{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:IDSYDG6U5JK2YT3TLTVRCHNLME","short_pith_number":"pith:IDSYDG6U","canonical_record":{"source":{"id":"2209.08580","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-18T15:06:26Z","cross_cats_sorted":[],"title_canon_sha256":"5ab817c7d8639061b3aa0123fae8b1670ff13969b862dfaf986847ca63b7782f","abstract_canon_sha256":"6a99121bfd792a2bc90b837dcbf5f7c83d12851d19ab484dc583736e94703e4c"},"schema_version":"1.0"},"canonical_sha256":"40e5819bd4ea55ac4f735ceb111dab613dbbb27624a4b90bfebac376fd219613","source":{"kind":"arxiv","id":"2209.08580","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08580","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08580v2","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08580","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"IDSYDG6U5JK2","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"pith_short_16","alias_value":"IDSYDG6U5JK2YT3T","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"pith_short_8","alias_value":"IDSYDG6U","created_at":"2026-07-05T05:00:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:IDSYDG6U5JK2YT3TLTVRCHNLME","target":"record","payload":{"canonical_record":{"source":{"id":"2209.08580","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-18T15:06:26Z","cross_cats_sorted":[],"title_canon_sha256":"5ab817c7d8639061b3aa0123fae8b1670ff13969b862dfaf986847ca63b7782f","abstract_canon_sha256":"6a99121bfd792a2bc90b837dcbf5f7c83d12851d19ab484dc583736e94703e4c"},"schema_version":"1.0"},"canonical_sha256":"40e5819bd4ea55ac4f735ceb111dab613dbbb27624a4b90bfebac376fd219613","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T05:00:17.960933Z","signature_b64":"eEtrEvuI8wL2X/pdqmNdsAU83JkA+X7ZUtSkforIv2DqFy1Tmp6iudwjPhauBRSkQ/i2wX419ztcZiYM0QmhAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"40e5819bd4ea55ac4f735ceb111dab613dbbb27624a4b90bfebac376fd219613","last_reissued_at":"2026-07-05T05:00:17.960465Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T05:00:17.960465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2209.08580","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":"2026-07-05T05:00:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AwIIR0X0DyPiQVKqfVmRXlYLbItd9BdsQFoaPEbux2KaL7pMeWn19yQp3F5XcxZDm+eY/Wn8IpS6S48lRpeMAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:34:12.535036Z"},"content_sha256":"e12edf489795f4ec4a00d323dc585d8020a06e77779bb5b0f1e595609f2779ba","schema_version":"1.0","event_id":"sha256:e12edf489795f4ec4a00d323dc585d8020a06e77779bb5b0f1e595609f2779ba"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:IDSYDG6U5JK2YT3TLTVRCHNLME","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A higher speed type II blow-up for the 4-d Fujita equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianfeng Zhao","submitted_at":"2022-09-18T15:06:26Z","abstract_excerpt":"This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation $u_t=\\Delta u + u^3$. Our main result is to show that the existence of type II blowup solutions, and $\\|u(\\cdot,t)\\|_\\infty\\sim(T-t)^{-k}|ln(T-t)|^{\\frac{2k}{2k-1}}, (k=1,2,3\\cdots)$.The inner-outer gluing method has been employed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08580","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2209.08580/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":"2026-07-05T05:00:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ji/Kq+BCNHCTMNLbeVA1srULbuR9wU5QzxyV5CsePlfKHO5FPvS7RGpz874ys0a6PyCAfdZfqdRzY+HwV6pMDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T22:34:12.535419Z"},"content_sha256":"ed16f4a2556f0df69c998cfad2f4381be7bbd55aee507dabbbbdefa5b1b12742","schema_version":"1.0","event_id":"sha256:ed16f4a2556f0df69c998cfad2f4381be7bbd55aee507dabbbbdefa5b1b12742"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IDSYDG6U5JK2YT3TLTVRCHNLME/bundle.json","state_url":"https://pith.science/pith/IDSYDG6U5JK2YT3TLTVRCHNLME/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IDSYDG6U5JK2YT3TLTVRCHNLME/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":"2026-08-03T22:34:12Z","links":{"resolver":"https://pith.science/pith/IDSYDG6U5JK2YT3TLTVRCHNLME","bundle":"https://pith.science/pith/IDSYDG6U5JK2YT3TLTVRCHNLME/bundle.json","state":"https://pith.science/pith/IDSYDG6U5JK2YT3TLTVRCHNLME/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IDSYDG6U5JK2YT3TLTVRCHNLME/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:IDSYDG6U5JK2YT3TLTVRCHNLME","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":"6a99121bfd792a2bc90b837dcbf5f7c83d12851d19ab484dc583736e94703e4c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-18T15:06:26Z","title_canon_sha256":"5ab817c7d8639061b3aa0123fae8b1670ff13969b862dfaf986847ca63b7782f"},"schema_version":"1.0","source":{"id":"2209.08580","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2209.08580","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"arxiv_version","alias_value":"2209.08580v2","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2209.08580","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"pith_short_12","alias_value":"IDSYDG6U5JK2","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"pith_short_16","alias_value":"IDSYDG6U5JK2YT3T","created_at":"2026-07-05T05:00:17Z"},{"alias_kind":"pith_short_8","alias_value":"IDSYDG6U","created_at":"2026-07-05T05:00:17Z"}],"graph_snapshots":[{"event_id":"sha256:ed16f4a2556f0df69c998cfad2f4381be7bbd55aee507dabbbbdefa5b1b12742","target":"graph","created_at":"2026-07-05T05:00:17Z","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/2209.08580/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation $u_t=\\Delta u + u^3$. Our main result is to show that the existence of type II blowup solutions, and $\\|u(\\cdot,t)\\|_\\infty\\sim(T-t)^{-k}|ln(T-t)|^{\\frac{2k}{2k-1}}, (k=1,2,3\\cdots)$.The inner-outer gluing method has been employed.","authors_text":"Jianfeng Zhao","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-18T15:06:26Z","title":"A higher speed type II blow-up for the 4-d Fujita equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2209.08580","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:e12edf489795f4ec4a00d323dc585d8020a06e77779bb5b0f1e595609f2779ba","target":"record","created_at":"2026-07-05T05:00:17Z","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":"6a99121bfd792a2bc90b837dcbf5f7c83d12851d19ab484dc583736e94703e4c","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2022-09-18T15:06:26Z","title_canon_sha256":"5ab817c7d8639061b3aa0123fae8b1670ff13969b862dfaf986847ca63b7782f"},"schema_version":"1.0","source":{"id":"2209.08580","kind":"arxiv","version":2}},"canonical_sha256":"40e5819bd4ea55ac4f735ceb111dab613dbbb27624a4b90bfebac376fd219613","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"40e5819bd4ea55ac4f735ceb111dab613dbbb27624a4b90bfebac376fd219613","first_computed_at":"2026-07-05T05:00:17.960465Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T05:00:17.960465Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"eEtrEvuI8wL2X/pdqmNdsAU83JkA+X7ZUtSkforIv2DqFy1Tmp6iudwjPhauBRSkQ/i2wX419ztcZiYM0QmhAw==","signature_status":"signed_v1","signed_at":"2026-07-05T05:00:17.960933Z","signed_message":"canonical_sha256_bytes"},"source_id":"2209.08580","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e12edf489795f4ec4a00d323dc585d8020a06e77779bb5b0f1e595609f2779ba","sha256:ed16f4a2556f0df69c998cfad2f4381be7bbd55aee507dabbbbdefa5b1b12742"],"state_sha256":"7b814954e7deb94f53e70fa817a55a2986d028d20371ac21f6f58292bc2108a0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4Nw/xDc0mReEE5KCBUplM1b1d0Wur/W1O45pZSjtW/6V2qii9TWInlhl2SYpJexuKi8i1oGeXpSNFdaaXctIDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T22:34:12.538366Z","bundle_sha256":"387c860323f4484618c7d219b50eb267e0eee092025b84fbf678e3ed20553764"}}