{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:JZHPJPCZJCLP6TW7JAJGHEF32E","short_pith_number":"pith:JZHPJPCZ","canonical_record":{"source":{"id":"2105.06613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-05-14T01:57:03Z","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"title_canon_sha256":"ab60700ffba7721c2ede1ebba5087ec860282777b0ad4250aca0410f21d47ebf","abstract_canon_sha256":"10931bf83a526ed78bab9c5bc08bd7ebd3e2ea80abeea194e1c4a94fe4b56038"},"schema_version":"1.0"},"canonical_sha256":"4e4ef4bc594896ff4edf48126390bbd10c9784269898cfb2600c42b7cf2ede7a","source":{"kind":"arxiv","id":"2105.06613","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.06613","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"2105.06613v1","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.06613","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"JZHPJPCZJCLP","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"JZHPJPCZJCLP6TW7","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"JZHPJPCZ","created_at":"2026-07-05T03:10:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:JZHPJPCZJCLP6TW7JAJGHEF32E","target":"record","payload":{"canonical_record":{"source":{"id":"2105.06613","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-05-14T01:57:03Z","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"title_canon_sha256":"ab60700ffba7721c2ede1ebba5087ec860282777b0ad4250aca0410f21d47ebf","abstract_canon_sha256":"10931bf83a526ed78bab9c5bc08bd7ebd3e2ea80abeea194e1c4a94fe4b56038"},"schema_version":"1.0"},"canonical_sha256":"4e4ef4bc594896ff4edf48126390bbd10c9784269898cfb2600c42b7cf2ede7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:10:08.537936Z","signature_b64":"TyI/YIaZ9OJ5Uocd4aojT5imqR0mZsFVk3AiukDvbrvMVyYvE1Tu8N/6QEjeuWpekwl/jxV9dm6WTkNiDLGoDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e4ef4bc594896ff4edf48126390bbd10c9784269898cfb2600c42b7cf2ede7a","last_reissued_at":"2026-07-05T03:10:08.537505Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:10:08.537505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2105.06613","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":"2026-07-05T03:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+dn3fHXeGZtN8XBVM+RXwsDWc/2JP7X1uBww1DFajg+b59zXcHM6Bn0AJsQAgovw61q4wFlGmCkL50z/VYmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:10:36.226373Z"},"content_sha256":"dab2da098bb6ae7717cdc09d47e4a38f44a17cfdb3db81a278ef5bd407e85124","schema_version":"1.0","event_id":"sha256:dab2da098bb6ae7717cdc09d47e4a38f44a17cfdb3db81a278ef5bd407e85124"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:JZHPJPCZJCLP6TW7JAJGHEF32E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA","math.AP","math.NA"],"primary_cat":"math.DG","authors_text":"Dan Knopf, David Garfinkle, Haotian Wu, James Isenberg","submitted_at":"2021-05-14T01:57:03Z","abstract_excerpt":"We present a numerical study of the local stability of mean curvature flow of rotationally symmetric, complete noncompact hypersurfaces with Type-II curvature blowup. Our numerical analysis employs a novel overlap method that constructs \"numerically global\" (i.e., with spatial domain arbitrarily large but finite) flow solutions with initial data covering analytically distinct regions. Our numerical results show that for certain prescribed families of perturbations, there are two classes of initial data that lead to distinct behaviors under mean curvature flow. Firstly, there is a \"near\" class "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.06613","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/2105.06613/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":"2026-07-05T03:10:08Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2qRGt2G3mgC2kvIyInfEYLZOO/E/u1STvAB2yyx44AVfhsoSjrHXxHya8be7p//ELM5R6BdhY69JBC29yLvGDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:10:36.227036Z"},"content_sha256":"5a93dadd966e22640f349a0a3c2d9d92538847f989d3db5d960fd8546f1a6d37","schema_version":"1.0","event_id":"sha256:5a93dadd966e22640f349a0a3c2d9d92538847f989d3db5d960fd8546f1a6d37"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JZHPJPCZJCLP6TW7JAJGHEF32E/bundle.json","state_url":"https://pith.science/pith/JZHPJPCZJCLP6TW7JAJGHEF32E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JZHPJPCZJCLP6TW7JAJGHEF32E/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":"2026-08-03T22:10:36Z","links":{"resolver":"https://pith.science/pith/JZHPJPCZJCLP6TW7JAJGHEF32E","bundle":"https://pith.science/pith/JZHPJPCZJCLP6TW7JAJGHEF32E/bundle.json","state":"https://pith.science/pith/JZHPJPCZJCLP6TW7JAJGHEF32E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JZHPJPCZJCLP6TW7JAJGHEF32E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:JZHPJPCZJCLP6TW7JAJGHEF32E","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":"10931bf83a526ed78bab9c5bc08bd7ebd3e2ea80abeea194e1c4a94fe4b56038","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-05-14T01:57:03Z","title_canon_sha256":"ab60700ffba7721c2ede1ebba5087ec860282777b0ad4250aca0410f21d47ebf"},"schema_version":"1.0","source":{"id":"2105.06613","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2105.06613","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"arxiv_version","alias_value":"2105.06613v1","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2105.06613","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"pith_short_12","alias_value":"JZHPJPCZJCLP","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"pith_short_16","alias_value":"JZHPJPCZJCLP6TW7","created_at":"2026-07-05T03:10:08Z"},{"alias_kind":"pith_short_8","alias_value":"JZHPJPCZ","created_at":"2026-07-05T03:10:08Z"}],"graph_snapshots":[{"event_id":"sha256:5a93dadd966e22640f349a0a3c2d9d92538847f989d3db5d960fd8546f1a6d37","target":"graph","created_at":"2026-07-05T03:10:08Z","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/2105.06613/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a numerical study of the local stability of mean curvature flow of rotationally symmetric, complete noncompact hypersurfaces with Type-II curvature blowup. Our numerical analysis employs a novel overlap method that constructs \"numerically global\" (i.e., with spatial domain arbitrarily large but finite) flow solutions with initial data covering analytically distinct regions. Our numerical results show that for certain prescribed families of perturbations, there are two classes of initial data that lead to distinct behaviors under mean curvature flow. Firstly, there is a \"near\" class ","authors_text":"Dan Knopf, David Garfinkle, Haotian Wu, James Isenberg","cross_cats":["cs.NA","math.AP","math.NA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-05-14T01:57:03Z","title":"A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.06613","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:dab2da098bb6ae7717cdc09d47e4a38f44a17cfdb3db81a278ef5bd407e85124","target":"record","created_at":"2026-07-05T03:10:08Z","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":"10931bf83a526ed78bab9c5bc08bd7ebd3e2ea80abeea194e1c4a94fe4b56038","cross_cats_sorted":["cs.NA","math.AP","math.NA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-05-14T01:57:03Z","title_canon_sha256":"ab60700ffba7721c2ede1ebba5087ec860282777b0ad4250aca0410f21d47ebf"},"schema_version":"1.0","source":{"id":"2105.06613","kind":"arxiv","version":1}},"canonical_sha256":"4e4ef4bc594896ff4edf48126390bbd10c9784269898cfb2600c42b7cf2ede7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e4ef4bc594896ff4edf48126390bbd10c9784269898cfb2600c42b7cf2ede7a","first_computed_at":"2026-07-05T03:10:08.537505Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:10:08.537505Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TyI/YIaZ9OJ5Uocd4aojT5imqR0mZsFVk3AiukDvbrvMVyYvE1Tu8N/6QEjeuWpekwl/jxV9dm6WTkNiDLGoDA==","signature_status":"signed_v1","signed_at":"2026-07-05T03:10:08.537936Z","signed_message":"canonical_sha256_bytes"},"source_id":"2105.06613","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dab2da098bb6ae7717cdc09d47e4a38f44a17cfdb3db81a278ef5bd407e85124","sha256:5a93dadd966e22640f349a0a3c2d9d92538847f989d3db5d960fd8546f1a6d37"],"state_sha256":"72134240a017e8c9ec7b73b20c1c1ad6bdee144e4c29269d82ff4a6cf400652b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YOcN+NwhvQ91WsAaMU926VfZNIZOGrNIIQnj4sBI1O2fJhF02I4x6GpwPndiWJIVfgwOIOB102NJGruh2UDoAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:10:36.303793Z","bundle_sha256":"f1b947505b4fbab76a63e8c883a449b9256f3217ad86fabdd8cd91ab7cdfe7bd"}}