{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:33E72C5FQ4O3GY52M366LI6Y2N","short_pith_number":"pith:33E72C5F","schema_version":"1.0","canonical_sha256":"dec9fd0ba5871db363ba66fde5a3d8d3552cfd5a545d60e397da639bf7ef8742","source":{"kind":"arxiv","id":"1508.06724","version":1},"attestation_state":"computed","paper":{"title":"Algebraic Local Cohomology with Parameters and Parametric Standard Bases for Zero-Dimensional Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Katsusuke Nabeshima, Shinichi Tajima","submitted_at":"2015-08-27T05:31:14Z","abstract_excerpt":"A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the structure of algebraic local cohomology classes. This decomposition informs us several properties of input ideals and the output of our algorithm completely describes the multiplicity structure of input ideals. An efficient algorithm for computing a parametric standard basis of a given zero-dimensional ideal, with respect to an arbitrary local term order, i"},"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":"1508.06724","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2015-08-27T05:31:14Z","cross_cats_sorted":[],"title_canon_sha256":"2fbb0955c4168f1a5e5c97c30fcd5510e6f7c31a15d52e717e357dc2cfc1edd2","abstract_canon_sha256":"6985b4e89b833465a6d6c105f1839424f75d73d3c950537e270f9b41c470f973"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:41.246584Z","signature_b64":"v4Ak4D+kWXi6l9KVwDoldPucok5pSyqi6zKHJINfbxav1NjEkFHeWxT2ub0+15r1no78BgvfkrLSSQahokVWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dec9fd0ba5871db363ba66fde5a3d8d3552cfd5a545d60e397da639bf7ef8742","last_reissued_at":"2026-05-18T01:34:41.245952Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:41.245952Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic Local Cohomology with Parameters and Parametric Standard Bases for Zero-Dimensional Ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.SC","authors_text":"Katsusuke Nabeshima, Shinichi Tajima","submitted_at":"2015-08-27T05:31:14Z","abstract_excerpt":"A computation method of algebraic local cohomology with parameters, associated with zero-dimensional ideal with parameter, is introduced. This computation method gives us in particular a decomposition of the parameter space depending on the structure of algebraic local cohomology classes. This decomposition informs us several properties of input ideals and the output of our algorithm completely describes the multiplicity structure of input ideals. An efficient algorithm for computing a parametric standard basis of a given zero-dimensional ideal, with respect to an arbitrary local term order, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06724","kind":"arxiv","version":1},"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":"1508.06724","created_at":"2026-05-18T01:34:41.246054+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.06724v1","created_at":"2026-05-18T01:34:41.246054+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.06724","created_at":"2026-05-18T01:34:41.246054+00:00"},{"alias_kind":"pith_short_12","alias_value":"33E72C5FQ4O3","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"33E72C5FQ4O3GY52","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"33E72C5F","created_at":"2026-05-18T12:29:02.477457+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/33E72C5FQ4O3GY52M366LI6Y2N","json":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N.json","graph_json":"https://pith.science/api/pith-number/33E72C5FQ4O3GY52M366LI6Y2N/graph.json","events_json":"https://pith.science/api/pith-number/33E72C5FQ4O3GY52M366LI6Y2N/events.json","paper":"https://pith.science/paper/33E72C5F"},"agent_actions":{"view_html":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N","download_json":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N.json","view_paper":"https://pith.science/paper/33E72C5F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.06724&json=true","fetch_graph":"https://pith.science/api/pith-number/33E72C5FQ4O3GY52M366LI6Y2N/graph.json","fetch_events":"https://pith.science/api/pith-number/33E72C5FQ4O3GY52M366LI6Y2N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N/action/storage_attestation","attest_author":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N/action/author_attestation","sign_citation":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N/action/citation_signature","submit_replication":"https://pith.science/pith/33E72C5FQ4O3GY52M366LI6Y2N/action/replication_record"}},"created_at":"2026-05-18T01:34:41.246054+00:00","updated_at":"2026-05-18T01:34:41.246054+00:00"}