{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2KQEXP5A2RHGJERFMUD3WCHZMB","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fe45ab4c745cd621ea156bffc97919908ce752e39373ef7ec29d0167005b3c68","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-01-20T20:17:26Z","title_canon_sha256":"1cf39cea059f4bd844bf4afe029a377deeb863948d50966addd4fc0dd15bcd46"},"schema_version":"1.0","source":{"id":"1501.04945","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.04945","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"arxiv_version","alias_value":"1501.04945v1","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.04945","created_at":"2026-05-18T02:29:01Z"},{"alias_kind":"pith_short_12","alias_value":"2KQEXP5A2RHG","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2KQEXP5A2RHGJERF","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2KQEXP5A","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:18445c76c1fd8c700740801838d06df315e5a4bb1a60e91fff2b957b4bff96a4","target":"graph","created_at":"2026-05-18T02:29:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"Alexander Schrijver","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-01-20T20:17:26Z","title":"On traces of tensor representations of diagrams"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04945","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:8d61c880b3f3ed026ab4b504f349a7abdcaa2cd3ab687d58d88e243045d3fcf8","target":"record","created_at":"2026-05-18T02:29:01Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fe45ab4c745cd621ea156bffc97919908ce752e39373ef7ec29d0167005b3c68","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.QA","submitted_at":"2015-01-20T20:17:26Z","title_canon_sha256":"1cf39cea059f4bd844bf4afe029a377deeb863948d50966addd4fc0dd15bcd46"},"schema_version":"1.0","source":{"id":"1501.04945","kind":"arxiv","version":1}},"canonical_sha256":"d2a04bbfa0d44e6492256507bb08f96054054190f995166df790c463392fdc31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2a04bbfa0d44e6492256507bb08f96054054190f995166df790c463392fdc31","first_computed_at":"2026-05-18T02:29:01.906104Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:29:01.906104Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ptAaDFDjkKbe4lrgCYlUalVtj8dN541wajA5R8q7FPTlpUQEA3KwBtSSCpz7t9y9/9MgnegWz5Zi/BrcQWpiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:29:01.906575Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.04945","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8d61c880b3f3ed026ab4b504f349a7abdcaa2cd3ab687d58d88e243045d3fcf8","sha256:18445c76c1fd8c700740801838d06df315e5a4bb1a60e91fff2b957b4bff96a4"],"state_sha256":"b0fb2c409252bb9a13542810b19d230bd7dc715bf72027505507b58b6c89e461"}