{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:XLTPZ3LPBFZUBU5ZPKXZL4VLWJ","short_pith_number":"pith:XLTPZ3LP","schema_version":"1.0","canonical_sha256":"bae6fced6f097340d3b97aaf95f2abb25e92062258170e2a4c0739f52ea20a6b","source":{"kind":"arxiv","id":"2207.12526","version":1},"attestation_state":"computed","paper":{"title":"Complexity of injective homomorphisms to small tournaments, and of injective oriented colourings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary MacGillivray, Nancy E. Clarke, Russell J. Campbell","submitted_at":"2022-07-25T20:47:12Z","abstract_excerpt":"Several possible definitions of local injectivity for a homomorphism of an oriented graph $G$ to an oriented graph $H$ are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when $G$ is given and $H$ is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case."},"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":"2207.12526","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2022-07-25T20:47:12Z","cross_cats_sorted":[],"title_canon_sha256":"f16a0c8f771bb2155ec313b73b7862d9230bc3a24fc00e7e88271e02358688f9","abstract_canon_sha256":"52cc091b1f0e726ca826fa6b6370e1cebd463c0dbcdbb6d6f715c7d296965e15"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:43:23.436510Z","signature_b64":"uC8gBM/g5pE9yyZj8FtOPUlHa7SuQGEpGn4es/wXP9gcxNnnlxSRxZ7LSwvqcJajfaxJPGrlnyvqV6JkSa+5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bae6fced6f097340d3b97aaf95f2abb25e92062258170e2a4c0739f52ea20a6b","last_reissued_at":"2026-07-05T04:43:23.436106Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:43:23.436106Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complexity of injective homomorphisms to small tournaments, and of injective oriented colourings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary MacGillivray, Nancy E. Clarke, Russell J. Campbell","submitted_at":"2022-07-25T20:47:12Z","abstract_excerpt":"Several possible definitions of local injectivity for a homomorphism of an oriented graph $G$ to an oriented graph $H$ are considered. In each case, we determine the complexity of deciding whether there exists such a homomorphism when $G$ is given and $H$ is a fixed tournament on three or fewer vertices. Each possible definition leads to a locally-injective oriented colouring problem. A dichotomy theorem is proved in each case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.12526","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.12526/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2207.12526","created_at":"2026-07-05T04:43:23.436162+00:00"},{"alias_kind":"arxiv_version","alias_value":"2207.12526v1","created_at":"2026-07-05T04:43:23.436162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.12526","created_at":"2026-07-05T04:43:23.436162+00:00"},{"alias_kind":"pith_short_12","alias_value":"XLTPZ3LPBFZU","created_at":"2026-07-05T04:43:23.436162+00:00"},{"alias_kind":"pith_short_16","alias_value":"XLTPZ3LPBFZUBU5Z","created_at":"2026-07-05T04:43:23.436162+00:00"},{"alias_kind":"pith_short_8","alias_value":"XLTPZ3LP","created_at":"2026-07-05T04:43:23.436162+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/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ","json":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ.json","graph_json":"https://pith.science/api/pith-number/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/graph.json","events_json":"https://pith.science/api/pith-number/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/events.json","paper":"https://pith.science/paper/XLTPZ3LP"},"agent_actions":{"view_html":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ","download_json":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ.json","view_paper":"https://pith.science/paper/XLTPZ3LP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2207.12526&json=true","fetch_graph":"https://pith.science/api/pith-number/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/graph.json","fetch_events":"https://pith.science/api/pith-number/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/action/storage_attestation","attest_author":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/action/author_attestation","sign_citation":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/action/citation_signature","submit_replication":"https://pith.science/pith/XLTPZ3LPBFZUBU5ZPKXZL4VLWJ/action/replication_record"}},"created_at":"2026-07-05T04:43:23.436162+00:00","updated_at":"2026-07-05T04:43:23.436162+00:00"}