{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:H7K5QLCPMTHF6P25PDQYYGF4S2","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":"861cc6e11626485bca4ba8d37de83cdf852e4fc0a5f9de445e972382affc9a47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-12T07:35:34Z","title_canon_sha256":"a16cc3d991d8474837468da9dd0bf575fe384f91b9afb2ae821ec5754a56dbfc"},"schema_version":"1.0","source":{"id":"1101.2280","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.2280","created_at":"2026-05-18T04:31:43Z"},{"alias_kind":"arxiv_version","alias_value":"1101.2280v1","created_at":"2026-05-18T04:31:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.2280","created_at":"2026-05-18T04:31:43Z"},{"alias_kind":"pith_short_12","alias_value":"H7K5QLCPMTHF","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"H7K5QLCPMTHF6P25","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"H7K5QLCP","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:9be7b69cc2a1d329530281893b63db54681e2b8d65c091d38dfdc2460853c419","target":"graph","created_at":"2026-05-18T04:31:43Z","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 $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various hyperplane sections. When applied to a homogeneous inclusion $A\\subseteq B$ of standard graded Noetherian algebras over an Artinian local ring, this formula yields the multiplicity of $A$ in terms of that of $B$ and of local $j$-multiplicities of hyperplane sections along ${\\rm Proj}\\,(B)$. Our formulas can be used to find the multiplicity of special fiber ring","authors_text":"Yu Xie","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-12T07:35:34Z","title":"Formulas for the multiplicity of graded algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.2280","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":"sha256:386e8a2e8853aa893a052167b5e37719b3dcc4d74764a17a33d5a5cbcc48797e","target":"record","created_at":"2026-05-18T04:31:43Z","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":"861cc6e11626485bca4ba8d37de83cdf852e4fc0a5f9de445e972382affc9a47","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2011-01-12T07:35:34Z","title_canon_sha256":"a16cc3d991d8474837468da9dd0bf575fe384f91b9afb2ae821ec5754a56dbfc"},"schema_version":"1.0","source":{"id":"1101.2280","kind":"arxiv","version":1}},"canonical_sha256":"3fd5d82c4f64ce5f3f5d78e18c18bc969933225b856de209b33dab35fbe8b6db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fd5d82c4f64ce5f3f5d78e18c18bc969933225b856de209b33dab35fbe8b6db","first_computed_at":"2026-05-18T04:31:43.211480Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:31:43.211480Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aj1UQGdv+VaDZCPnpQ8Cc/FtSBvS0NXQcUNt1l9xtOjQ7QnSDQasUk6HA8mRA6Uxqy9JoHbDEE3AE4ROmxq3Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:31:43.211966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.2280","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:386e8a2e8853aa893a052167b5e37719b3dcc4d74764a17a33d5a5cbcc48797e","sha256:9be7b69cc2a1d329530281893b63db54681e2b8d65c091d38dfdc2460853c419"],"state_sha256":"ab7b20c5fcf01f9052aa4542ae3d8d9939a7d71233caa4dbbe68ee53450b5f8b"}