{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PQ3RS72FFUEAMUZAKQX2UZDAOC","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":"8ce124a5c04af521633d4679d81860b79e5a2ec74ff3e1c2d990dad45a2ccab9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T10:03:04Z","title_canon_sha256":"03c1ce0be04f4d603b5a9f35509a788a6c7b7177584c480d93b4d331d38c584d"},"schema_version":"1.0","source":{"id":"1407.0168","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0168","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0168v2","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0168","created_at":"2026-05-18T00:36:33Z"},{"alias_kind":"pith_short_12","alias_value":"PQ3RS72FFUEA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQ3RS72FFUEAMUZA","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQ3RS72F","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e3dec3b23b2daf1f6fe58adfa2bfd8c58964111143e7bebd120db591cbda8f88","target":"graph","created_at":"2026-05-18T00:36:33Z","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 $V$ be a projective hypersurface having only isolated singularities. We show that these singularities are weighted homogeneous if and only if the Koszul syzygies among the partial derivatives of an equation for $V$ are exactly the syzygies with a generic first component vanishing on the singular locus subscheme of $V$. This yields in particular a positive answer in this setting to a question raised by Morihiko Saito and the first author. Finally we explain how our result can be used to improve the listing of Jacobian syzygies of a given degree by a computer algebra system such as Singular,","authors_text":"Alexandru Dimca, Gabriel Sticlaru","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T10:03:04Z","title":"Syzygies of Jacobian ideals and weighted homogeneous singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0168","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:e69ec506a50747e32dc9e13a0db7ea2f5f90c85230f0dc8d63d49a08e474e2ba","target":"record","created_at":"2026-05-18T00:36:33Z","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":"8ce124a5c04af521633d4679d81860b79e5a2ec74ff3e1c2d990dad45a2ccab9","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-07-01T10:03:04Z","title_canon_sha256":"03c1ce0be04f4d603b5a9f35509a788a6c7b7177584c480d93b4d331d38c584d"},"schema_version":"1.0","source":{"id":"1407.0168","kind":"arxiv","version":2}},"canonical_sha256":"7c37197f452d08065320542faa646070bc7f01b75d4c20c93a648fcf3c2aa6a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c37197f452d08065320542faa646070bc7f01b75d4c20c93a648fcf3c2aa6a5","first_computed_at":"2026-05-18T00:36:33.702173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:36:33.702173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fQRmy9UxpHAxHtSM6wo3MpWmQ3vHIg34pQM7KzU1epXRZonUcKNiY+8yb2YriRRktrvnRY9FGu6ChQwN1dYcAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:36:33.702698Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0168","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e69ec506a50747e32dc9e13a0db7ea2f5f90c85230f0dc8d63d49a08e474e2ba","sha256:e3dec3b23b2daf1f6fe58adfa2bfd8c58964111143e7bebd120db591cbda8f88"],"state_sha256":"a21956ab843726c53c1e86874b6f93d12013c2021798c511b65ebae9804bc48d"}