{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:Z6QJXADE64SBYAK45WP275FKWA","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":"ff84a7f45e0ff893bbf42608c6fad636a42659b4360aecf24f49dc792b0a19be","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-12T14:57:17Z","title_canon_sha256":"0e9687f2f9e010da109d16b78a7e08544b92efa925e0540d102fdcbdc389df35"},"schema_version":"1.0","source":{"id":"1004.1981","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1981","created_at":"2026-07-04T17:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1981v2","created_at":"2026-07-04T17:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1981","created_at":"2026-07-04T17:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"Z6QJXADE64SB","created_at":"2026-07-04T17:26:39Z"},{"alias_kind":"pith_short_16","alias_value":"Z6QJXADE64SBYAK4","created_at":"2026-07-04T17:26:39Z"},{"alias_kind":"pith_short_8","alias_value":"Z6QJXADE","created_at":"2026-07-04T17:26:39Z"}],"graph_snapshots":[{"event_id":"sha256:d4ff851801d95a02bfef36358054320b65cdb4f5487a43b656e9b5100b3d7913","target":"graph","created_at":"2026-07-04T17:26:39Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1004.1981/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Rank functors on a quiver $Q$ are certain additive functors from the category of representations of $Q$ to the category of finite-dimensional vector spaces.  Composing with the dimension function on vector spaces gives a rank function on $Q$.  These induce functions on $\\rep(Q, \\alpha)$, the variety of representations of $Q$ of dimension vector $\\alpha$, and thus can be used to define \"rank loci\" in $\\rep(Q, \\alpha)$ as collections of points satisfying finite lists of linear inequalities of rank functions. Although quiver rank functions are not generally semicontinuous like the rank of a linea","authors_text":"Ryan Kinser","cross_cats":["math.RT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-12T14:57:17Z","title":"Rank loci in representation spaces of quivers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1981","kind":"arxiv","version":2},"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:ce0cbde3df224727f6b0d4c5bfd7a5ed5efca8b4af4a815d23cc86b0d4b0e5fc","target":"record","created_at":"2026-07-04T17:26:39Z","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":"ff84a7f45e0ff893bbf42608c6fad636a42659b4360aecf24f49dc792b0a19be","cross_cats_sorted":["math.RT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-12T14:57:17Z","title_canon_sha256":"0e9687f2f9e010da109d16b78a7e08544b92efa925e0540d102fdcbdc389df35"},"schema_version":"1.0","source":{"id":"1004.1981","kind":"arxiv","version":2}},"canonical_sha256":"cfa09b8064f7241c015ced9faff4aab0280c75c1a84d3785c2095a857e1893ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cfa09b8064f7241c015ced9faff4aab0280c75c1a84d3785c2095a857e1893ff","first_computed_at":"2026-07-04T17:26:39.175041Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:26:39.175041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KHq1be2mrCvcU3+ptpkglDhpkj9YHrs85i6Mctlcx0hsH+SMzR4pkEF9HQVHfkobqC+xLlfMjyprZgD1p0t9Aw==","signature_status":"signed_v1","signed_at":"2026-07-04T17:26:39.175440Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1981","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ce0cbde3df224727f6b0d4c5bfd7a5ed5efca8b4af4a815d23cc86b0d4b0e5fc","sha256:d4ff851801d95a02bfef36358054320b65cdb4f5487a43b656e9b5100b3d7913"],"state_sha256":"ef327000afec1cb5d9b3d60f5c5d46cdac86c1741f66acda6164c44d5aab49b1"}