{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:H6CD6PLGJLRZ7A7YOQVINVHUZD","short_pith_number":"pith:H6CD6PLG","schema_version":"1.0","canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","source":{"kind":"arxiv","id":"1705.04024","version":1},"attestation_state":"computed","paper":{"title":"On Regular Sequences in the Form Module with Applications to Local B\\'ezout Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"M. Azeem Khadam","submitted_at":"2017-05-11T06:08:37Z","abstract_excerpt":"Let $\\mathfrak{q}$ denote an ideal in a Noetherian local ring $(A,\\mathfrak{m})$. Let $\\underline{a}=a_1,\\ldots,a_d \\subset \\mathfrak{q}$ denote a system of parameters in a finitely generated $A$-module $M$. This note investigate an improvement of the inequality $c_1\\cdot \\ldots \\cdot c_d \\cdot e_0(\\mathfrak{q};M) \\leq \\ell_A(M/\\underline{a}\\,M)$, where $c_i$ denote the initial degrees of $a_i$ in the form ring $G_A(\\mathfrak{q})$. To this end, there is an investigation of regular sequences in the form module $G_M(\\mathfrak{q})$ by homology of a factor complex of the Koszul complex. In a parti"},"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":"1705.04024","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-05-11T06:08:37Z","cross_cats_sorted":[],"title_canon_sha256":"881271ff8939827dab8c28157dcab99db3e94f0181ec286d349d0724c6673bd7","abstract_canon_sha256":"e94098e0fcd48dd961972faf0dede878edfd47870eb9137c32d52ee4974b6d37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:41.594001Z","signature_b64":"j7NxASk1Si4DgVg0BcXc6bgZJGn6DSnHkldHksbQL3UvAnKDoC2BJkOhkD4vYgdZyedCRWEUQu2fFCvrVajYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f843f3d664ae39f83f8742a86d4f4c8fb991e927488b6278bf4b3a64186bec8","last_reissued_at":"2026-05-18T00:44:41.593392Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:41.593392Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Regular Sequences in the Form Module with Applications to Local B\\'ezout Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"M. Azeem Khadam","submitted_at":"2017-05-11T06:08:37Z","abstract_excerpt":"Let $\\mathfrak{q}$ denote an ideal in a Noetherian local ring $(A,\\mathfrak{m})$. Let $\\underline{a}=a_1,\\ldots,a_d \\subset \\mathfrak{q}$ denote a system of parameters in a finitely generated $A$-module $M$. This note investigate an improvement of the inequality $c_1\\cdot \\ldots \\cdot c_d \\cdot e_0(\\mathfrak{q};M) \\leq \\ell_A(M/\\underline{a}\\,M)$, where $c_i$ denote the initial degrees of $a_i$ in the form ring $G_A(\\mathfrak{q})$. To this end, there is an investigation of regular sequences in the form module $G_M(\\mathfrak{q})$ by homology of a factor complex of the Koszul complex. In a parti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04024","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":"1705.04024","created_at":"2026-05-18T00:44:41.593494+00:00"},{"alias_kind":"arxiv_version","alias_value":"1705.04024v1","created_at":"2026-05-18T00:44:41.593494+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.04024","created_at":"2026-05-18T00:44:41.593494+00:00"},{"alias_kind":"pith_short_12","alias_value":"H6CD6PLGJLRZ","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_16","alias_value":"H6CD6PLGJLRZ7A7Y","created_at":"2026-05-18T12:31:18.294218+00:00"},{"alias_kind":"pith_short_8","alias_value":"H6CD6PLG","created_at":"2026-05-18T12:31:18.294218+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/H6CD6PLGJLRZ7A7YOQVINVHUZD","json":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD.json","graph_json":"https://pith.science/api/pith-number/H6CD6PLGJLRZ7A7YOQVINVHUZD/graph.json","events_json":"https://pith.science/api/pith-number/H6CD6PLGJLRZ7A7YOQVINVHUZD/events.json","paper":"https://pith.science/paper/H6CD6PLG"},"agent_actions":{"view_html":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD","download_json":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD.json","view_paper":"https://pith.science/paper/H6CD6PLG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1705.04024&json=true","fetch_graph":"https://pith.science/api/pith-number/H6CD6PLGJLRZ7A7YOQVINVHUZD/graph.json","fetch_events":"https://pith.science/api/pith-number/H6CD6PLGJLRZ7A7YOQVINVHUZD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/action/storage_attestation","attest_author":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/action/author_attestation","sign_citation":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/action/citation_signature","submit_replication":"https://pith.science/pith/H6CD6PLGJLRZ7A7YOQVINVHUZD/action/replication_record"}},"created_at":"2026-05-18T00:44:41.593494+00:00","updated_at":"2026-05-18T00:44:41.593494+00:00"}