{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:G3CGIO2SGLDVEDX4FY3Z4XRY73","short_pith_number":"pith:G3CGIO2S","canonical_record":{"source":{"id":"1404.2209","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T16:52:46Z","cross_cats_sorted":[],"title_canon_sha256":"c0232ba6c507fa112749317286e77dca9179dc7487504e6cbb09350fdbe7ec9b","abstract_canon_sha256":"d581924cfb5a9d13e46ed0eda808e34b99cb0875bbb2be80b326666f464579f4"},"schema_version":"1.0"},"canonical_sha256":"36c4643b5232c7520efc2e379e5e38fed8128c35cefcc1b160a94f99a03cf923","source":{"kind":"arxiv","id":"1404.2209","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2209","created_at":"2026-05-18T01:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2209v3","created_at":"2026-05-18T01:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2209","created_at":"2026-05-18T01:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"G3CGIO2SGLDV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G3CGIO2SGLDVEDX4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G3CGIO2S","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:G3CGIO2SGLDVEDX4FY3Z4XRY73","target":"record","payload":{"canonical_record":{"source":{"id":"1404.2209","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T16:52:46Z","cross_cats_sorted":[],"title_canon_sha256":"c0232ba6c507fa112749317286e77dca9179dc7487504e6cbb09350fdbe7ec9b","abstract_canon_sha256":"d581924cfb5a9d13e46ed0eda808e34b99cb0875bbb2be80b326666f464579f4"},"schema_version":"1.0"},"canonical_sha256":"36c4643b5232c7520efc2e379e5e38fed8128c35cefcc1b160a94f99a03cf923","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:36.378308Z","signature_b64":"yFHA45B1w7uSykKSHQdhqWIpid3WIQ4rMzW7oW8FGPRMgtTAbQn0cnfe7eVrQvT+7zVElLVJoCPvBj8EfO6IDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36c4643b5232c7520efc2e379e5e38fed8128c35cefcc1b160a94f99a03cf923","last_reissued_at":"2026-05-18T01:43:36.377661Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:36.377661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.2209","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":"2026-05-18T01:43:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bo5FXCRlTc/+QZJbEMnGH2TB+YvrMzXbmwyBV650iZp7rPphxBvJFn1+EL9zSNsSciJpVUKsnzM9KWvZYjENCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:17:16.846539Z"},"content_sha256":"b71bdff3a6b671c1ff7f1f255f7df5ac9357cb4c5b655e224e14c82cba9b63cd","schema_version":"1.0","event_id":"sha256:b71bdff3a6b671c1ff7f1f255f7df5ac9357cb4c5b655e224e14c82cba9b63cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:G3CGIO2SGLDVEDX4FY3Z4XRY73","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Pawe{\\l} Biernat","submitted_at":"2014-04-08T16:52:46Z","abstract_excerpt":"We analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\\mathbb R^d\\to S^d$. For each dimension $d>2+k(2+2\\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched asymptotics by glueing a re-scaled harmonic map to the singular self-similar solution: the equatorial map. We find that the blow-up rates of the constructed solutions are closely related to the eigenvalues of the self-similar solution. In the case of $1$-corotational maps our solutions are stable and represent the generic blow-up."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2209","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":"2026-05-18T01:43:36Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+2FnshlXLxXBuQ6PMItNQ+8YWlnmtHegYwq5LouCPG/pgzPmbBGniy+rKa44TNkkX4fVCi21Dkya25t5xJ5Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T15:17:16.847091Z"},"content_sha256":"01b36f3e41549b708762ce8449574df5e491675f39416d9777bd661afe2f185d","schema_version":"1.0","event_id":"sha256:01b36f3e41549b708762ce8449574df5e491675f39416d9777bd661afe2f185d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73/bundle.json","state_url":"https://pith.science/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73/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":"2026-06-06T15:17:16Z","links":{"resolver":"https://pith.science/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73","bundle":"https://pith.science/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73/bundle.json","state":"https://pith.science/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73/state.json","well_known_bundle":"https://pith.science/.well-known/pith/G3CGIO2SGLDVEDX4FY3Z4XRY73/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:G3CGIO2SGLDVEDX4FY3Z4XRY73","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":"d581924cfb5a9d13e46ed0eda808e34b99cb0875bbb2be80b326666f464579f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T16:52:46Z","title_canon_sha256":"c0232ba6c507fa112749317286e77dca9179dc7487504e6cbb09350fdbe7ec9b"},"schema_version":"1.0","source":{"id":"1404.2209","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.2209","created_at":"2026-05-18T01:43:36Z"},{"alias_kind":"arxiv_version","alias_value":"1404.2209v3","created_at":"2026-05-18T01:43:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.2209","created_at":"2026-05-18T01:43:36Z"},{"alias_kind":"pith_short_12","alias_value":"G3CGIO2SGLDV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"G3CGIO2SGLDVEDX4","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"G3CGIO2S","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:01b36f3e41549b708762ce8449574df5e491675f39416d9777bd661afe2f185d","target":"graph","created_at":"2026-05-18T01:43:36Z","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 analyze the finite-time blow-up of solutions of the heat flow for $k$-corotational maps $\\mathbb R^d\\to S^d$. For each dimension $d>2+k(2+2\\sqrt{2})$ we construct a countable family of blow-up solutions via a method of matched asymptotics by glueing a re-scaled harmonic map to the singular self-similar solution: the equatorial map. We find that the blow-up rates of the constructed solutions are closely related to the eigenvalues of the self-similar solution. In the case of $1$-corotational maps our solutions are stable and represent the generic blow-up.","authors_text":"Pawe{\\l} Biernat","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T16:52:46Z","title":"Non-self-similar blow-up in the heat flow for harmonic maps in higher dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.2209","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:b71bdff3a6b671c1ff7f1f255f7df5ac9357cb4c5b655e224e14c82cba9b63cd","target":"record","created_at":"2026-05-18T01:43:36Z","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":"d581924cfb5a9d13e46ed0eda808e34b99cb0875bbb2be80b326666f464579f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2014-04-08T16:52:46Z","title_canon_sha256":"c0232ba6c507fa112749317286e77dca9179dc7487504e6cbb09350fdbe7ec9b"},"schema_version":"1.0","source":{"id":"1404.2209","kind":"arxiv","version":3}},"canonical_sha256":"36c4643b5232c7520efc2e379e5e38fed8128c35cefcc1b160a94f99a03cf923","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"36c4643b5232c7520efc2e379e5e38fed8128c35cefcc1b160a94f99a03cf923","first_computed_at":"2026-05-18T01:43:36.377661Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:36.377661Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yFHA45B1w7uSykKSHQdhqWIpid3WIQ4rMzW7oW8FGPRMgtTAbQn0cnfe7eVrQvT+7zVElLVJoCPvBj8EfO6IDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:36.378308Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.2209","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b71bdff3a6b671c1ff7f1f255f7df5ac9357cb4c5b655e224e14c82cba9b63cd","sha256:01b36f3e41549b708762ce8449574df5e491675f39416d9777bd661afe2f185d"],"state_sha256":"3a13f946b199d8fd4d006a1ee4c8429ae041fd3085664ba01f324aec01999249"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2GyiJjufEb7LKO0ypuH+nnWUW4gdDWKlaM1D2nhZOd4aXpDtW0IkL/zu383WxX48pHTPhFbP5T4njH4ZHX1ECg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T15:17:16.851051Z","bundle_sha256":"b15484f2f608e63714e54cf9a6dcb3468c850b3cedfd29fb2f968294abc7a81a"}}