{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:7Q4QKEHXUHIRPHVHUZUUNARXP3","short_pith_number":"pith:7Q4QKEHX","schema_version":"1.0","canonical_sha256":"fc390510f7a1d1179ea7a6694682377ed5e392262a7faa2d5703fc8a6ac54d93","source":{"kind":"arxiv","id":"1712.08824","version":2},"attestation_state":"computed","paper":{"title":"$L^p$-operator algebras associated with oriented graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guillermo Corti\\~nas, Ma. Eugenia Rodr\\'i guez","submitted_at":"2017-12-23T19:17:30Z","abstract_excerpt":"For each $1\\le p<\\infty$ and each countable oriented graph $Q$ we introduce an $L^p$-operator algebra $\\mathcal{O}^p(Q)$ which contains the Leavitt path $\\mathbb{C}$-algebra $L_Q$ as a dense subalgebra and is universal for those $L^p$-representations of $L_Q$ which are spatial in the sense of N.C. Phillips. For $\\mathcal{R}_n$ the graph with one vertex and $n$ loops ($2\\le n\\le \\infty$), $\\mathcal{O}^p(\\mathcal{R}_n)=\\mathcal{O}^p_n$, the $L^p$-Cuntz algebra introduced by Phillips. If $p\\notin\\{1,2\\}$ and $\\mathcal{S}(Q)$ is the inverse semigroup generated by $Q$, $\\mathcal{O}^p(Q)=F_{\\operato"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1712.08824","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-23T19:17:30Z","cross_cats_sorted":[],"title_canon_sha256":"1e27aac578219f56742f556215388ff186c412f8e5c230c4ec17b5e2185496d2","abstract_canon_sha256":"594a9e7ef71e7f9e664937cb9f853117c54e69942a20beb88d3460e3664a1bb0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:33.398711Z","signature_b64":"lD1TLJVWFgGzi5HH7H8FHNxAYrRb1RBE2SMKQg6crgcIfsgd5yJxgEq7hWCF3ILtAwacPk65b7SQEKUCpV4qBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc390510f7a1d1179ea7a6694682377ed5e392262a7faa2d5703fc8a6ac54d93","last_reissued_at":"2026-05-18T00:25:33.397971Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:33.397971Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"$L^p$-operator algebras associated with oriented graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Guillermo Corti\\~nas, Ma. Eugenia Rodr\\'i guez","submitted_at":"2017-12-23T19:17:30Z","abstract_excerpt":"For each $1\\le p<\\infty$ and each countable oriented graph $Q$ we introduce an $L^p$-operator algebra $\\mathcal{O}^p(Q)$ which contains the Leavitt path $\\mathbb{C}$-algebra $L_Q$ as a dense subalgebra and is universal for those $L^p$-representations of $L_Q$ which are spatial in the sense of N.C. Phillips. For $\\mathcal{R}_n$ the graph with one vertex and $n$ loops ($2\\le n\\le \\infty$), $\\mathcal{O}^p(\\mathcal{R}_n)=\\mathcal{O}^p_n$, the $L^p$-Cuntz algebra introduced by Phillips. If $p\\notin\\{1,2\\}$ and $\\mathcal{S}(Q)$ is the inverse semigroup generated by $Q$, $\\mathcal{O}^p(Q)=F_{\\operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.08824","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":"1712.08824","created_at":"2026-05-18T00:25:33.398076+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.08824v2","created_at":"2026-05-18T00:25:33.398076+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.08824","created_at":"2026-05-18T00:25:33.398076+00:00"},{"alias_kind":"pith_short_12","alias_value":"7Q4QKEHXUHIR","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_16","alias_value":"7Q4QKEHXUHIRPHVH","created_at":"2026-05-18T12:31:05.417338+00:00"},{"alias_kind":"pith_short_8","alias_value":"7Q4QKEHX","created_at":"2026-05-18T12:31:05.417338+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/7Q4QKEHXUHIRPHVHUZUUNARXP3","json":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3.json","graph_json":"https://pith.science/api/pith-number/7Q4QKEHXUHIRPHVHUZUUNARXP3/graph.json","events_json":"https://pith.science/api/pith-number/7Q4QKEHXUHIRPHVHUZUUNARXP3/events.json","paper":"https://pith.science/paper/7Q4QKEHX"},"agent_actions":{"view_html":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3","download_json":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3.json","view_paper":"https://pith.science/paper/7Q4QKEHX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.08824&json=true","fetch_graph":"https://pith.science/api/pith-number/7Q4QKEHXUHIRPHVHUZUUNARXP3/graph.json","fetch_events":"https://pith.science/api/pith-number/7Q4QKEHXUHIRPHVHUZUUNARXP3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3/action/storage_attestation","attest_author":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3/action/author_attestation","sign_citation":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3/action/citation_signature","submit_replication":"https://pith.science/pith/7Q4QKEHXUHIRPHVHUZUUNARXP3/action/replication_record"}},"created_at":"2026-05-18T00:25:33.398076+00:00","updated_at":"2026-05-18T00:25:33.398076+00:00"}