{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:TABGO47KYF42Y7FIFJBJKPFACO","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":"c8ecf43e10279fe8d8d975d3986cc747e77c89a3f4bc91c1d971d4d9678c7864","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-27T13:43:41Z","title_canon_sha256":"f78f90635a02d79cd3bd2523c2d69da18cd99bcc3d7854d7ebad13838d1f4efc"},"schema_version":"1.0","source":{"id":"1407.7228","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.7228","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"arxiv_version","alias_value":"1407.7228v3","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.7228","created_at":"2026-05-18T01:18:52Z"},{"alias_kind":"pith_short_12","alias_value":"TABGO47KYF42","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"TABGO47KYF42Y7FI","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"TABGO47K","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:ba79f2d3589e7e6e4c895a8bf9f5bc21ffb168f79389985bbee3ab67c4f9ace0","target":"graph","created_at":"2026-05-18T01:18:52Z","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":"We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are trivial representations and whose principal apolar submodules are generated by the sum of the orbit of a power of a linear form.","authors_text":"Andrew H. Hoefel, Anthony V. Geramita, David L. Wehlau","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-27T13:43:41Z","title":"Hilbert Functions of $\\mathfrak S_n$-Stable Artinian Gorenstein Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.7228","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:a7189dd6bf8e2295eea7f296428c8cb1483065146419dfb11410ec678a65b447","target":"record","created_at":"2026-05-18T01:18:52Z","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":"c8ecf43e10279fe8d8d975d3986cc747e77c89a3f4bc91c1d971d4d9678c7864","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2014-07-27T13:43:41Z","title_canon_sha256":"f78f90635a02d79cd3bd2523c2d69da18cd99bcc3d7854d7ebad13838d1f4efc"},"schema_version":"1.0","source":{"id":"1407.7228","kind":"arxiv","version":3}},"canonical_sha256":"98026773eac179ac7ca82a42953ca013b1d9be0f54b5374c28759bf44cc16709","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98026773eac179ac7ca82a42953ca013b1d9be0f54b5374c28759bf44cc16709","first_computed_at":"2026-05-18T01:18:52.930583Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:52.930583Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"90fFQG4cc1lJEZAwgJeo0nxquVFDVY67k1cKZBJTxSwbPXJnEbsy4EeS+SNzGJEYvqKrBpTVNPARjQ0zL/orCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:52.931164Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.7228","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a7189dd6bf8e2295eea7f296428c8cb1483065146419dfb11410ec678a65b447","sha256:ba79f2d3589e7e6e4c895a8bf9f5bc21ffb168f79389985bbee3ab67c4f9ace0"],"state_sha256":"ba039bf4ef34cd456f8281fcd9c3b9327181c43fccaf1785d0f6870ddfa53d47"}