{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:KXQLTDCRGG6MIRQFTCYEKCJBTO","short_pith_number":"pith:KXQLTDCR","canonical_record":{"source":{"id":"1111.4813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T10:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"5b1ab8c7a8daa57c4387577e219c5222d00a9a6b8361ccd13154fa08d484f3d0","abstract_canon_sha256":"f73658ac88a41c32129d66c410f5f897a8061a5015d0192cc129c1e144cc40d7"},"schema_version":"1.0"},"canonical_sha256":"55e0b98c5131bcc4460598b04509219b9c8591ef9c76bee9128f9848e4810ed9","source":{"kind":"arxiv","id":"1111.4813","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4813","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4813v2","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4813","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"KXQLTDCRGG6M","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KXQLTDCRGG6MIRQF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KXQLTDCR","created_at":"2026-05-18T12:26:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:KXQLTDCRGG6MIRQFTCYEKCJBTO","target":"record","payload":{"canonical_record":{"source":{"id":"1111.4813","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T10:30:21Z","cross_cats_sorted":[],"title_canon_sha256":"5b1ab8c7a8daa57c4387577e219c5222d00a9a6b8361ccd13154fa08d484f3d0","abstract_canon_sha256":"f73658ac88a41c32129d66c410f5f897a8061a5015d0192cc129c1e144cc40d7"},"schema_version":"1.0"},"canonical_sha256":"55e0b98c5131bcc4460598b04509219b9c8591ef9c76bee9128f9848e4810ed9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:52.265856Z","signature_b64":"6FRobLMPA78iGIq+5kATvqoxP0ftjzIEjuoo6srtV2ZMPwJJBlR6UCzNg8aNA4/+8XS43vg8Klibrm9Fqme0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"55e0b98c5131bcc4460598b04509219b9c8591ef9c76bee9128f9848e4810ed9","last_reissued_at":"2026-05-18T04:07:52.265270Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:52.265270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1111.4813","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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5fwKyL6gU/S4SGifLcfUw26y7IJrR2HYQhBaISLK9rLQVZ0Ovvl5fa1YbGSk5u8dP2Dx3QQpIWd5wBBV9E6CDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:09:39.880522Z"},"content_sha256":"3a81cfdb48f42fdb410ca78d6011bf53647053bca13f81a6c8bc594b03e0e630","schema_version":"1.0","event_id":"sha256:3a81cfdb48f42fdb410ca78d6011bf53647053bca13f81a6c8bc594b03e0e630"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:KXQLTDCRGG6MIRQFTCYEKCJBTO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The inducibility of small oriented graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Konrad Sperfeld","submitted_at":"2011-11-21T10:30:21Z","abstract_excerpt":"We use Razborov's flag algebra method to show an asymptotic upper bound for the maximal induced density $i(\\vec P_3)$ of the orgraph $\\vec P_3$ in an arbitrary orgraph. A conjecture of Thomass\\'e states that $i(\\vec P_3)=2/5$. The hitherto best known upper bound $i(\\vec P_3)\\leq12/25$ was given by Bondy. We can show that $i(\\vec P_3)\\leq 0.4446$. Further, we consider such a maximal density for some other small orgraphs. With easy arguments one can see that $i(\\vec C_3)=1/4$, $i(\\vec K_2 \\cup \\vec E_1)=3/4$ and $2/21\\leq i(\\vec C_4)$. We show that $i(\\vec C_4)\\leq 0.1104$ and conjecture that th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4813","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":"2026-05-18T04:07:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FeyZHr0B6Vg5Jtmv2JuU5SVktnwOZmTWiRgQWN11v6S+yU9xaq8lB4kgWi3wJxYI+WMXUX/xPGq/OTQAMs+SAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T13:09:39.881024Z"},"content_sha256":"13d27ee4a39f917ab18f6a61b9d4f634d7fdf9633e7f646e3ae24fb7e15b668d","schema_version":"1.0","event_id":"sha256:13d27ee4a39f917ab18f6a61b9d4f634d7fdf9633e7f646e3ae24fb7e15b668d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/bundle.json","state_url":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/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":"2026-06-09T13:09:39Z","links":{"resolver":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO","bundle":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/bundle.json","state":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KXQLTDCRGG6MIRQFTCYEKCJBTO","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":"f73658ac88a41c32129d66c410f5f897a8061a5015d0192cc129c1e144cc40d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T10:30:21Z","title_canon_sha256":"5b1ab8c7a8daa57c4387577e219c5222d00a9a6b8361ccd13154fa08d484f3d0"},"schema_version":"1.0","source":{"id":"1111.4813","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4813","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4813v2","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4813","created_at":"2026-05-18T04:07:52Z"},{"alias_kind":"pith_short_12","alias_value":"KXQLTDCRGG6M","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_16","alias_value":"KXQLTDCRGG6MIRQF","created_at":"2026-05-18T12:26:34Z"},{"alias_kind":"pith_short_8","alias_value":"KXQLTDCR","created_at":"2026-05-18T12:26:34Z"}],"graph_snapshots":[{"event_id":"sha256:13d27ee4a39f917ab18f6a61b9d4f634d7fdf9633e7f646e3ae24fb7e15b668d","target":"graph","created_at":"2026-05-18T04:07:52Z","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":"We use Razborov's flag algebra method to show an asymptotic upper bound for the maximal induced density $i(\\vec P_3)$ of the orgraph $\\vec P_3$ in an arbitrary orgraph. A conjecture of Thomass\\'e states that $i(\\vec P_3)=2/5$. The hitherto best known upper bound $i(\\vec P_3)\\leq12/25$ was given by Bondy. We can show that $i(\\vec P_3)\\leq 0.4446$. Further, we consider such a maximal density for some other small orgraphs. With easy arguments one can see that $i(\\vec C_3)=1/4$, $i(\\vec K_2 \\cup \\vec E_1)=3/4$ and $2/21\\leq i(\\vec C_4)$. We show that $i(\\vec C_4)\\leq 0.1104$ and conjecture that th","authors_text":"Konrad Sperfeld","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T10:30:21Z","title":"The inducibility of small oriented graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4813","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":"sha256:3a81cfdb48f42fdb410ca78d6011bf53647053bca13f81a6c8bc594b03e0e630","target":"record","created_at":"2026-05-18T04:07:52Z","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":"f73658ac88a41c32129d66c410f5f897a8061a5015d0192cc129c1e144cc40d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-21T10:30:21Z","title_canon_sha256":"5b1ab8c7a8daa57c4387577e219c5222d00a9a6b8361ccd13154fa08d484f3d0"},"schema_version":"1.0","source":{"id":"1111.4813","kind":"arxiv","version":2}},"canonical_sha256":"55e0b98c5131bcc4460598b04509219b9c8591ef9c76bee9128f9848e4810ed9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"55e0b98c5131bcc4460598b04509219b9c8591ef9c76bee9128f9848e4810ed9","first_computed_at":"2026-05-18T04:07:52.265270Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:07:52.265270Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6FRobLMPA78iGIq+5kATvqoxP0ftjzIEjuoo6srtV2ZMPwJJBlR6UCzNg8aNA4/+8XS43vg8Klibrm9Fqme0Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T04:07:52.265856Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4813","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3a81cfdb48f42fdb410ca78d6011bf53647053bca13f81a6c8bc594b03e0e630","sha256:13d27ee4a39f917ab18f6a61b9d4f634d7fdf9633e7f646e3ae24fb7e15b668d"],"state_sha256":"5fe6b2430e2f25d7d31b9f31b226fb693c37cb28ff39c0314249c28df3856d6c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ul/TnJHz2LMFc3ZY5PWRPOA0J6/PbMw4x5C78ueYdWbl5SLH9VdcyLpaOB3/rm2vv/W9VOTcT/X0wWW9lMmoBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T13:09:39.883222Z","bundle_sha256":"dacf0b875e0039e743bdd1af91a86b5c566bec4525a9de68b3b82a02aad17fd1"}}