{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:C6BU4K5QL2M7D2PP2CMMOHRCYA","short_pith_number":"pith:C6BU4K5Q","schema_version":"1.0","canonical_sha256":"17834e2bb05e99f1e9efd098c71e22c02eac6cc6c0e19593cb9f6dfbe85965f2","source":{"kind":"arxiv","id":"1208.2187","version":2},"attestation_state":"computed","paper":{"title":"The lex-plus-power inequality for local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Enrico Sbarra, Giulio Caviglia","submitted_at":"2012-08-10T14:25:11Z","abstract_excerpt":"We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framework of embeddings of posets of Hilbert functions. As a main application, we prove an analogue for local cohomology of Evans' Lex-Plus-Power Conjecture for Betti numbers. This results implies some cases of the classical Lex-Plus-Power Conjecture, namely an inequality between extremal Betti numbers. In particular, for the classes of ideals for which the Eisenbud-Green-Harris Conjecture is currently known, the projective"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1208.2187","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-08-10T14:25:11Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"9336120f90e1a3d7d3345bb9f093ecf23cc11a126e1ae72f8f9a29d316defb46","abstract_canon_sha256":"9eb89348fe57c2e53af09cf70bcbaf9366e413d22c21d88125d81e07c1556761"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:31:17.379655Z","signature_b64":"GkSbdn+G7ZzTs5qg8CdjU1uKEEJ1ub7rg9BuwKUxybtcYp1dws7fYZqPjuZRojkYiMOBl1pB/+VOhWweflacCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17834e2bb05e99f1e9efd098c71e22c02eac6cc6c0e19593cb9f6dfbe85965f2","last_reissued_at":"2026-05-18T03:31:17.378831Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:31:17.378831Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The lex-plus-power inequality for local cohomology modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Enrico Sbarra, Giulio Caviglia","submitted_at":"2012-08-10T14:25:11Z","abstract_excerpt":"We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framework of embeddings of posets of Hilbert functions. As a main application, we prove an analogue for local cohomology of Evans' Lex-Plus-Power Conjecture for Betti numbers. This results implies some cases of the classical Lex-Plus-Power Conjecture, namely an inequality between extremal Betti numbers. In particular, for the classes of ideals for which the Eisenbud-Green-Harris Conjecture is currently known, the projective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.2187","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1208.2187","created_at":"2026-05-18T03:31:17.378974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.2187v2","created_at":"2026-05-18T03:31:17.378974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.2187","created_at":"2026-05-18T03:31:17.378974+00:00"},{"alias_kind":"pith_short_12","alias_value":"C6BU4K5QL2M7","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"C6BU4K5QL2M7D2PP","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"C6BU4K5Q","created_at":"2026-05-18T12:27:01.376967+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA","json":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA.json","graph_json":"https://pith.science/api/pith-number/C6BU4K5QL2M7D2PP2CMMOHRCYA/graph.json","events_json":"https://pith.science/api/pith-number/C6BU4K5QL2M7D2PP2CMMOHRCYA/events.json","paper":"https://pith.science/paper/C6BU4K5Q"},"agent_actions":{"view_html":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA","download_json":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA.json","view_paper":"https://pith.science/paper/C6BU4K5Q","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.2187&json=true","fetch_graph":"https://pith.science/api/pith-number/C6BU4K5QL2M7D2PP2CMMOHRCYA/graph.json","fetch_events":"https://pith.science/api/pith-number/C6BU4K5QL2M7D2PP2CMMOHRCYA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA/action/storage_attestation","attest_author":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA/action/author_attestation","sign_citation":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA/action/citation_signature","submit_replication":"https://pith.science/pith/C6BU4K5QL2M7D2PP2CMMOHRCYA/action/replication_record"}},"created_at":"2026-05-18T03:31:17.378974+00:00","updated_at":"2026-05-18T03:31:17.378974+00:00"}