{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2KQEXP5A2RHGJERFMUD3WCHZMB","short_pith_number":"pith:2KQEXP5A","schema_version":"1.0","canonical_sha256":"d2a04bbfa0d44e6492256507bb08f96054054190f995166df790c463392fdc31","source":{"kind":"arxiv","id":"1501.04945","version":1},"attestation_state":"computed","paper":{"title":"On traces of tensor representations of diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Alexander Schrijver","submitted_at":"2015-01-20T20:17:26Z","abstract_excerpt":"Let $T$ be a set, of {\\em types}, and let $\\iota,o:T\\to\\oZ_+$. A {\\em $T$-diagram} is a locally ordered directed graph $G$ equipped with a function $\\tau:V(G)\\to T$ such that each vertex $v$ of $G$ has indegree $\\iota(\\tau(v))$ and outdegree $o(\\tau(v))$. (A directed graph is {\\em locally ordered} if at each vertex $v$, linear orders of the edges entering $v$ and of the edges leaving $v$ are specified.)\n  Let $V$ be a finite-dimensional $\\oF$-linear space, where $\\oF$ is an algebraically closed field of characteristic 0. A function $R$ on $T$ assigning to each $t\\in T$ a tensor $R(t)\\in V^{*\\o"},"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":"1501.04945","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-01-20T20:17:26Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"1cf39cea059f4bd844bf4afe029a377deeb863948d50966addd4fc0dd15bcd46","abstract_canon_sha256":"fe45ab4c745cd621ea156bffc97919908ce752e39373ef7ec29d0167005b3c68"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:29:01.906575Z","signature_b64":"ptAaDFDjkKbe4lrgCYlUalVtj8dN541wajA5R8q7FPTlpUQEA3KwBtSSCpz7t9y9/9MgnegWz5Zi/BrcQWpiBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2a04bbfa0d44e6492256507bb08f96054054190f995166df790c463392fdc31","last_reissued_at":"2026-05-18T02:29:01.906104Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:29:01.906104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On traces of tensor representations of diagrams","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Alexander Schrijver","submitted_at":"2015-01-20T20:17:26Z","abstract_excerpt":"Let $T$ be a set, of {\\em types}, and let $\\iota,o:T\\to\\oZ_+$. A {\\em $T$-diagram} is a locally ordered directed graph $G$ equipped with a function $\\tau:V(G)\\to T$ such that each vertex $v$ of $G$ has indegree $\\iota(\\tau(v))$ and outdegree $o(\\tau(v))$. (A directed graph is {\\em locally ordered} if at each vertex $v$, linear orders of the edges entering $v$ and of the edges leaving $v$ are specified.)\n  Let $V$ be a finite-dimensional $\\oF$-linear space, where $\\oF$ is an algebraically closed field of characteristic 0. A function $R$ on $T$ assigning to each $t\\in T$ a tensor $R(t)\\in V^{*\\o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04945","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":"1501.04945","created_at":"2026-05-18T02:29:01.906173+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.04945v1","created_at":"2026-05-18T02:29:01.906173+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04945","created_at":"2026-05-18T02:29:01.906173+00:00"},{"alias_kind":"pith_short_12","alias_value":"2KQEXP5A2RHG","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"2KQEXP5A2RHGJERF","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"2KQEXP5A","created_at":"2026-05-18T12:29:02.477457+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/2KQEXP5A2RHGJERFMUD3WCHZMB","json":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB.json","graph_json":"https://pith.science/api/pith-number/2KQEXP5A2RHGJERFMUD3WCHZMB/graph.json","events_json":"https://pith.science/api/pith-number/2KQEXP5A2RHGJERFMUD3WCHZMB/events.json","paper":"https://pith.science/paper/2KQEXP5A"},"agent_actions":{"view_html":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB","download_json":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB.json","view_paper":"https://pith.science/paper/2KQEXP5A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.04945&json=true","fetch_graph":"https://pith.science/api/pith-number/2KQEXP5A2RHGJERFMUD3WCHZMB/graph.json","fetch_events":"https://pith.science/api/pith-number/2KQEXP5A2RHGJERFMUD3WCHZMB/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB/action/storage_attestation","attest_author":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB/action/author_attestation","sign_citation":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB/action/citation_signature","submit_replication":"https://pith.science/pith/2KQEXP5A2RHGJERFMUD3WCHZMB/action/replication_record"}},"created_at":"2026-05-18T02:29:01.906173+00:00","updated_at":"2026-05-18T02:29:01.906173+00:00"}