{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:KHSRQDIM22WSMLIUBWNTDFTDEX","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":"e6ceed7a862e58a132f518b22bcc951df6febf8805fe9054580aa053603400e4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-19T13:39:37Z","title_canon_sha256":"0f0d5dd6b17bc520a49a6fd0e673e7261f85e10391a1b1eba758e09ff5503b88"},"schema_version":"1.0","source":{"id":"1508.04643","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.04643","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"arxiv_version","alias_value":"1508.04643v2","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.04643","created_at":"2026-05-18T01:04:37Z"},{"alias_kind":"pith_short_12","alias_value":"KHSRQDIM22WS","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"KHSRQDIM22WSMLIU","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"KHSRQDIM","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:05be1e1779bd98c1aa3b7db8254035e5ab523a67ea6013b4bbc7635324669936","target":"graph","created_at":"2026-05-18T01:04:37Z","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":"For an acyclic quiver with three vertices, we consider the canonical decomposition of a non-Schurian root and associate certain representations of a generalized Kronecker quiver. These representations correspond to points contained in the intersection of two subvarieties of a Grassmannian and give rise to representations of the original quiver, preserving indecomposability. We show that these subvarieties intersect using Schubert calculus. Provided that the intersection contains a Schurian representation, it already contains an open subset of Schurian representations whose dimension is what we","authors_text":"Hans Franzen, Thorsten Weist","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-19T13:39:37Z","title":"Non-Schurian indecomposables via intersection theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.04643","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:aa917b49648fe5e9879cf5eaa28d1fe3a025ad8d7a79fa717479658cdb15dc55","target":"record","created_at":"2026-05-18T01:04:37Z","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":"e6ceed7a862e58a132f518b22bcc951df6febf8805fe9054580aa053603400e4","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2015-08-19T13:39:37Z","title_canon_sha256":"0f0d5dd6b17bc520a49a6fd0e673e7261f85e10391a1b1eba758e09ff5503b88"},"schema_version":"1.0","source":{"id":"1508.04643","kind":"arxiv","version":2}},"canonical_sha256":"51e5180d0cd6ad262d140d9b31966325f9e2fff2383d0a0cc50d5d30ec7a19d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"51e5180d0cd6ad262d140d9b31966325f9e2fff2383d0a0cc50d5d30ec7a19d9","first_computed_at":"2026-05-18T01:04:37.800651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:04:37.800651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Ne1bgOmdnmxsFLZVk9kDbcoiK9nWdf7Oq0/hYTjlW6apxSipukNGhht7euqjjpY0EUiU0Un6TcgjtG79y1KAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:04:37.801363Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.04643","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aa917b49648fe5e9879cf5eaa28d1fe3a025ad8d7a79fa717479658cdb15dc55","sha256:05be1e1779bd98c1aa3b7db8254035e5ab523a67ea6013b4bbc7635324669936"],"state_sha256":"a561bab1a6fa63cf009da383046a0cdfc99a9614c334e6f07ffccb682221ad5f"}