{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:UV6RGSCPYH4TJYOOVUIVS25A7I","short_pith_number":"pith:UV6RGSCP","schema_version":"1.0","canonical_sha256":"a57d13484fc1f934e1cead11596ba0fa0ec28011ab22830801c604c034cf89d9","source":{"kind":"arxiv","id":"1907.02378","version":1},"attestation_state":"computed","paper":{"title":"The Bruce-Roberts number of a function on a hypersurface with isolated singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"B\\'arbara K. L. Pereira, Bruna Or\\'efice-Okamoto, Jo\\~ao N. Tomazella, Juan J. Nu\\~no-Ballesteros","submitted_at":"2019-07-04T12:53:21Z","abstract_excerpt":"Let $(X,0)$ be an isolated hypersurface singularity defined by $\\phi\\colon(\\mathbb C^n,0)\\to(\\mathbb C,0)$ and $f\\colon(\\mathbb C^n,0)\\to\\mathbb C$ such that the Bruce-Roberts number $\\mu_{BR}(f,X)$ is finite. We first prove that $\\mu_{BR}(f,X)=\\mu(f)+\\mu(\\phi,f)+\\mu(X,0)-\\tau(X,0)$, where $\\mu$ and $\\tau$ are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety $LC(X,0)$ is Cohen-Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which t"},"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":"1907.02378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2019-07-04T12:53:21Z","cross_cats_sorted":[],"title_canon_sha256":"ffe59654576e7acab67b10d2e5428e57bad37c8c3c8e1bc1e97eb743c108020c","abstract_canon_sha256":"8497f6a41a340b7de098f56cf4b57ae12e5ba1f9550368a3459e2d9e757509e9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:28.754967Z","signature_b64":"ymO9vioPG7TkbutXY/3ueNZr1mTslIkhj+Q1zOU6ZTHm7y5IDgs0Vwknr4JbAc3zKTojGlOhG6Crmt0HhCE8Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a57d13484fc1f934e1cead11596ba0fa0ec28011ab22830801c604c034cf89d9","last_reissued_at":"2026-05-17T23:41:28.754279Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:28.754279Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Bruce-Roberts number of a function on a hypersurface with isolated singularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"B\\'arbara K. L. Pereira, Bruna Or\\'efice-Okamoto, Jo\\~ao N. Tomazella, Juan J. Nu\\~no-Ballesteros","submitted_at":"2019-07-04T12:53:21Z","abstract_excerpt":"Let $(X,0)$ be an isolated hypersurface singularity defined by $\\phi\\colon(\\mathbb C^n,0)\\to(\\mathbb C,0)$ and $f\\colon(\\mathbb C^n,0)\\to\\mathbb C$ such that the Bruce-Roberts number $\\mu_{BR}(f,X)$ is finite. We first prove that $\\mu_{BR}(f,X)=\\mu(f)+\\mu(\\phi,f)+\\mu(X,0)-\\tau(X,0)$, where $\\mu$ and $\\tau$ are the Milnor and Tjurina numbers respectively of a function or an isolated complete intersection singularity. Second, we show that the logarithmic characteristic variety $LC(X,0)$ is Cohen-Macaulay. Both theorems generalize the results of a previous paper by some of the authors, in which t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.02378","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":"1907.02378","created_at":"2026-05-17T23:41:28.754399+00:00"},{"alias_kind":"arxiv_version","alias_value":"1907.02378v1","created_at":"2026-05-17T23:41:28.754399+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.02378","created_at":"2026-05-17T23:41:28.754399+00:00"},{"alias_kind":"pith_short_12","alias_value":"UV6RGSCPYH4T","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_16","alias_value":"UV6RGSCPYH4TJYOO","created_at":"2026-05-18T12:33:30.264802+00:00"},{"alias_kind":"pith_short_8","alias_value":"UV6RGSCP","created_at":"2026-05-18T12:33:30.264802+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/UV6RGSCPYH4TJYOOVUIVS25A7I","json":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I.json","graph_json":"https://pith.science/api/pith-number/UV6RGSCPYH4TJYOOVUIVS25A7I/graph.json","events_json":"https://pith.science/api/pith-number/UV6RGSCPYH4TJYOOVUIVS25A7I/events.json","paper":"https://pith.science/paper/UV6RGSCP"},"agent_actions":{"view_html":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I","download_json":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I.json","view_paper":"https://pith.science/paper/UV6RGSCP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1907.02378&json=true","fetch_graph":"https://pith.science/api/pith-number/UV6RGSCPYH4TJYOOVUIVS25A7I/graph.json","fetch_events":"https://pith.science/api/pith-number/UV6RGSCPYH4TJYOOVUIVS25A7I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I/action/storage_attestation","attest_author":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I/action/author_attestation","sign_citation":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I/action/citation_signature","submit_replication":"https://pith.science/pith/UV6RGSCPYH4TJYOOVUIVS25A7I/action/replication_record"}},"created_at":"2026-05-17T23:41:28.754399+00:00","updated_at":"2026-05-17T23:41:28.754399+00:00"}