{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:UIPLETLX42C25MTMVVFFMKGZS6","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"8c01ab883868275b77fbbbaca24ae079b26f0b1324ce25926f12e66f155f1047","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-06T10:10:29Z","title_canon_sha256":"90211b7741775e9261817adc6648823cc30164706581c6da8702230f0d119885"},"schema_version":"1.0","source":{"id":"1112.1214","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.1214","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"arxiv_version","alias_value":"1112.1214v2","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.1214","created_at":"2026-05-18T02:45:32Z"},{"alias_kind":"pith_short_12","alias_value":"UIPLETLX42C2","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_16","alias_value":"UIPLETLX42C25MTM","created_at":"2026-05-18T12:26:42Z"},{"alias_kind":"pith_short_8","alias_value":"UIPLETLX","created_at":"2026-05-18T12:26:42Z"}],"graph_snapshots":[{"event_id":"sha256:3176d79c0ecf4e26d7eac446cef17c788aa51eff0ab73b1389e1203661a9ab0a","target":"graph","created_at":"2026-05-18T02:45:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this paper, we propose one index $i_1(f)-i_2(f)$ which measures how well-behaved a given finitely determined multigerm $f: (\\mathbb{K}^n,S)\\to (\\mathbb{K}^p,0)$ $(n\\le p)$ of corank at most one is from the viewpoint of liftable vector fields; and we answer the following problems when the index indicates that the given multigerm $f$ is best-behaved.\n1) When is the module of vector fields liftable over $f$ finitely generated?\n2) How can we characterize the minimal number of generators when the module of vector fields liftable over $f$ is finitely generated?\n3) How can we calculate the minimal","authors_text":"Takashi Nishimura","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-06T10:10:29Z","title":"Vector fields liftable over finitely determined multigerms of corank at most one"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.1214","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:fd44df4a3b2102de4b5f92adaa466c15c586e8d3e47495aea80f3b24ed7fc7ab","target":"record","created_at":"2026-05-18T02:45:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"8c01ab883868275b77fbbbaca24ae079b26f0b1324ce25926f12e66f155f1047","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-06T10:10:29Z","title_canon_sha256":"90211b7741775e9261817adc6648823cc30164706581c6da8702230f0d119885"},"schema_version":"1.0","source":{"id":"1112.1214","kind":"arxiv","version":2}},"canonical_sha256":"a21eb24d77e685aeb26cad4a5628d99798064f08f19811ea3cedd05093bcb5b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a21eb24d77e685aeb26cad4a5628d99798064f08f19811ea3cedd05093bcb5b8","first_computed_at":"2026-05-18T02:45:32.436073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:32.436073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nrnZty36AUapK+Kp6AesmKoW8gqGuBO5EPD+0kfkkoxAbj9RW3BTrnVLa4ZA7Dnln8yNJX3xguWXrXxw2ji0Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:32.436785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.1214","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fd44df4a3b2102de4b5f92adaa466c15c586e8d3e47495aea80f3b24ed7fc7ab","sha256:3176d79c0ecf4e26d7eac446cef17c788aa51eff0ab73b1389e1203661a9ab0a"],"state_sha256":"69acb2fd60c42c315680a921fb90c05666bbf6c5f05a67e6b7e2ef50c3dc471a"}