{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:MY35K3KO2I333VITME7QEQMKTD","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":"0fbf745e6830fbc8556717a4c0410aa64995a79a11314475042d92aa75c00a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-06T17:23:28Z","title_canon_sha256":"bc7e8f390a786411bfcdc389b2ac5ab06bafd841f38dd7207b20e1b62acb85d2"},"schema_version":"1.0","source":{"id":"1211.1316","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.1316","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"arxiv_version","alias_value":"1211.1316v1","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.1316","created_at":"2026-05-18T03:41:21Z"},{"alias_kind":"pith_short_12","alias_value":"MY35K3KO2I33","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"MY35K3KO2I333VIT","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"MY35K3KO","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:c1c6d36229e1066206acb39a15a55638e8b31d73c1ccde36ddc156ea6d1120ec","target":"graph","created_at":"2026-05-18T03:41:21Z","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 prove upper bounds for the Hilbert-Samuel multiplicity of standard graded Gorenstein algebras. The main tool that we use is Boij-S\\\"oderberg theory to obtain a decomposition of the Betti table of a Gorenstein algebra as the sum of rational multiples of symmetrized pure tables. Our bound agrees with the one in the quasi-pure case obtained by Srinivasan [J. Algebra, vol.~208, no.~2, (1998)].","authors_text":"Hema Srinivasan, Manoj Kummini, Sabine El Khoury","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-06T17:23:28Z","title":"Bounds for the Multiplicity of Gorenstein algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.1316","kind":"arxiv","version":1},"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":"sha256:97ded250171e84b9b0b36a49fdff174b791b58b782ae72cb9fde532d4b485bd6","target":"record","created_at":"2026-05-18T03:41:21Z","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":"0fbf745e6830fbc8556717a4c0410aa64995a79a11314475042d92aa75c00a7c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-11-06T17:23:28Z","title_canon_sha256":"bc7e8f390a786411bfcdc389b2ac5ab06bafd841f38dd7207b20e1b62acb85d2"},"schema_version":"1.0","source":{"id":"1211.1316","kind":"arxiv","version":1}},"canonical_sha256":"6637d56d4ed237bdd513613f02418a98e1354ec62386c3e88d664de90f61e29d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6637d56d4ed237bdd513613f02418a98e1354ec62386c3e88d664de90f61e29d","first_computed_at":"2026-05-18T03:41:21.854063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:41:21.854063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZKGXvW4t5gZR04gyd5CCINyPc4B1M7nANAIuSOCwKYAxMs9sqZfSxtNvSqsf5YWutmuRZgzCxb8FlyoUSTfmBA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:41:21.854463Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.1316","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97ded250171e84b9b0b36a49fdff174b791b58b782ae72cb9fde532d4b485bd6","sha256:c1c6d36229e1066206acb39a15a55638e8b31d73c1ccde36ddc156ea6d1120ec"],"state_sha256":"8ddb13bb0bba226a7761bd8a39f435afab59e80f0f3f95c88241489967c72725"}