{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:6P5W5G44J7DGBXPHQKU2D27BOJ","short_pith_number":"pith:6P5W5G44","schema_version":"1.0","canonical_sha256":"f3fb6e9b9c4fc660dde782a9a1ebe172619a7be3a182866880765cfd3fddf70f","source":{"kind":"arxiv","id":"1604.01079","version":1},"attestation_state":"computed","paper":{"title":"Using the Steinberg algebra model to determine the center of any Leavitt path algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"C\\'andido Mart\\'in Gonz\\'alez, Dolores Mart\\'in Barquero, Lisa Orloff Clark, Mercedes Siles Molina","submitted_at":"2016-04-04T22:12:37Z","abstract_excerpt":"Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization of compact open invariant subsets of the unit space of the graph groupoid in terms of the underlying graph: an open invariant subset is compact if and only if its associated hereditary and saturated set of vertices satisfies Condition (F). We also give a basis of the center. Its cardinality depends on the number of minimal compact open invariant subsets of the unit space."},"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":"1604.01079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RA","submitted_at":"2016-04-04T22:12:37Z","cross_cats_sorted":[],"title_canon_sha256":"1ea2e82c038f6a466eb2bd746f36f1e637abc528fac12efae76fcf970e8466d3","abstract_canon_sha256":"5f063ad8b3cc93de851f4e1f77cc881daa4242145afd7103e6b98b8550c8e28f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:17:44.822327Z","signature_b64":"AjHDVghiGN60jREbuhW2KIMK4IFXVpJMUzXE0yVEhZ4CGgxDJLJ7Y8nsY/hQrc8TYMfp/NkYdv+b39vlCSehDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f3fb6e9b9c4fc660dde782a9a1ebe172619a7be3a182866880765cfd3fddf70f","last_reissued_at":"2026-05-18T01:17:44.821629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:17:44.821629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Using the Steinberg algebra model to determine the center of any Leavitt path algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"C\\'andido Mart\\'in Gonz\\'alez, Dolores Mart\\'in Barquero, Lisa Orloff Clark, Mercedes Siles Molina","submitted_at":"2016-04-04T22:12:37Z","abstract_excerpt":"Given an arbitrary graph, we describe the center of its Leavitt path algebra over a commutative unital ring. Our proof uses the Steinberg algebra model of the Leavitt path algebra. A key ingredient is a characterization of compact open invariant subsets of the unit space of the graph groupoid in terms of the underlying graph: an open invariant subset is compact if and only if its associated hereditary and saturated set of vertices satisfies Condition (F). We also give a basis of the center. Its cardinality depends on the number of minimal compact open invariant subsets of the unit space."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01079","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":"1604.01079","created_at":"2026-05-18T01:17:44.821739+00:00"},{"alias_kind":"arxiv_version","alias_value":"1604.01079v1","created_at":"2026-05-18T01:17:44.821739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1604.01079","created_at":"2026-05-18T01:17:44.821739+00:00"},{"alias_kind":"pith_short_12","alias_value":"6P5W5G44J7DG","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_16","alias_value":"6P5W5G44J7DGBXPH","created_at":"2026-05-18T12:30:01.593930+00:00"},{"alias_kind":"pith_short_8","alias_value":"6P5W5G44","created_at":"2026-05-18T12:30:01.593930+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/6P5W5G44J7DGBXPHQKU2D27BOJ","json":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ.json","graph_json":"https://pith.science/api/pith-number/6P5W5G44J7DGBXPHQKU2D27BOJ/graph.json","events_json":"https://pith.science/api/pith-number/6P5W5G44J7DGBXPHQKU2D27BOJ/events.json","paper":"https://pith.science/paper/6P5W5G44"},"agent_actions":{"view_html":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ","download_json":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ.json","view_paper":"https://pith.science/paper/6P5W5G44","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1604.01079&json=true","fetch_graph":"https://pith.science/api/pith-number/6P5W5G44J7DGBXPHQKU2D27BOJ/graph.json","fetch_events":"https://pith.science/api/pith-number/6P5W5G44J7DGBXPHQKU2D27BOJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ/action/storage_attestation","attest_author":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ/action/author_attestation","sign_citation":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ/action/citation_signature","submit_replication":"https://pith.science/pith/6P5W5G44J7DGBXPHQKU2D27BOJ/action/replication_record"}},"created_at":"2026-05-18T01:17:44.821739+00:00","updated_at":"2026-05-18T01:17:44.821739+00:00"}