{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:EG2IABXJR6ZNR57LROHANMSB3B","short_pith_number":"pith:EG2IABXJ","schema_version":"1.0","canonical_sha256":"21b48006e98fb2d8f7eb8b8e06b241d85e60bfe31039909cbc75df0d054a39af","source":{"kind":"arxiv","id":"1812.00614","version":1},"attestation_state":"computed","paper":{"title":"L\\^e numbers and Newton diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adam R\\'o\\.zycki, Christophe Eyral, Grzegorz Oleksik","submitted_at":"2018-12-03T09:17:11Z","abstract_excerpt":"We give an algorithm to compute the L\\^e numbers of (the germ of) a Newton non-degenerate complex analytic function $f\\colon(\\mathbb{C}^n,0) \\rightarrow (\\mathbb{C},0)$ in terms of certain invariants attached to the Newton diagram of the function $f+z_1^{\\alpha_1}+\\cdots +z_d^{\\alpha_d}$, where $d$ is the dimension of the critical locus of $f$ and $\\alpha_1,\\ldots, \\alpha_d$ are sufficiently large integers. This is a version for non-isolated singularities of a famous theorem of A. G. Kouchnirenko. As a corollary, we obtain that Newton non-degenerate functions with the same Newton diagram have "},"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":"1812.00614","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2018-12-03T09:17:11Z","cross_cats_sorted":[],"title_canon_sha256":"0c201c866525fef2e73fd4d6bfa6a9428b42e7872df6cdd54981033c97cb1bee","abstract_canon_sha256":"db633cfe3307b2df31afc985b5c7da06574841ae69cde1f81adfd602802a53f7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:59:20.865454Z","signature_b64":"gvrtSsGr/mHSVtl23erAGHZirfcvDQ4E0IkkFTfZliXBN4pmm+HV0aQPTBxLIYOjmTDk02H1B/ZN5tNGFUpfDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"21b48006e98fb2d8f7eb8b8e06b241d85e60bfe31039909cbc75df0d054a39af","last_reissued_at":"2026-05-17T23:59:20.865088Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:59:20.865088Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"L\\^e numbers and Newton diagram","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Adam R\\'o\\.zycki, Christophe Eyral, Grzegorz Oleksik","submitted_at":"2018-12-03T09:17:11Z","abstract_excerpt":"We give an algorithm to compute the L\\^e numbers of (the germ of) a Newton non-degenerate complex analytic function $f\\colon(\\mathbb{C}^n,0) \\rightarrow (\\mathbb{C},0)$ in terms of certain invariants attached to the Newton diagram of the function $f+z_1^{\\alpha_1}+\\cdots +z_d^{\\alpha_d}$, where $d$ is the dimension of the critical locus of $f$ and $\\alpha_1,\\ldots, \\alpha_d$ are sufficiently large integers. This is a version for non-isolated singularities of a famous theorem of A. G. Kouchnirenko. As a corollary, we obtain that Newton non-degenerate functions with the same Newton diagram have "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.00614","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":"1812.00614","created_at":"2026-05-17T23:59:20.865151+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.00614v1","created_at":"2026-05-17T23:59:20.865151+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.00614","created_at":"2026-05-17T23:59:20.865151+00:00"},{"alias_kind":"pith_short_12","alias_value":"EG2IABXJR6ZN","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_16","alias_value":"EG2IABXJR6ZNR57L","created_at":"2026-05-18T12:32:22.470017+00:00"},{"alias_kind":"pith_short_8","alias_value":"EG2IABXJ","created_at":"2026-05-18T12:32:22.470017+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/EG2IABXJR6ZNR57LROHANMSB3B","json":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B.json","graph_json":"https://pith.science/api/pith-number/EG2IABXJR6ZNR57LROHANMSB3B/graph.json","events_json":"https://pith.science/api/pith-number/EG2IABXJR6ZNR57LROHANMSB3B/events.json","paper":"https://pith.science/paper/EG2IABXJ"},"agent_actions":{"view_html":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B","download_json":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B.json","view_paper":"https://pith.science/paper/EG2IABXJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.00614&json=true","fetch_graph":"https://pith.science/api/pith-number/EG2IABXJR6ZNR57LROHANMSB3B/graph.json","fetch_events":"https://pith.science/api/pith-number/EG2IABXJR6ZNR57LROHANMSB3B/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B/action/storage_attestation","attest_author":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B/action/author_attestation","sign_citation":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B/action/citation_signature","submit_replication":"https://pith.science/pith/EG2IABXJR6ZNR57LROHANMSB3B/action/replication_record"}},"created_at":"2026-05-17T23:59:20.865151+00:00","updated_at":"2026-05-17T23:59:20.865151+00:00"}