{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2025:HAU2OP67FDUXLDVJSBCORQAP3X","short_pith_number":"pith:HAU2OP67","canonical_record":{"source":{"id":"2501.16678","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-01-28T03:24:31Z","cross_cats_sorted":["math.AP","math.GT"],"title_canon_sha256":"af459dea8849fda77d2f0f93abd37427a1172ab9cffb59c4768fa416b8184af2","abstract_canon_sha256":"795132dd99ac94362a7a14e6b82ceafe87f153de88add366c965376a51c8b9c2"},"schema_version":"1.0"},"canonical_sha256":"3829a73fdf28e9758ea99044e8c00fddc28a90cd76798504d17b829531808002","source":{"kind":"arxiv","id":"2501.16678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16678","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16678v1","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16678","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"HAU2OP67FDUX","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"HAU2OP67FDUXLDVJ","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"HAU2OP67","created_at":"2026-07-05T10:06:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2025:HAU2OP67FDUXLDVJSBCORQAP3X","target":"record","payload":{"canonical_record":{"source":{"id":"2501.16678","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-01-28T03:24:31Z","cross_cats_sorted":["math.AP","math.GT"],"title_canon_sha256":"af459dea8849fda77d2f0f93abd37427a1172ab9cffb59c4768fa416b8184af2","abstract_canon_sha256":"795132dd99ac94362a7a14e6b82ceafe87f153de88add366c965376a51c8b9c2"},"schema_version":"1.0"},"canonical_sha256":"3829a73fdf28e9758ea99044e8c00fddc28a90cd76798504d17b829531808002","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:06:16.959696Z","signature_b64":"7FMefRukx6gbPdPQNRgpDoeH+UJVQ+fgk9zwy6K92P8I+3ZuyuU4lnkgD9plKzk8AnU811QqOYz+xczDKbeSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3829a73fdf28e9758ea99044e8c00fddc28a90cd76798504d17b829531808002","last_reissued_at":"2026-07-05T10:06:16.959234Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:06:16.959234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2501.16678","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T10:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mhsNX2SlYCRy5/dqDh1QDfKaCHW4SV25Zrxa5cac5cEDjwZ7Xnj5Np2ZZ/CqVuHa9x3NIGk//xwGyAkCakekCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:44:47.299861Z"},"content_sha256":"513d79148c02a8f2dc218eded20407349fda27a1f9fbf4079aaf68216e8c1bfe","schema_version":"1.0","event_id":"sha256:513d79148c02a8f2dc218eded20407349fda27a1f9fbf4079aaf68216e8c1bfe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2025:HAU2OP67FDUXLDVJSBCORQAP3X","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Passing through nondegenerate singularities in mean curvature flows","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.GT"],"primary_cat":"math.DG","authors_text":"Ao Sun, Jinxin Xue, Zhihan Wang","submitted_at":"2025-01-28T03:24:31Z","abstract_excerpt":"In this paper, we study the properties of nondegenerate cylindrical singularities of mean curvature flow. We prove they are isolated in spacetime and provide a complete description of the geometry and topology change of the flow passing through the singularities. Particularly, the topology change agrees with the level sets change near a critical point of a Morse function, which is the same as performing surgery. The proof is based on a new $L^2$-distance monotonicity formula, which allows us to derive a discrete almost monotonicity of the ``decay order\", a discrete mean curvature flow analog t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16678","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2501.16678/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T10:06:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mOLxGaMAda8hoFmvmGkWT7/edxozsVK5VJPNwIDKmHrmGsWTSjak/v+DLom60bHs++E7cDghuB0J94sVe4JeCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T21:44:47.300670Z"},"content_sha256":"73b57fbd9d5942a79d46f7739d6ad256d133c59d7e7efb84538533d4ddb4d111","schema_version":"1.0","event_id":"sha256:73b57fbd9d5942a79d46f7739d6ad256d133c59d7e7efb84538533d4ddb4d111"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HAU2OP67FDUXLDVJSBCORQAP3X/bundle.json","state_url":"https://pith.science/pith/HAU2OP67FDUXLDVJSBCORQAP3X/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HAU2OP67FDUXLDVJSBCORQAP3X/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":"2026-08-11T21:44:47Z","links":{"resolver":"https://pith.science/pith/HAU2OP67FDUXLDVJSBCORQAP3X","bundle":"https://pith.science/pith/HAU2OP67FDUXLDVJSBCORQAP3X/bundle.json","state":"https://pith.science/pith/HAU2OP67FDUXLDVJSBCORQAP3X/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HAU2OP67FDUXLDVJSBCORQAP3X/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:HAU2OP67FDUXLDVJSBCORQAP3X","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":"795132dd99ac94362a7a14e6b82ceafe87f153de88add366c965376a51c8b9c2","cross_cats_sorted":["math.AP","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-01-28T03:24:31Z","title_canon_sha256":"af459dea8849fda77d2f0f93abd37427a1172ab9cffb59c4768fa416b8184af2"},"schema_version":"1.0","source":{"id":"2501.16678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2501.16678","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"arxiv_version","alias_value":"2501.16678v1","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2501.16678","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"pith_short_12","alias_value":"HAU2OP67FDUX","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"pith_short_16","alias_value":"HAU2OP67FDUXLDVJ","created_at":"2026-07-05T10:06:16Z"},{"alias_kind":"pith_short_8","alias_value":"HAU2OP67","created_at":"2026-07-05T10:06:16Z"}],"graph_snapshots":[{"event_id":"sha256:73b57fbd9d5942a79d46f7739d6ad256d133c59d7e7efb84538533d4ddb4d111","target":"graph","created_at":"2026-07-05T10:06:16Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2501.16678/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we study the properties of nondegenerate cylindrical singularities of mean curvature flow. We prove they are isolated in spacetime and provide a complete description of the geometry and topology change of the flow passing through the singularities. Particularly, the topology change agrees with the level sets change near a critical point of a Morse function, which is the same as performing surgery. The proof is based on a new $L^2$-distance monotonicity formula, which allows us to derive a discrete almost monotonicity of the ``decay order\", a discrete mean curvature flow analog t","authors_text":"Ao Sun, Jinxin Xue, Zhihan Wang","cross_cats":["math.AP","math.GT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-01-28T03:24:31Z","title":"Passing through nondegenerate singularities in mean curvature flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2501.16678","kind":"arxiv","version":1},"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":"sha256:513d79148c02a8f2dc218eded20407349fda27a1f9fbf4079aaf68216e8c1bfe","target":"record","created_at":"2026-07-05T10:06:16Z","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":"795132dd99ac94362a7a14e6b82ceafe87f153de88add366c965376a51c8b9c2","cross_cats_sorted":["math.AP","math.GT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.DG","submitted_at":"2025-01-28T03:24:31Z","title_canon_sha256":"af459dea8849fda77d2f0f93abd37427a1172ab9cffb59c4768fa416b8184af2"},"schema_version":"1.0","source":{"id":"2501.16678","kind":"arxiv","version":1}},"canonical_sha256":"3829a73fdf28e9758ea99044e8c00fddc28a90cd76798504d17b829531808002","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3829a73fdf28e9758ea99044e8c00fddc28a90cd76798504d17b829531808002","first_computed_at":"2026-07-05T10:06:16.959234Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:06:16.959234Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7FMefRukx6gbPdPQNRgpDoeH+UJVQ+fgk9zwy6K92P8I+3ZuyuU4lnkgD9plKzk8AnU811QqOYz+xczDKbeSAw==","signature_status":"signed_v1","signed_at":"2026-07-05T10:06:16.959696Z","signed_message":"canonical_sha256_bytes"},"source_id":"2501.16678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:513d79148c02a8f2dc218eded20407349fda27a1f9fbf4079aaf68216e8c1bfe","sha256:73b57fbd9d5942a79d46f7739d6ad256d133c59d7e7efb84538533d4ddb4d111"],"state_sha256":"3c2bf82f8a9e9eaea98c4584a5bd5d32eb014c0bf1238eca66f15ce6ffdc69bb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RE3d73jyYbeBo/iQL/l6nGDG6SlHldp8avmBMRyJEZDLdi/n4tl5/w9YWyl2Qh3xSiETV7l+p/zIVyMA/W04Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T21:44:47.306190Z","bundle_sha256":"06ba82d7252048d3140eabe1433d8ab963fa5889063d685ed32dab38a9c2a066"}}