{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:335PPZT2YPO6UKAHZRQ2NOO3VF","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":"99a34f075c8172805042372718618da0a2e8735a07b5272a888db5df4c72c233","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-01T02:15:57Z","title_canon_sha256":"36ac7eaa3b8a7e2bf362ced63e2d75548628d1ac05ee9b75552e2acb947dfa0a"},"schema_version":"1.0","source":{"id":"1107.0094","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1107.0094","created_at":"2026-05-18T03:58:04Z"},{"alias_kind":"arxiv_version","alias_value":"1107.0094v2","created_at":"2026-05-18T03:58:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1107.0094","created_at":"2026-05-18T03:58:04Z"},{"alias_kind":"pith_short_12","alias_value":"335PPZT2YPO6","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_16","alias_value":"335PPZT2YPO6UKAH","created_at":"2026-05-18T12:26:18Z"},{"alias_kind":"pith_short_8","alias_value":"335PPZT2","created_at":"2026-05-18T12:26:18Z"}],"graph_snapshots":[{"event_id":"sha256:ae389410280b811280a7df50c78efb271a30856a8c8d51758d889ba6c104101d","target":"graph","created_at":"2026-05-18T03:58:04Z","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":"The authors construct the global Macaulay inverse system for a zero-dimensional subscheme Z of projective n-space P^n, from the local inverse systems of the irreducible components of Z. They show that when Z is locally Gorenstein a generic homogeneous form F of degree d apolar to Z determines Z when d is larger than an invariant b(Z). They also show that a natural upper bound for the Hiilbert function of Gorenstein Artin quotient of the coordinate ring is achieved for large socle degree. They show the uniqueness of generalized additive decompositions of a homogeneous form F into powers of line","authors_text":"Anthony Iarrobino, Young Hyun Cho","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-01T02:15:57Z","title":"Inverse Systems of Zero-dimensional Schemes in P^n"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0094","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":"sha256:5141ef0aa05d2159bb62ea7c5017bd9ade33a349994aeda11f88d92f78f875b3","target":"record","created_at":"2026-05-18T03:58:04Z","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":"99a34f075c8172805042372718618da0a2e8735a07b5272a888db5df4c72c233","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-07-01T02:15:57Z","title_canon_sha256":"36ac7eaa3b8a7e2bf362ced63e2d75548628d1ac05ee9b75552e2acb947dfa0a"},"schema_version":"1.0","source":{"id":"1107.0094","kind":"arxiv","version":2}},"canonical_sha256":"defaf7e67ac3ddea2807cc61a6b9dba948fbcc194c3a279d385fa6a03ba77ab6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"defaf7e67ac3ddea2807cc61a6b9dba948fbcc194c3a279d385fa6a03ba77ab6","first_computed_at":"2026-05-18T03:58:04.532975Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:04.532975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RIk1R46BT/H72OIrm6TxAeeobXmgO6a7xQd+ni+O6PFsLHUn73GSgWm9Ls8U/+RMvlmwz1obJhXxZFb5WGwxCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:04.533601Z","signed_message":"canonical_sha256_bytes"},"source_id":"1107.0094","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5141ef0aa05d2159bb62ea7c5017bd9ade33a349994aeda11f88d92f78f875b3","sha256:ae389410280b811280a7df50c78efb271a30856a8c8d51758d889ba6c104101d"],"state_sha256":"21598f901ac2702b6ac51adbffc45100b230b0329509d8a46cb42c9dec7ee7bb"}