_sha256":"6f3f64b4b0310e8785562f1035cc2e96c0a0423756c194fa14e19ecc7f1f0dc9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:17:34.418255Z","signature_b64":"AsOdX80nDBLJIDz/++M+/sTrD6T42k37McxwnNqUa13CpsDraFVn+gz7QqLiVYFZLaqK5SM+671b4eStB9EpCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f3f64b4b0310e8785562f1035cc2e96c0a0423756c194fa14e19ecc7f1f0dc9","last_reissued_at":"2026-05-18T03:17:34.417773Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:17:34.417773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1109.4472","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":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+AooLszoFHyU7+nCfoqUT821xdyvQvVXXVXwNDB+fCu5uNSoydP5xmrEbXf1Dj9fAfoKAZf6955Ui0K2yVTjAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:13:15.871115Z"},"content_sha256":"037a854f1fc383a90fe3317deddb52d777449f66a2de5d592ca689ffc2803c3d","schema_version":"1.0","event_id":"sha256:037a854f1fc383a90fe3317deddb52d777449f66a2de5d592ca689ffc2803c3d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:N47WJNFQGEHIPBKWF4IDLTBOS3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Exact Ramsey-Tur\\'an Numbers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"John Lenz, J\\'ozsef Balogh","submitted_at":"2011-09-21T04:25:59Z","abstract_excerpt":"Let r be an integer, f(n) a function, and H a graph. Introduced by Erd\\H{o}s, Hajnal, S\\'{o}s, and Szemer\\'edi, the r-Ramsey-Tur\\'{a}n number of H, RT_r(n, H, f(n)), is defined to be the maximum number of edges in an n-vertex, H-free graph G with \\alpha_r(G) <= f(n) where \\alpha_r(G) denotes the K_r-independence number of G. In this note, using isoperimetric properties of the high dimensional unit sphere, we construct graphs providing lower bounds for RT_r(n,K_{r+s},o(n)) for every 2 <= s <= r. These constructions are sharp for an infinite family of pairs of r and s. The only previous sharp co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4472","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":"2026-05-18T03:17:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FGiqgRhpGpTqrpgDEgJrYd7DddqUYc2BbNKqHlm44VllIcZyMIrPDPHRb+LZ+bcceGvNH57DCwGIQ+GQHt0IDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T22:13:15.871484Z"},"content_sha256":"685a5f16ece07947ddf98207d5595748d491c9117039196229b7d95af7591209","schema_version":"1.0","event_id":"sha256:685a5f16ece07947ddf98207d5595748d491c9117039196229b7d95af7591209"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N47WJNFQGEHIPBKWF4IDLTBOS3/bundle.json","state_url":"https://pith.science/pith/N47WJNFQGEHIPBKWF4IDLTBOS3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N47WJNFQGEHIPBKWF4IDLTBOS3/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":"2026-05-31T22:13:15Z","links":{"resolver":"https://pith.science/pith/N47WJNFQGEHIPBKWF4IDLTBOS3","bundle":"https://pith.science/pith/N47WJNFQGEHIPBKWF4IDLTBOS3/bundle.json","state":"https://pith.science/pith/N47WJNFQGEHIPBKWF4IDLTBOS3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N47WJNFQGEHIPBKWF4IDLTBOS3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N47WJNFQGEHIPBKWF4IDLTBOS3","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":"45d6778de701809deb62ec67333052f5f56a472ba0900ceceeb0f8da42032d9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-21T04:25:59Z","title_canon_sha256":"20c9685b0601396a5ad09099979b484bb1fee913825b80ce880302754474266a"},"schema_version":"1.0","source":{"id":"1109.4472","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1109.4472","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"arxiv_version","alias_value":"1109.4472v2","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.4472","created_at":"2026-05-18T03:17:34Z"},{"alias_kind":"pith_short_12","alias_value":"N47WJNFQGEHI","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N47WJNFQGEHIPBKW","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N47WJNFQ","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:685a5f16ece07947ddf98207d5595748d491c9117039196229b7d95af7591209","target":"graph","created_at":"2026-05-18T03:17:34Z","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":"Let r be an integer, f(n) a function, and H a graph. Introduced by Erd\\H{o}s, Hajnal, S\\'{o}s, and Szemer\\'edi, the r-Ramsey-Tur\\'{a}n number of H, RT_r(n, H, f(n)), is defined to be the maximum number of edges in an n-vertex, H-free graph G with \\alpha_r(G) <= f(n) where \\alpha_r(G) denotes the K_r-independence number of G. In this note, using isoperimetric properties of the high dimensional unit sphere, we construct graphs providing lower bounds for RT_r(n,K_{r+s},o(n)) for every 2 <= s <= r. These constructions are sharp for an infinite family of pairs of r and s. The only previous sharp co","authors_text":"John Lenz, J\\'ozsef Balogh","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-21T04:25:59Z","title":"Some Exact Ramsey-Tur\\'an Numbers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.4472","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":"sha256:037a854f1fc383a90fe3317deddb52d777449f66a2de5d592ca689ffc2803c3d","target":"record","created_at":"2026-05-18T03:17:34Z","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":"45d6778de701809deb62ec67333052f5f56a472ba0900ceceeb0f8da42032d9a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-09-21T04:25:59Z","title_canon_sha256":"20c9685b0601396a5ad09099979b484bb1fee913825b80ce880302754474266a"},"schema_version":"1.0","source":{"id":"1109.4472","kind":"arxiv","version":2}},"canonical_sha256":"6f3f64b4b0310e8785562f1035cc2e96c0a0423756c194fa14e19ecc7f1f0dc9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f3f64b4b0310e8785562f1035cc2e96c0a0423756c194fa14e19ecc7f1f0dc9","first_computed_at":"2026-05-18T03:17:34.417773Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:34.417773Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AsOdX80nDBLJIDz/++M+/sTrD6T42k37McxwnNqUa13CpsDraFVn+gz7QqLiVYFZLaqK5SM+671b4eStB9EpCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:34.418255Z","signed_message":"canonical_sha256_bytes"},"source_id":"1109.4472","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:037a854f1fc383a90fe3317deddb52d777449f66a2de5d592ca689ffc2803c3d","sha256:685a5f16ece07947ddf98207d5595748d491c9117039196229b7d95af7591209"],"state_sha256":"6ac01ee4d87f0e339c075ee5d8c51d257d8c8dd7689cbbd0cca08be022949ef7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"78Dm3+sDoIxOvwd1q9KGn5opm5UTIz1UuYR0o0sWi1CUoy4itSn2+9HfBDO6H+ytWpJt+D4A6B95/vKxUZ5fAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T22:13:15.874140Z","bundle_sha256":"f2b1610fe8e7b9d921a13e0de0a252aa8413b85d8e363275f7d0856f57b91040"}}