{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GK7WF4UDZSRCJI7QWHHHJGQMTC","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":"04adbe330328bf1fd525eb0d81866e899d87151e5a733e3c0618c0fec5d50866","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-04T20:34:29Z","title_canon_sha256":"a0195d668e12d7d798d69b68dce1f02aefda1f45fa01d85cb829d3d7726dcc2f"},"schema_version":"1.0","source":{"id":"1104.0685","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.0685","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"arxiv_version","alias_value":"1104.0685v3","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.0685","created_at":"2026-05-18T03:39:51Z"},{"alias_kind":"pith_short_12","alias_value":"GK7WF4UDZSRC","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GK7WF4UDZSRCJI7Q","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GK7WF4UD","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:28d125bcac4bbb012b3b2103c30c09bec950ecd19e68be6a1ac53679f4b3261f","target":"graph","created_at":"2026-05-18T03:39:51Z","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":"A generalized Euler sequence over a complete normal variety X is the unique extension of the trivial bundle V \\otimes O_X by the sheaf of differentials \\Omega_X, given by the inclusion of a linear space V in Ext^1(O_X,\\Omega_X). For \\Lambda, a lattice of Cartier divisors, let R_\\Lambda denote the corresponding sheaf associated to V spanned by the first Chern classes of divisors in \\Lambda. We prove that any projective, smooth variety on which the bundle R_\\Lambda splits into a direct sum of line bundles is toric. We describe the bundle R_\\Lambda in terms of the sheaf of differentials on the ch","authors_text":"Jaroslaw A. Wisniewski, Oskar Kedzierski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-04T20:34:29Z","title":"Differentials of Cox rings: Jaczewski's theorem revisited"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0685","kind":"arxiv","version":3},"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:e16309100d0743a8085735372c4106f23a4821dafcd8df355eeda8c7bed50bc1","target":"record","created_at":"2026-05-18T03:39:51Z","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":"04adbe330328bf1fd525eb0d81866e899d87151e5a733e3c0618c0fec5d50866","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-04-04T20:34:29Z","title_canon_sha256":"a0195d668e12d7d798d69b68dce1f02aefda1f45fa01d85cb829d3d7726dcc2f"},"schema_version":"1.0","source":{"id":"1104.0685","kind":"arxiv","version":3}},"canonical_sha256":"32bf62f283cca224a3f0b1ce749a0c9892f4c1f1cca3da4177003538265424d9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"32bf62f283cca224a3f0b1ce749a0c9892f4c1f1cca3da4177003538265424d9","first_computed_at":"2026-05-18T03:39:51.195431Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:39:51.195431Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IGk4zm0Tz9QPhIPycQF0+rT224xZKDHaOW5kFJHCTPm98levonMvB1SG8JImYjA/+rKZOhRlNEjyFKtg3tX7DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:39:51.195861Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.0685","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e16309100d0743a8085735372c4106f23a4821dafcd8df355eeda8c7bed50bc1","sha256:28d125bcac4bbb012b3b2103c30c09bec950ecd19e68be6a1ac53679f4b3261f"],"state_sha256":"66a2544024b057c74be8124d85dcc14fefdd52e45da3296a4b73e9a3546a2f89"}