{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2INYMR7SS2YB4TKBWPB6CDYGT6","short_pith_number":"pith:2INYMR7S","schema_version":"1.0","canonical_sha256":"d21b8647f296b01e4d41b3c3e10f069f8c22dd4110ec62051ca546f29096855a","source":{"kind":"arxiv","id":"1405.0472","version":5},"attestation_state":"computed","paper":{"title":"Border Bases for Polynomial Rings over Noetherian Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Ambedkar Dukkipati, Maria Francis, Nithish Pai","submitted_at":"2014-05-02T18:49:07Z","abstract_excerpt":"The theory of border bases for zero-dimensional ideals has attracted several researchers in symbolic computation due to their numerical stability and mathematical elegance. As shown in (Francis & Dukkipati, J. Symb. Comp., 2014), one can extend the concept of border bases over Noetherian rings whenever the corresponding residue class ring is finitely generated and free. In this paper we address the following problem: Can the concept of border basis over Noetherian rings exists for ideals when the corresponding residue class rings are finitely generated but need not necessarily be free modules?"},"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":"1405.0472","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SC","submitted_at":"2014-05-02T18:49:07Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"78b16f8af027e22d3ca2196b520ea7da591d9080b4082910ff647d499caa635e","abstract_canon_sha256":"727ba44864f0e10a34eb326d3d420756f2199e99946f75bde8c236d48367a18f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:34.385010Z","signature_b64":"SYymQqgKnV4+KN1rt7JLPBEDAAFSHUt/n7OZ2868It0kHDfBgIMnHVAQ4IvJKbar4iLEctb4xeBIlOP+EK3CAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d21b8647f296b01e4d41b3c3e10f069f8c22dd4110ec62051ca546f29096855a","last_reissued_at":"2026-05-18T00:51:34.384591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:34.384591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Border Bases for Polynomial Rings over Noetherian Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"cs.SC","authors_text":"Ambedkar Dukkipati, Maria Francis, Nithish Pai","submitted_at":"2014-05-02T18:49:07Z","abstract_excerpt":"The theory of border bases for zero-dimensional ideals has attracted several researchers in symbolic computation due to their numerical stability and mathematical elegance. As shown in (Francis & Dukkipati, J. Symb. Comp., 2014), one can extend the concept of border bases over Noetherian rings whenever the corresponding residue class ring is finitely generated and free. In this paper we address the following problem: Can the concept of border basis over Noetherian rings exists for ideals when the corresponding residue class rings are finitely generated but need not necessarily be free modules?"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.0472","kind":"arxiv","version":5},"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":"1405.0472","created_at":"2026-05-18T00:51:34.384651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.0472v5","created_at":"2026-05-18T00:51:34.384651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.0472","created_at":"2026-05-18T00:51:34.384651+00:00"},{"alias_kind":"pith_short_12","alias_value":"2INYMR7SS2YB","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2INYMR7SS2YB4TKB","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2INYMR7S","created_at":"2026-05-18T12:28:11.866339+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/2INYMR7SS2YB4TKBWPB6CDYGT6","json":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6.json","graph_json":"https://pith.science/api/pith-number/2INYMR7SS2YB4TKBWPB6CDYGT6/graph.json","events_json":"https://pith.science/api/pith-number/2INYMR7SS2YB4TKBWPB6CDYGT6/events.json","paper":"https://pith.science/paper/2INYMR7S"},"agent_actions":{"view_html":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6","download_json":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6.json","view_paper":"https://pith.science/paper/2INYMR7S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.0472&json=true","fetch_graph":"https://pith.science/api/pith-number/2INYMR7SS2YB4TKBWPB6CDYGT6/graph.json","fetch_events":"https://pith.science/api/pith-number/2INYMR7SS2YB4TKBWPB6CDYGT6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6/action/storage_attestation","attest_author":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6/action/author_attestation","sign_citation":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6/action/citation_signature","submit_replication":"https://pith.science/pith/2INYMR7SS2YB4TKBWPB6CDYGT6/action/replication_record"}},"created_at":"2026-05-18T00:51:34.384651+00:00","updated_at":"2026-05-18T00:51:34.384651+00:00"}