{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:IBULBAJTXCBEIVINNHUFIQTC3J","short_pith_number":"pith:IBULBAJT","schema_version":"1.0","canonical_sha256":"4068b08133b88244550d69e8544262da6977b930749f7790c02ff1604bd56d8d","source":{"kind":"arxiv","id":"1605.01320","version":1},"attestation_state":"computed","paper":{"title":"Minimal Asymmetric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pascal Schweitzer, Patrick Schweitzer","submitted_at":"2016-05-04T15:41:05Z","abstract_excerpt":"Confirming a conjecture of Ne\\v{s}et\\v{r}il, we show that up to isomorphism there is only a finite number of finite minimal asymmetric undirected graphs. In fact, there are exactly 18 such graphs. We also show that these graphs are exactly the finite minimal involution-free graphs."},"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":"1605.01320","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-05-04T15:41:05Z","cross_cats_sorted":[],"title_canon_sha256":"53f7188a63e0cf20816cf9b3a216adf37b07961624e7c2d2c15f59a712f18855","abstract_canon_sha256":"15d76606e822bd52f156698f8ddc3445330bfcdb9cbcb73e86cf4bc3aececfd3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:15:37.147106Z","signature_b64":"SeFmrYfDP6W1rw2Q99hwkGyPcgq5D+fuC0chJQQWSQRnt5yU9/U4soMc8BpRX5WHCqAJ/NWy64IDIN53rMLOBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4068b08133b88244550d69e8544262da6977b930749f7790c02ff1604bd56d8d","last_reissued_at":"2026-05-18T01:15:37.146399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:15:37.146399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal Asymmetric Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Pascal Schweitzer, Patrick Schweitzer","submitted_at":"2016-05-04T15:41:05Z","abstract_excerpt":"Confirming a conjecture of Ne\\v{s}et\\v{r}il, we show that up to isomorphism there is only a finite number of finite minimal asymmetric undirected graphs. In fact, there are exactly 18 such graphs. We also show that these graphs are exactly the finite minimal involution-free graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.01320","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.01320","created_at":"2026-05-18T01:15:37.146517+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.01320v1","created_at":"2026-05-18T01:15:37.146517+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.01320","created_at":"2026-05-18T01:15:37.146517+00:00"},{"alias_kind":"pith_short_12","alias_value":"IBULBAJTXCBE","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_16","alias_value":"IBULBAJTXCBEIVIN","created_at":"2026-05-18T12:30:22.444734+00:00"},{"alias_kind":"pith_short_8","alias_value":"IBULBAJT","created_at":"2026-05-18T12:30:22.444734+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/IBULBAJTXCBEIVINNHUFIQTC3J","json":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J.json","graph_json":"https://pith.science/api/pith-number/IBULBAJTXCBEIVINNHUFIQTC3J/graph.json","events_json":"https://pith.science/api/pith-number/IBULBAJTXCBEIVINNHUFIQTC3J/events.json","paper":"https://pith.science/paper/IBULBAJT"},"agent_actions":{"view_html":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J","download_json":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J.json","view_paper":"https://pith.science/paper/IBULBAJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.01320&json=true","fetch_graph":"https://pith.science/api/pith-number/IBULBAJTXCBEIVINNHUFIQTC3J/graph.json","fetch_events":"https://pith.science/api/pith-number/IBULBAJTXCBEIVINNHUFIQTC3J/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J/action/storage_attestation","attest_author":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J/action/author_attestation","sign_citation":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J/action/citation_signature","submit_replication":"https://pith.science/pith/IBULBAJTXCBEIVINNHUFIQTC3J/action/replication_record"}},"created_at":"2026-05-18T01:15:37.146517+00:00","updated_at":"2026-05-18T01:15:37.146517+00:00"}