{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:E5UH2NRP3WXBFTGEYKRRPH2M3A","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":"4075c34664901db5bbf06f38cfced084dba9816f771e96c63960b8b24aab1d72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-06T14:47:43Z","title_canon_sha256":"e7b7a0cde98805dc1f445e8869f06e51d2fb09f04b71ad2696077535d85c539d"},"schema_version":"1.0","source":{"id":"1507.01483","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01483","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01483v3","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01483","created_at":"2026-05-18T01:12:49Z"},{"alias_kind":"pith_short_12","alias_value":"E5UH2NRP3WXB","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"E5UH2NRP3WXBFTGE","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"E5UH2NRP","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:daef3d5372894d85e96a8396114934689ce4faaa2aa0891e91d0cbcbadd77e2b","target":"graph","created_at":"2026-05-18T01:12:49Z","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":"Let $(X,0)$ be an ICIS of dimension 2 and let $f:(X,0)\\to (\\C^2,0)$ be a map germ with an isolated instability. We look at the invariants that appear when $X_s$ is a smoothing of $(X,0)$ and $f_s:X_s\\to B_\\epsilon$ is a stabilization of $f$. We find relations between these invariants and also give necessary and sufficient conditions for a $1$-parameter family to be Whitney equisingular. As an application, we show that a family $(X_t,0)$ is Zariski equisingular if and only if it is Whitney equisingular and the numbers of cusps and double folds of a generic linear projection are constant on $t$.","authors_text":"B. Or\\'efice-Okamoto, J. J. Nu\\~no-Ballesteros, J. N. Tomazella","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-06T14:47:43Z","title":"Equisingularity of map germs from a surface to the plane"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01483","kind":"arxiv","version":3},"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":"sha256:2059b00c63b1d13732c150b0bc809e4635a791e2e7d473bc817e71555d501e8f","target":"record","created_at":"2026-05-18T01:12:49Z","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":"4075c34664901db5bbf06f38cfced084dba9816f771e96c63960b8b24aab1d72","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-07-06T14:47:43Z","title_canon_sha256":"e7b7a0cde98805dc1f445e8869f06e51d2fb09f04b71ad2696077535d85c539d"},"schema_version":"1.0","source":{"id":"1507.01483","kind":"arxiv","version":3}},"canonical_sha256":"27687d362fddae12ccc4c2a3179f4cd806b02b3682b0cc06f1fba891200dd019","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"27687d362fddae12ccc4c2a3179f4cd806b02b3682b0cc06f1fba891200dd019","first_computed_at":"2026-05-18T01:12:49.830936Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:49.830936Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nM+2TH/6bICq77/qqsKcFFaNjnYKbLzXTyqjzlCriHW4E6qDP7SswQUBpQNcQn+LKPXXsH+4ffvO3W42+NcbDA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:49.831424Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01483","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2059b00c63b1d13732c150b0bc809e4635a791e2e7d473bc817e71555d501e8f","sha256:daef3d5372894d85e96a8396114934689ce4faaa2aa0891e91d0cbcbadd77e2b"],"state_sha256":"bda12946c5054b094290c3bd255f7c691391dd4c4a20b9f486cb296b094e2557"}