{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:DPJIUCVDLDWSPS5ZWFNYK3EJGP","short_pith_number":"pith:DPJIUCVD","schema_version":"1.0","canonical_sha256":"1bd28a0aa358ed27cbb9b15b856c8933c7f4a1b222dd02cc1bc16ccf8c9532dd","source":{"kind":"arxiv","id":"1709.04939","version":1},"attestation_state":"computed","paper":{"title":"On strongly anisotropic type I blow up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Merle, Jeremie Szeftel, Pierre Raphael","submitted_at":"2017-09-14T18:24:49Z","abstract_excerpt":"We consider the energy super critical 4 dimensional semilinear heat equation $$\\partial_tu=\\Delta u+|u|^{p-1}u, \\ \\ x\\in \\Bbb R^4, \\ \\ p>5.$$ Let $\\Phi(r)$ be a  three dimensional radial self similar solution for the three supercritical probmem as exhibited and studied in \\cite{CRS}. We show the finite codimensional transversal stability of the corresponding blow up solution by exhibiting a manifold of finite energy blow up solutions of the four dimensional problem with cylindrical symmetry which blows up as $$u(t,x)\\sim \\frac{1}{(T-t)^{\\frac{1}{p-1}}}U(t,Y), \\ \\ Y=\\frac{x}{\\sqrt{T-t}}$$ with "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1709.04939","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-09-14T18:24:49Z","cross_cats_sorted":[],"title_canon_sha256":"b6a62b10dc0b3c9d9eadbcfefbd55364391e5acc745dbc0869c329c0503dd925","abstract_canon_sha256":"7729a701c05b913e431d5a6af89536ec026cdd14d15332cd6bdd08a420381a52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:08.768811Z","signature_b64":"hqz+wdDYgU5ynfYqrxOkMRtuBgqxaz6S0ZSnw2wj9k04upXp4vbVuBlFiPcCvX23Q1l0/MWPspaGPPnEx7ZJDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1bd28a0aa358ed27cbb9b15b856c8933c7f4a1b222dd02cc1bc16ccf8c9532dd","last_reissued_at":"2026-05-18T00:35:08.768396Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:08.768396Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On strongly anisotropic type I blow up","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Frank Merle, Jeremie Szeftel, Pierre Raphael","submitted_at":"2017-09-14T18:24:49Z","abstract_excerpt":"We consider the energy super critical 4 dimensional semilinear heat equation $$\\partial_tu=\\Delta u+|u|^{p-1}u, \\ \\ x\\in \\Bbb R^4, \\ \\ p>5.$$ Let $\\Phi(r)$ be a  three dimensional radial self similar solution for the three supercritical probmem as exhibited and studied in \\cite{CRS}. We show the finite codimensional transversal stability of the corresponding blow up solution by exhibiting a manifold of finite energy blow up solutions of the four dimensional problem with cylindrical symmetry which blows up as $$u(t,x)\\sim \\frac{1}{(T-t)^{\\frac{1}{p-1}}}U(t,Y), \\ \\ Y=\\frac{x}{\\sqrt{T-t}}$$ with "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.04939","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":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1709.04939","created_at":"2026-05-18T00:35:08.768474+00:00"},{"alias_kind":"arxiv_version","alias_value":"1709.04939v1","created_at":"2026-05-18T00:35:08.768474+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1709.04939","created_at":"2026-05-18T00:35:08.768474+00:00"},{"alias_kind":"pith_short_12","alias_value":"DPJIUCVDLDWS","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_16","alias_value":"DPJIUCVDLDWSPS5Z","created_at":"2026-05-18T12:31:12.930513+00:00"},{"alias_kind":"pith_short_8","alias_value":"DPJIUCVD","created_at":"2026-05-18T12:31:12.930513+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP","json":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP.json","graph_json":"https://pith.science/api/pith-number/DPJIUCVDLDWSPS5ZWFNYK3EJGP/graph.json","events_json":"https://pith.science/api/pith-number/DPJIUCVDLDWSPS5ZWFNYK3EJGP/events.json","paper":"https://pith.science/paper/DPJIUCVD"},"agent_actions":{"view_html":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP","download_json":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP.json","view_paper":"https://pith.science/paper/DPJIUCVD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1709.04939&json=true","fetch_graph":"https://pith.science/api/pith-number/DPJIUCVDLDWSPS5ZWFNYK3EJGP/graph.json","fetch_events":"https://pith.science/api/pith-number/DPJIUCVDLDWSPS5ZWFNYK3EJGP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP/action/storage_attestation","attest_author":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP/action/author_attestation","sign_citation":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP/action/citation_signature","submit_replication":"https://pith.science/pith/DPJIUCVDLDWSPS5ZWFNYK3EJGP/action/replication_record"}},"created_at":"2026-05-18T00:35:08.768474+00:00","updated_at":"2026-05-18T00:35:08.768474+00:00"}