{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:L5B3WRGVR66NX5MFH2V5UTG3YO","short_pith_number":"pith:L5B3WRGV","canonical_record":{"source":{"id":"1707.04951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-16T21:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"8de72b7f2fee9439fa797db1d8fb4c2993f3a1a9694682478dc69e1433d7c6ab","abstract_canon_sha256":"f5cd77ffc1507f36511151a963327a6516017daa9da0b9882ad59ec464edc2b4"},"schema_version":"1.0"},"canonical_sha256":"5f43bb44d58fbcdbf5853eabda4cdbc39e404bee94b001b40928dd0fcae94b69","source":{"kind":"arxiv","id":"1707.04951","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:L5B3WRGVR66NX5MFH2V5UTG3YO","target":"record","payload":{"canonical_record":{"source":{"id":"1707.04951","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-07-16T21:46:14Z","cross_cats_sorted":[],"title_canon_sha256":"8de72b7f2fee9439fa797db1d8fb4c2993f3a1a9694682478dc69e1433d7c6ab","abstract_canon_sha256":"f5cd77ffc1507f36511151a963327a6516017daa9da0b9882ad59ec464edc2b4"},"schema_version":"1.0"},"canonical_sha256":"5f43bb44d58fbcdbf5853eabda4cdbc39e404bee94b001b40928dd0fcae94b69","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:50.409376Z","signature_b64":"ZlEjzCIFNVFjQIjrLQP6hQEmd+lmIpcV61g55SnkaAktmlcDLlLvIvTWABJ6EQfwaESi9aN+tYcx/j3Aqn3JBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5f43bb44d58fbcdbf5853eabda4cdbc39e404bee94b001b40928dd0fcae94b69","last_reissued_at":"2026-05-18T00:32:50.408753Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:50.408753Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1707.04951","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AyFgRWZKgLQBZsVS80UMJK67YRtDvyWzRl2c5zT0RaLI6Syf3Z3F8MXJsz8HkduEntsHl1+/xcr6U3TX2FhqCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:18:49.720298Z"},"content_sha256":"151df33bf289454ac90294cd3f8804feedc1f72d9caedcda182f45f8468e5de5","schema_version":"1.0","event_id":"sha256:151df33bf289454ac90294cd3f8804feedc1f72d9caedcda182f45f8468e5de5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:L5B3WRGVR66NX5MFH2V5UTG3YO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ambient Lipschitz equivalence of real surface singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Andrei Gabrielov, Lev Birbrair","submitted_at":"2017-07-16T21:46:14Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.04951","kind":"arxiv","version":2},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:32:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DyrEfsrt5Rwpq2GIF2H9J0y9tV31LJSWRYbGZn4NzKU2susKDB8hm6stZh8XHrnyfhwGM4wQR6GiWMkv99B1AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T06:18:49.721113Z"},"content_sha256":"0343b087df0fc0e2658281cca02f9c479f0152653ec6a0c3f19d559cc1623391","schema_version":"1.0","event_id":"sha256:0343b087df0fc0e2658281cca02f9c479f0152653ec6a0c3f19d559cc1623391"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/L5B3WRGVR66NX5MFH2V5UTG3YO/bundle.json","state_url":"https://pith.science/pith/L5B3WRGVR66NX5MFH2V5UTG3YO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/L5B3WRGVR66NX5MFH2V5UTG3YO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-11T06:18:49Z","links":{"resolver":"https://pith.science/pith/L5B3WRGVR66NX5MFH2V5UTG3YO","bundle":"https://pith.science/pith/L5B3WRGVR66NX5MFH2V5UTG3YO/bundle.json","state":"https://pith.science/pith/L5B3WRGVR66NX5MFH2V5UTG3YO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/L5B3WRGVR66NX5MFH2V5UTG3YO/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I5sCSCoP71m1KvP58gxiSzVsOeVV/bPDkDDjWOVoRtahIi045x8lFuEQla60AJB5TJ7fFDoUV5Ce7/U8VfKtDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T06:18:49.728208Z","bundle_sha256":"d74ef7357d3611f64a6a8a23512c26a12b9ef38670e634e54f80a171020dcea3"}}