{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:P5JDKBMROMTCRGAY4FBDY7DMYF","short_pith_number":"pith:P5JDKBMR","schema_version":"1.0","canonical_sha256":"7f523505917326289818e1423c7c6cc153182ed0bfc8eb78c5421af625687c35","source":{"kind":"arxiv","id":"1205.4196","version":1},"attestation_state":"computed","paper":{"title":"Functions with isolated singularities on surfaces, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Sergiy Maksymenko","submitted_at":"2012-05-18T16:50:24Z","abstract_excerpt":"Let M be a smooth connected compact surface, P be either the real line R^1 or the circle S^1. For a subset X of M denote by D(M,X) the group of diffeomorphisms of M fixed on X. In this note we consider a special class F of smooth maps f:M\\to P with isolated singularities which includes all Morse maps. For each such map f from F we consider certain submanifolds X of M that are \"adopted\" with f in a natural sense, and study the right action of the group D(M,X) on C^{\\infty}(M,P). The main result describes the homotopy types of the connected components of the stabilizers S(f) and orbits O(f) for "},"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":"1205.4196","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2012-05-18T16:50:24Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"259458255e05b112e936302751bed1c21a41fc81c1bb92ef61e8a4faf8d5a28b","abstract_canon_sha256":"b45cb9cf7987e1cdb9a78a8af538f50941d9a8c9f7e9be44876bf3ef581feccc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:22.517374Z","signature_b64":"haG7ba1fdXb2WA1xlESMulc27cEuWZumLf5waoLoJCmTO9MyA8rW9FbVNOaM7uPHqSEH5JfoNiqwBMijmRbLCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f523505917326289818e1423c7c6cc153182ed0bfc8eb78c5421af625687c35","last_reissued_at":"2026-05-18T03:55:22.516581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:22.516581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functions with isolated singularities on surfaces, II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.GT","authors_text":"Sergiy Maksymenko","submitted_at":"2012-05-18T16:50:24Z","abstract_excerpt":"Let M be a smooth connected compact surface, P be either the real line R^1 or the circle S^1. For a subset X of M denote by D(M,X) the group of diffeomorphisms of M fixed on X. In this note we consider a special class F of smooth maps f:M\\to P with isolated singularities which includes all Morse maps. For each such map f from F we consider certain submanifolds X of M that are \"adopted\" with f in a natural sense, and study the right action of the group D(M,X) on C^{\\infty}(M,P). The main result describes the homotopy types of the connected components of the stabilizers S(f) and orbits O(f) for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4196","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":"1205.4196","created_at":"2026-05-18T03:55:22.516713+00:00"},{"alias_kind":"arxiv_version","alias_value":"1205.4196v1","created_at":"2026-05-18T03:55:22.516713+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4196","created_at":"2026-05-18T03:55:22.516713+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5JDKBMROMTC","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5JDKBMROMTCRGAY","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5JDKBMR","created_at":"2026-05-18T12:27:18.751474+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/P5JDKBMROMTCRGAY4FBDY7DMYF","json":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF.json","graph_json":"https://pith.science/api/pith-number/P5JDKBMROMTCRGAY4FBDY7DMYF/graph.json","events_json":"https://pith.science/api/pith-number/P5JDKBMROMTCRGAY4FBDY7DMYF/events.json","paper":"https://pith.science/paper/P5JDKBMR"},"agent_actions":{"view_html":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF","download_json":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF.json","view_paper":"https://pith.science/paper/P5JDKBMR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1205.4196&json=true","fetch_graph":"https://pith.science/api/pith-number/P5JDKBMROMTCRGAY4FBDY7DMYF/graph.json","fetch_events":"https://pith.science/api/pith-number/P5JDKBMROMTCRGAY4FBDY7DMYF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF/action/storage_attestation","attest_author":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF/action/author_attestation","sign_citation":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF/action/citation_signature","submit_replication":"https://pith.science/pith/P5JDKBMROMTCRGAY4FBDY7DMYF/action/replication_record"}},"created_at":"2026-05-18T03:55:22.516713+00:00","updated_at":"2026-05-18T03:55:22.516713+00:00"}