{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:L5B3WRGVR66NX5MFH2V5UTG3YO","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":"f5cd77ffc1507f36511151a963327a6516017daa9da0b9882ad59ec464edc2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-16T21:46:14Z","title_canon_sha256":"8de72b7f2fee9439fa797db1d8fb4c2993f3a1a9694682478dc69e1433d7c6ab"},"schema_version":"1.0","source":{"id":"1707.04951","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1707.04951","created_at":"2026-05-18T00:32:50Z"},{"alias_kind":"arxiv_version","alias_value":"1707.04951v2","created_at":"2026-05-18T00:32:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.04951","created_at":"2026-05-18T00:32:50Z"},{"alias_kind":"pith_short_12","alias_value":"L5B3WRGVR66N","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"L5B3WRGVR66NX5MF","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"L5B3WRGV","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:0343b087df0fc0e2658281cca02f9c479f0152653ec6a0c3f19d559cc1623391","target":"graph","created_at":"2026-05-18T00:32:50Z","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":"We present a series of examples of pairs of singular semialgebraic surfaces (real semialgebraic sets of dimension two) in ${\\mathbb R}^3$ and ${\\mathbb R}^4$ which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent, but not ambient Lipschitz equivalent. For each singular semialgebraic surface $S\\subset {\\mathbb R}^4$, we construct infinitely many semialgebraic surfaces which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent to $S$, but pairwise ambient Lipschitz non-equivalent.","authors_text":"Andrei Gabrielov, Lev Birbrair","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-16T21:46:14Z","title":"Ambient Lipschitz equivalence of real surface singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04951","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":"sha256:151df33bf289454ac90294cd3f8804feedc1f72d9caedcda182f45f8468e5de5","target":"record","created_at":"2026-05-18T00:32:50Z","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":"f5cd77ffc1507f36511151a963327a6516017daa9da0b9882ad59ec464edc2b4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-16T21:46:14Z","title_canon_sha256":"8de72b7f2fee9439fa797db1d8fb4c2993f3a1a9694682478dc69e1433d7c6ab"},"schema_version":"1.0","source":{"id":"1707.04951","kind":"arxiv","version":2}},"canonical_sha256":"5f43bb44d58fbcdbf5853eabda4cdbc39e404bee94b001b40928dd0fcae94b69","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5f43bb44d58fbcdbf5853eabda4cdbc39e404bee94b001b40928dd0fcae94b69","first_computed_at":"2026-05-18T00:32:50.408753Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:32:50.408753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZlEjzCIFNVFjQIjrLQP6hQEmd+lmIpcV61g55SnkaAktmlcDLlLvIvTWABJ6EQfwaESi9aN+tYcx/j3Aqn3JBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:32:50.409376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1707.04951","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:151df33bf289454ac90294cd3f8804feedc1f72d9caedcda182f45f8468e5de5","sha256:0343b087df0fc0e2658281cca02f9c479f0152653ec6a0c3f19d559cc1623391"],"state_sha256":"8827e34a5683cd8f37cc96e29b968f8ff1aa6a43754356f47d0486f802660cce"}