{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BHZEL5SIWT7UUIOQBSXKIM6DGD","short_pith_number":"pith:BHZEL5SI","schema_version":"1.0","canonical_sha256":"09f245f648b4ff4a21d00caea433c330cecfb5c6785cce5e6938abb42f49a858","source":{"kind":"arxiv","id":"1505.02532","version":2},"attestation_state":"computed","paper":{"title":"On the last fall degree of zero-dimensional Weil descent systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Michiel Kosters, Ming-Deh A. Huang, Sze Ling Yeo, Yun Yang","submitted_at":"2015-05-11T09:20:25Z","abstract_excerpt":"In this article we will discuss a new, mostly theoretical, method for solving (zero-dimensional) polynomial systems, which lies in between Gr\\\"obner basis computations and the heuristic first fall degree assumption and is not based on any heuristic. This method relies on the new concept of last fall degree.\n  Let $k$ be a finite field of cardinality $q^n$ and let $k'$ be its subfield of cardinality $q$. Let $\\mathcal{F} \\subset k[X_0,\\ldots,X_{m-1}]$ be a finite subset generating a zero-dimensional ideal. We give an upper bound of the last fall degree of the Weil descent system of $\\mathcal{F}"},"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":"1505.02532","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-05-11T09:20:25Z","cross_cats_sorted":["cs.SC"],"title_canon_sha256":"f4b7a90a3f7eed2ba44b5749a296481834b0a750fb6d3538e24e7409d12fcc21","abstract_canon_sha256":"5f69e1026af57eb8adc07205b6b9f84546225fd51c8bed37815f3f3ade074fe3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:10.978673Z","signature_b64":"rvatCk7TXiK2Mq5VeUeJ51ycz+nO0A+5YC/J1s6Vi4DsNtuKbQ3pNxRAP7jlGCbZiukVFJScoyC3I4xrCNOLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"09f245f648b4ff4a21d00caea433c330cecfb5c6785cce5e6938abb42f49a858","last_reissued_at":"2026-05-18T01:44:10.977955Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:10.977955Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the last fall degree of zero-dimensional Weil descent systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.SC"],"primary_cat":"math.AC","authors_text":"Michiel Kosters, Ming-Deh A. Huang, Sze Ling Yeo, Yun Yang","submitted_at":"2015-05-11T09:20:25Z","abstract_excerpt":"In this article we will discuss a new, mostly theoretical, method for solving (zero-dimensional) polynomial systems, which lies in between Gr\\\"obner basis computations and the heuristic first fall degree assumption and is not based on any heuristic. This method relies on the new concept of last fall degree.\n  Let $k$ be a finite field of cardinality $q^n$ and let $k'$ be its subfield of cardinality $q$. Let $\\mathcal{F} \\subset k[X_0,\\ldots,X_{m-1}]$ be a finite subset generating a zero-dimensional ideal. We give an upper bound of the last fall degree of the Weil descent system of $\\mathcal{F}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.02532","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":"1505.02532","created_at":"2026-05-18T01:44:10.978066+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.02532v2","created_at":"2026-05-18T01:44:10.978066+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.02532","created_at":"2026-05-18T01:44:10.978066+00:00"},{"alias_kind":"pith_short_12","alias_value":"BHZEL5SIWT7U","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BHZEL5SIWT7UUIOQ","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BHZEL5SI","created_at":"2026-05-18T12:29:14.074870+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/BHZEL5SIWT7UUIOQBSXKIM6DGD","json":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD.json","graph_json":"https://pith.science/api/pith-number/BHZEL5SIWT7UUIOQBSXKIM6DGD/graph.json","events_json":"https://pith.science/api/pith-number/BHZEL5SIWT7UUIOQBSXKIM6DGD/events.json","paper":"https://pith.science/paper/BHZEL5SI"},"agent_actions":{"view_html":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD","download_json":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD.json","view_paper":"https://pith.science/paper/BHZEL5SI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.02532&json=true","fetch_graph":"https://pith.science/api/pith-number/BHZEL5SIWT7UUIOQBSXKIM6DGD/graph.json","fetch_events":"https://pith.science/api/pith-number/BHZEL5SIWT7UUIOQBSXKIM6DGD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD/action/storage_attestation","attest_author":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD/action/author_attestation","sign_citation":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD/action/citation_signature","submit_replication":"https://pith.science/pith/BHZEL5SIWT7UUIOQBSXKIM6DGD/action/replication_record"}},"created_at":"2026-05-18T01:44:10.978066+00:00","updated_at":"2026-05-18T01:44:10.978066+00:00"}