{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P3XUYPQNVF2AZQCUE5VETUW23I","short_pith_number":"pith:P3XUYPQN","canonical_record":{"source":{"id":"1711.03864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-10T15:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"46224e597f23d5735ed7a09bcc305f552a0e459df77b77527fd90a15ff7e3ce5","abstract_canon_sha256":"dbeaa3b50543f2b1034d857d447c960732c10ce10e7f9c7132ee6a144fdc98d5"},"schema_version":"1.0"},"canonical_sha256":"7eef4c3e0da9740cc054276a49d2dada2dc2d61d0d720702dadf19edd11bf721","source":{"kind":"arxiv","id":"1711.03864","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03864","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03864v2","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03864","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"P3XUYPQNVF2A","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P3XUYPQNVF2AZQCU","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P3XUYPQN","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P3XUYPQNVF2AZQCUE5VETUW23I","target":"record","payload":{"canonical_record":{"source":{"id":"1711.03864","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-10T15:20:59Z","cross_cats_sorted":[],"title_canon_sha256":"46224e597f23d5735ed7a09bcc305f552a0e459df77b77527fd90a15ff7e3ce5","abstract_canon_sha256":"dbeaa3b50543f2b1034d857d447c960732c10ce10e7f9c7132ee6a144fdc98d5"},"schema_version":"1.0"},"canonical_sha256":"7eef4c3e0da9740cc054276a49d2dada2dc2d61d0d720702dadf19edd11bf721","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:05:39.551132Z","signature_b64":"XZc0CF3j7Eje7iF/+d/5Sl9/rdQco0MJP1Ebi938O2+lmqNMXt1PkXot7TsZ/SlkbNK4uegtbudIGUm/WFPHBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eef4c3e0da9740cc054276a49d2dada2dc2d61d0d720702dadf19edd11bf721","last_reissued_at":"2026-05-18T00:05:39.550698Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:05:39.550698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.03864","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":"2026-05-18T00:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qBfdy+A+EUZiR+1ySyACihezxsQpvhk7pd+0IS/OH7g75gDjTrb8Oura9qFN8T+li2QqnbnaFtsLqDjZl4bwAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:34:28.078849Z"},"content_sha256":"8e854e3d82415204117f0e9f2f8d1666d079bb5b3233f8f24227aa582bd519c4","schema_version":"1.0","event_id":"sha256:8e854e3d82415204117f0e9f2f8d1666d079bb5b3233f8f24227aa582bd519c4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P3XUYPQNVF2AZQCUE5VETUW23I","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniformly compressing mean curvature flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dmitry Vorotnikov, Wenhui Shi","submitted_at":"2017-11-10T15:20:59Z","abstract_excerpt":"Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a related geometric flow which is free of these drawbacks. Our flow can be viewed as a formal gradient flow on a certain submanifold of the Wasserstein space of probability measures endowed with Otto's Riemannian structure. We obtain a number of analytic results concerning well-posedness and long-time stability which are however restricted to the 1D case of ev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03864","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":"2026-05-18T00:05:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vJpToS2aQ0jxiAg1C50v1Pjtni1sxseiSxXwp4m/G0/XuaSYaU2wlxG6N9t0ARr2qaCdcYxDiUh79zrnefyoBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T00:34:28.079198Z"},"content_sha256":"1eb13769d3e740220c9bfdad73ea13ee84dd38e970a385831889ec196c7afdaa","schema_version":"1.0","event_id":"sha256:1eb13769d3e740220c9bfdad73ea13ee84dd38e970a385831889ec196c7afdaa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P3XUYPQNVF2AZQCUE5VETUW23I/bundle.json","state_url":"https://pith.science/pith/P3XUYPQNVF2AZQCUE5VETUW23I/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P3XUYPQNVF2AZQCUE5VETUW23I/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":"2026-05-31T00:34:28Z","links":{"resolver":"https://pith.science/pith/P3XUYPQNVF2AZQCUE5VETUW23I","bundle":"https://pith.science/pith/P3XUYPQNVF2AZQCUE5VETUW23I/bundle.json","state":"https://pith.science/pith/P3XUYPQNVF2AZQCUE5VETUW23I/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P3XUYPQNVF2AZQCUE5VETUW23I/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P3XUYPQNVF2AZQCUE5VETUW23I","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":"dbeaa3b50543f2b1034d857d447c960732c10ce10e7f9c7132ee6a144fdc98d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-10T15:20:59Z","title_canon_sha256":"46224e597f23d5735ed7a09bcc305f552a0e459df77b77527fd90a15ff7e3ce5"},"schema_version":"1.0","source":{"id":"1711.03864","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.03864","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"arxiv_version","alias_value":"1711.03864v2","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.03864","created_at":"2026-05-18T00:05:39Z"},{"alias_kind":"pith_short_12","alias_value":"P3XUYPQNVF2A","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P3XUYPQNVF2AZQCU","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P3XUYPQN","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:1eb13769d3e740220c9bfdad73ea13ee84dd38e970a385831889ec196c7afdaa","target":"graph","created_at":"2026-05-18T00:05:39Z","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":"Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform density of gridpoints on the evolving surfaces. We introduce a related geometric flow which is free of these drawbacks. Our flow can be viewed as a formal gradient flow on a certain submanifold of the Wasserstein space of probability measures endowed with Otto's Riemannian structure. We obtain a number of analytic results concerning well-posedness and long-time stability which are however restricted to the 1D case of ev","authors_text":"Dmitry Vorotnikov, Wenhui Shi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-10T15:20:59Z","title":"Uniformly compressing mean curvature flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.03864","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":"sha256:8e854e3d82415204117f0e9f2f8d1666d079bb5b3233f8f24227aa582bd519c4","target":"record","created_at":"2026-05-18T00:05:39Z","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":"dbeaa3b50543f2b1034d857d447c960732c10ce10e7f9c7132ee6a144fdc98d5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-10T15:20:59Z","title_canon_sha256":"46224e597f23d5735ed7a09bcc305f552a0e459df77b77527fd90a15ff7e3ce5"},"schema_version":"1.0","source":{"id":"1711.03864","kind":"arxiv","version":2}},"canonical_sha256":"7eef4c3e0da9740cc054276a49d2dada2dc2d61d0d720702dadf19edd11bf721","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7eef4c3e0da9740cc054276a49d2dada2dc2d61d0d720702dadf19edd11bf721","first_computed_at":"2026-05-18T00:05:39.550698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:39.550698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XZc0CF3j7Eje7iF/+d/5Sl9/rdQco0MJP1Ebi938O2+lmqNMXt1PkXot7TsZ/SlkbNK4uegtbudIGUm/WFPHBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:39.551132Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.03864","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e854e3d82415204117f0e9f2f8d1666d079bb5b3233f8f24227aa582bd519c4","sha256:1eb13769d3e740220c9bfdad73ea13ee84dd38e970a385831889ec196c7afdaa"],"state_sha256":"c44a3bb1e9771c29f8c713887866660dab46f0e74cb54e07f0250ae62a09b6bd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dF2sZSGr4WyjCuiSazBsW4dl8lPNndi0FX3QZmJ0iRtzrhg+nQq9U+5byGpS4q4MZsVl6Y92G/OwGMMetlmXCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T00:34:28.081559Z","bundle_sha256":"be3dd301fdad9b960daaf392366dfc36945aedb99ed28a99bdc8320da639c1be"}}