{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:6JYL4IPMGLG7SNLALLJOJSX7HW","short_pith_number":"pith:6JYL4IPM","schema_version":"1.0","canonical_sha256":"f270be21ec32cdf935605ad2e4caff3d898b8c1c1389eb93b3d33aa634364520","source":{"kind":"arxiv","id":"1702.03292","version":4},"attestation_state":"computed","paper":{"title":"Extremal behaviour in sectional matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Anna Maria Bigatti, Elisa Palezzato, Michele Torielli","submitted_at":"2017-02-10T11:54:59Z","abstract_excerpt":"In this paper we want to revive the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprove recent results in this language. Moreover, some new results are shown about their maximal growth and Persistence Theorem, a gen- eralization of Gotzmann's persistence Theorem. This suggests that further investigation of this object might cast a new light in the study of geometric consequences of maximal growth of the Hilbert function."},"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":"1702.03292","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-02-10T11:54:59Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"e626785186fc950660846222e7ab514e6c4856f1b9d1ccc5b2c9f33bdb72c676","abstract_canon_sha256":"944a7b8930936014c5cbf7fe88e4c952735ea338c09bd4db7a3d4cb3cb22137a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:31.119038Z","signature_b64":"ruCdSQRPxIZwWWI2F2bZ68wXwDOIYSmpPvjV3YJuSWYlc0eXXKQqdQ/b63pT3IhAL7jLpLNQ+mT+90oNi0elDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f270be21ec32cdf935605ad2e4caff3d898b8c1c1389eb93b3d33aa634364520","last_reissued_at":"2026-05-18T00:32:31.118232Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:31.118232Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal behaviour in sectional matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Anna Maria Bigatti, Elisa Palezzato, Michele Torielli","submitted_at":"2017-02-10T11:54:59Z","abstract_excerpt":"In this paper we want to revive the object sectional matrix which encodes the Hilbert functions of successive hyperplane sections of a homogeneous ideal. We translate and/or reprove recent results in this language. Moreover, some new results are shown about their maximal growth and Persistence Theorem, a gen- eralization of Gotzmann's persistence Theorem. This suggests that further investigation of this object might cast a new light in the study of geometric consequences of maximal growth of the Hilbert function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.03292","kind":"arxiv","version":4},"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":"1702.03292","created_at":"2026-05-18T00:32:31.118364+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.03292v4","created_at":"2026-05-18T00:32:31.118364+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.03292","created_at":"2026-05-18T00:32:31.118364+00:00"},{"alias_kind":"pith_short_12","alias_value":"6JYL4IPMGLG7","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_16","alias_value":"6JYL4IPMGLG7SNLA","created_at":"2026-05-18T12:31:03.183658+00:00"},{"alias_kind":"pith_short_8","alias_value":"6JYL4IPM","created_at":"2026-05-18T12:31:03.183658+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/6JYL4IPMGLG7SNLALLJOJSX7HW","json":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW.json","graph_json":"https://pith.science/api/pith-number/6JYL4IPMGLG7SNLALLJOJSX7HW/graph.json","events_json":"https://pith.science/api/pith-number/6JYL4IPMGLG7SNLALLJOJSX7HW/events.json","paper":"https://pith.science/paper/6JYL4IPM"},"agent_actions":{"view_html":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW","download_json":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW.json","view_paper":"https://pith.science/paper/6JYL4IPM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.03292&json=true","fetch_graph":"https://pith.science/api/pith-number/6JYL4IPMGLG7SNLALLJOJSX7HW/graph.json","fetch_events":"https://pith.science/api/pith-number/6JYL4IPMGLG7SNLALLJOJSX7HW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW/action/storage_attestation","attest_author":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW/action/author_attestation","sign_citation":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW/action/citation_signature","submit_replication":"https://pith.science/pith/6JYL4IPMGLG7SNLALLJOJSX7HW/action/replication_record"}},"created_at":"2026-05-18T00:32:31.118364+00:00","updated_at":"2026-05-18T00:32:31.118364+00:00"}