{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:6HLN473OVRONRIDQLYY2EE6ZP7","short_pith_number":"pith:6HLN473O","schema_version":"1.0","canonical_sha256":"f1d6de7f6eac5cd8a0705e31a213d97fef9ca5bb6d137ce4ad23b4d289258c9e","source":{"kind":"arxiv","id":"1512.04306","version":2},"attestation_state":"computed","paper":{"title":"Local B\\'ezout Theorem for Henselian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Henri Lombardi, M.-Emilia Alonso","submitted_at":"2015-12-14T13:36:49Z","abstract_excerpt":"This paper gives an elementary proof of an improved version of the algebraic Local B\\'ezout Theorem (given by the authors in JSC 45 (2010) 975--985). Here we remove some ad hoc hypotheses and obtain an optimal algebraic version of the theorem. Given a system of $n$ polynomials in $n$ indeterminates with coefficients in a local normal domain $(A, m,k)$ with an algebraically closed quotient field, which residually defines an isolated point in $k^n$ of multiplicity $r$, we prove that there are finitely many zeroes of the system above the residual zero (i.e., with coordinates in $m$), and the sum "},"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":"1512.04306","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-12-14T13:36:49Z","cross_cats_sorted":[],"title_canon_sha256":"dc5b94fa0e9866ef546ec207d8dce2ec687b82d964f82294e34f9c6ff32c3c91","abstract_canon_sha256":"8b49e6731dd477833183bfedff062bc7622c9a65f4753ef5e8355cc1a00698c5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:00:03.241188Z","signature_b64":"MfsC+3kdKAB+mQhIrJSHdlrRFrAo3ekAF0K0rtyWDHz7bbxY2Sk1sFOeCvrH7j6/fnrRJCofwO0vTeY35H+NAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f1d6de7f6eac5cd8a0705e31a213d97fef9ca5bb6d137ce4ad23b4d289258c9e","last_reissued_at":"2026-05-18T01:00:03.240745Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:00:03.240745Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local B\\'ezout Theorem for Henselian rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Henri Lombardi, M.-Emilia Alonso","submitted_at":"2015-12-14T13:36:49Z","abstract_excerpt":"This paper gives an elementary proof of an improved version of the algebraic Local B\\'ezout Theorem (given by the authors in JSC 45 (2010) 975--985). Here we remove some ad hoc hypotheses and obtain an optimal algebraic version of the theorem. Given a system of $n$ polynomials in $n$ indeterminates with coefficients in a local normal domain $(A, m,k)$ with an algebraically closed quotient field, which residually defines an isolated point in $k^n$ of multiplicity $r$, we prove that there are finitely many zeroes of the system above the residual zero (i.e., with coordinates in $m$), and the sum "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04306","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":"1512.04306","created_at":"2026-05-18T01:00:03.240812+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.04306v2","created_at":"2026-05-18T01:00:03.240812+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04306","created_at":"2026-05-18T01:00:03.240812+00:00"},{"alias_kind":"pith_short_12","alias_value":"6HLN473OVRON","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_16","alias_value":"6HLN473OVRONRIDQ","created_at":"2026-05-18T12:29:07.941421+00:00"},{"alias_kind":"pith_short_8","alias_value":"6HLN473O","created_at":"2026-05-18T12:29:07.941421+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/6HLN473OVRONRIDQLYY2EE6ZP7","json":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7.json","graph_json":"https://pith.science/api/pith-number/6HLN473OVRONRIDQLYY2EE6ZP7/graph.json","events_json":"https://pith.science/api/pith-number/6HLN473OVRONRIDQLYY2EE6ZP7/events.json","paper":"https://pith.science/paper/6HLN473O"},"agent_actions":{"view_html":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7","download_json":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7.json","view_paper":"https://pith.science/paper/6HLN473O","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.04306&json=true","fetch_graph":"https://pith.science/api/pith-number/6HLN473OVRONRIDQLYY2EE6ZP7/graph.json","fetch_events":"https://pith.science/api/pith-number/6HLN473OVRONRIDQLYY2EE6ZP7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7/action/storage_attestation","attest_author":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7/action/author_attestation","sign_citation":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7/action/citation_signature","submit_replication":"https://pith.science/pith/6HLN473OVRONRIDQLYY2EE6ZP7/action/replication_record"}},"created_at":"2026-05-18T01:00:03.240812+00:00","updated_at":"2026-05-18T01:00:03.240812+00:00"}