{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:KXQLTDCRGG6MIRQFTCYEKCJBTO","short_pith_number":"pith:KXQLTDCR","schema_version":"1.0","canonical_sha256":"55e0b98c5131bcc4460598b04509219b9c8591ef9c76bee9128f9848e4810ed9","source":{"kind":"arxiv","id":"1111.4813","version":2},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"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"},"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"},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1111.4813","created_at":"2026-05-18T04:07:52.265356+00:00"},{"alias_kind":"arxiv_version","alias_value":"1111.4813v2","created_at":"2026-05-18T04:07:52.265356+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4813","created_at":"2026-05-18T04:07:52.265356+00:00"},{"alias_kind":"pith_short_12","alias_value":"KXQLTDCRGG6M","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_16","alias_value":"KXQLTDCRGG6MIRQF","created_at":"2026-05-18T12:26:34.985390+00:00"},{"alias_kind":"pith_short_8","alias_value":"KXQLTDCR","created_at":"2026-05-18T12:26:34.985390+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO","json":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO.json","graph_json":"https://pith.science/api/pith-number/KXQLTDCRGG6MIRQFTCYEKCJBTO/graph.json","events_json":"https://pith.science/api/pith-number/KXQLTDCRGG6MIRQFTCYEKCJBTO/events.json","paper":"https://pith.science/paper/KXQLTDCR"},"agent_actions":{"view_html":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO","download_json":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO.json","view_paper":"https://pith.science/paper/KXQLTDCR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1111.4813&json=true","fetch_graph":"https://pith.science/api/pith-number/KXQLTDCRGG6MIRQFTCYEKCJBTO/graph.json","fetch_events":"https://pith.science/api/pith-number/KXQLTDCRGG6MIRQFTCYEKCJBTO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/action/storage_attestation","attest_author":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/action/author_attestation","sign_citation":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/action/citation_signature","submit_replication":"https://pith.science/pith/KXQLTDCRGG6MIRQFTCYEKCJBTO/action/replication_record"}},"created_at":"2026-05-18T04:07:52.265356+00:00","updated_at":"2026-05-18T04:07:52.265356+00:00"}