{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:3QJHFB67ZAVPOVRIY7YVEET24S","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":"3c9c264b33ea572ea0a457ea90d12e8e3b12cea20979e69bcd05402607d59ba1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-09T14:55:58Z","title_canon_sha256":"e3f43aa93fb8d4c34621a18a7202794b4550e49a5706ae6eb587a83262512ff1"},"schema_version":"1.0","source":{"id":"1005.1405","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1005.1405","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"1005.1405v2","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1005.1405","created_at":"2026-05-18T03:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"3QJHFB67ZAVP","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"3QJHFB67ZAVPOVRI","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"3QJHFB67","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:783f6cd4831fa5cb90fbe93d2ca65168f9499d82ad8f1c97544ab39efd66e869","target":"graph","created_at":"2026-05-18T03:40:49Z","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":"In recent articles, the investigation of atomic bases in cluster algebras associated to affine quivers led the second-named author to introduce a variety called transverse quiver Grassmannian and the first-named and third-named authors to consider the smooth loci of quiver Grassmannians. In this paper, we prove that, for any affine quiver Q, the transverse quiver Grassmannian of an indecomposable representation M is the set of points N in the quiver Grassmannian of M such that Ext^1(N,M/N)=0. As a corollary we prove that the transverse quiver Grassmannian coincides with the smooth locus of the","authors_text":"Francesco Esposito, Giovanni Cerulli Irelli, Gregoire Dupont","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-09T14:55:58Z","title":"A homological interpretation of the transverse quiver Grassmannians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.1405","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:e58cd5ee932fd455e5fdb17d6add440ffecdb933b68589cfcbe021abb5c99d11","target":"record","created_at":"2026-05-18T03:40:49Z","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":"3c9c264b33ea572ea0a457ea90d12e8e3b12cea20979e69bcd05402607d59ba1","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2010-05-09T14:55:58Z","title_canon_sha256":"e3f43aa93fb8d4c34621a18a7202794b4550e49a5706ae6eb587a83262512ff1"},"schema_version":"1.0","source":{"id":"1005.1405","kind":"arxiv","version":2}},"canonical_sha256":"dc127287dfc82af75628c7f152127ae481a58302576978164afa2316b14dbf1d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc127287dfc82af75628c7f152127ae481a58302576978164afa2316b14dbf1d","first_computed_at":"2026-05-18T03:40:49.798448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:40:49.798448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8r/jpP4XgA4qjEZJVVHuV9wJD4ogEiomZ2h9fUwD32Mb41cAKKdT0VkhH9ZHhzLVrvXFfP0GwP5k2qmdiKGQBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:40:49.799159Z","signed_message":"canonical_sha256_bytes"},"source_id":"1005.1405","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e58cd5ee932fd455e5fdb17d6add440ffecdb933b68589cfcbe021abb5c99d11","sha256:783f6cd4831fa5cb90fbe93d2ca65168f9499d82ad8f1c97544ab39efd66e869"],"state_sha256":"bae5ab5fe2101cbe83e4973c370decaea2e0d70abca76bca21c62f8e441e1bab"}