{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:TIKSDVKNHYBRNNPIBN4ZSQR77V","short_pith_number":"pith:TIKSDVKN","canonical_record":{"source":{"id":"1603.01664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-05T00:43:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"557a2ab3939cf9f81802654cf9f4d305c0f9b86e5dfe5efd655dde9ae5f8a72b","abstract_canon_sha256":"7f89cd8659f446792c4084503e9f760a4b4b377081398941b2e2b26d3c25302d"},"schema_version":"1.0"},"canonical_sha256":"9a1521d54d3e0316b5e80b7999423ffd4a8e9c630d878ae22282f74b98943ea8","source":{"kind":"arxiv","id":"1603.01664","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01664","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01664v3","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01664","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"TIKSDVKNHYBR","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIKSDVKNHYBRNNPI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIKSDVKN","created_at":"2026-05-18T12:30:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:TIKSDVKNHYBRNNPIBN4ZSQR77V","target":"record","payload":{"canonical_record":{"source":{"id":"1603.01664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-05T00:43:11Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"557a2ab3939cf9f81802654cf9f4d305c0f9b86e5dfe5efd655dde9ae5f8a72b","abstract_canon_sha256":"7f89cd8659f446792c4084503e9f760a4b4b377081398941b2e2b26d3c25302d"},"schema_version":"1.0"},"canonical_sha256":"9a1521d54d3e0316b5e80b7999423ffd4a8e9c630d878ae22282f74b98943ea8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:58.154182Z","signature_b64":"ER+PdKQo3DV9DGPqNNX4YEYTYk5k4Ts2Wlquhb3q4EjJ793Ytv6EZ4RUtjcxUDCy9M4r2e0z0QIEAL0shCbmAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9a1521d54d3e0316b5e80b7999423ffd4a8e9c630d878ae22282f74b98943ea8","last_reissued_at":"2026-05-18T00:44:58.153652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:58.153652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.01664","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qT20PIyr4kdPP9w1/cdSnCV4x0MCsl9f08IG6Sx8kNteFo36VbRuHHvljrvEQQrSAmQ/llIi+EqL13fBdu3LCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:26:11.291792Z"},"content_sha256":"cb49b4690bd426172bf4768132ff61f1ad7b0a34e7b2c239dd480734d3867783","schema_version":"1.0","event_id":"sha256:cb49b4690bd426172bf4768132ff61f1ad7b0a34e7b2c239dd480734d3867783"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:TIKSDVKNHYBRNNPIBN4ZSQR77V","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Haotian Wu, James Isenberg","submitted_at":"2016-03-05T00:43:11Z","abstract_excerpt":"We study the phenomenon of Type-II curvature blow-up in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions enveloping formal solutions with prescribed behavior, we show that for each initial hypersurface considered, a mean curvature flow solution exhibits the following behavior near the \"vanishing\" time $T$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilic point), and for each choice of the parameter $\\gamma>1/2$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01664","kind":"arxiv","version":3},"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":"2026-05-18T00:44:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0hpoN51bxi8Y6s+d/2Ev6KnCcHijzxHl1pCI9TNYSi/xZqitAlpUq/CEBIkzZZmmKMY2hmkrBiKmP+2yNlC/Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T19:26:11.292123Z"},"content_sha256":"3e111ccf931eae1aab6dfe2a16804b383f05d9fd30c4d3a0d37ceb839acf2234","schema_version":"1.0","event_id":"sha256:3e111ccf931eae1aab6dfe2a16804b383f05d9fd30c4d3a0d37ceb839acf2234"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V/bundle.json","state_url":"https://pith.science/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V/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":"2026-06-01T19:26:11Z","links":{"resolver":"https://pith.science/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V","bundle":"https://pith.science/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V/bundle.json","state":"https://pith.science/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TIKSDVKNHYBRNNPIBN4ZSQR77V/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TIKSDVKNHYBRNNPIBN4ZSQR77V","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":"7f89cd8659f446792c4084503e9f760a4b4b377081398941b2e2b26d3c25302d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-05T00:43:11Z","title_canon_sha256":"557a2ab3939cf9f81802654cf9f4d305c0f9b86e5dfe5efd655dde9ae5f8a72b"},"schema_version":"1.0","source":{"id":"1603.01664","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.01664","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"arxiv_version","alias_value":"1603.01664v3","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.01664","created_at":"2026-05-18T00:44:58Z"},{"alias_kind":"pith_short_12","alias_value":"TIKSDVKNHYBR","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TIKSDVKNHYBRNNPI","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TIKSDVKN","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:3e111ccf931eae1aab6dfe2a16804b383f05d9fd30c4d3a0d37ceb839acf2234","target":"graph","created_at":"2026-05-18T00:44:58Z","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 study the phenomenon of Type-II curvature blow-up in mean curvature flows of rotationally symmetric noncompact embedded hypersurfaces. Using analytic techniques based on formal matched asymptotics and the construction of upper and lower barrier solutions enveloping formal solutions with prescribed behavior, we show that for each initial hypersurface considered, a mean curvature flow solution exhibits the following behavior near the \"vanishing\" time $T$: (1) The highest curvature concentrates at the tip of the hypersurface (an umbilic point), and for each choice of the parameter $\\gamma>1/2$","authors_text":"Haotian Wu, James Isenberg","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-05T00:43:11Z","title":"Mean curvature flow of noncompact hypersurfaces with Type-II curvature blow-up"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.01664","kind":"arxiv","version":3},"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:cb49b4690bd426172bf4768132ff61f1ad7b0a34e7b2c239dd480734d3867783","target":"record","created_at":"2026-05-18T00:44:58Z","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":"7f89cd8659f446792c4084503e9f760a4b4b377081398941b2e2b26d3c25302d","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2016-03-05T00:43:11Z","title_canon_sha256":"557a2ab3939cf9f81802654cf9f4d305c0f9b86e5dfe5efd655dde9ae5f8a72b"},"schema_version":"1.0","source":{"id":"1603.01664","kind":"arxiv","version":3}},"canonical_sha256":"9a1521d54d3e0316b5e80b7999423ffd4a8e9c630d878ae22282f74b98943ea8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9a1521d54d3e0316b5e80b7999423ffd4a8e9c630d878ae22282f74b98943ea8","first_computed_at":"2026-05-18T00:44:58.153652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:58.153652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ER+PdKQo3DV9DGPqNNX4YEYTYk5k4Ts2Wlquhb3q4EjJ793Ytv6EZ4RUtjcxUDCy9M4r2e0z0QIEAL0shCbmAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:58.154182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.01664","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb49b4690bd426172bf4768132ff61f1ad7b0a34e7b2c239dd480734d3867783","sha256:3e111ccf931eae1aab6dfe2a16804b383f05d9fd30c4d3a0d37ceb839acf2234"],"state_sha256":"8eb251daf7f14aa3bc0a61906bfb6f14724308eb55ee8f410f24935385b9e386"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LamHmqHOF+9OKWlD7S7ISi4dggP1pWd/Q4qMVDuOU1nHJzGoAbr3CHPYyORpLCOOePAQ2z5MbM/Ar1Y46ffCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T19:26:11.294129Z","bundle_sha256":"1eed8bb48c8a64a18671e12524f06eb34a91b2dbeb6163de1edd8b440eb2aaa5"}}