{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:F5B5XZYRAT7YUJN4SXPKJHKYYF","short_pith_number":"pith:F5B5XZYR","canonical_record":{"source":{"id":"1805.06616","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-05-17T06:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"20d316a4b2f0dd683e196e84282aa289de0f46fe95f1f8fde75a212576a35563","abstract_canon_sha256":"64f8e113e26d423d01166b7702ef6be5bc26b4ee51c03eb315be7297f84aa98f"},"schema_version":"1.0"},"canonical_sha256":"2f43dbe71104ff8a25bc95dea49d58c165127fdecf849256e7f20e82a23ce0dd","source":{"kind":"arxiv","id":"1805.06616","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06616","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06616v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06616","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"F5B5XZYRAT7Y","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F5B5XZYRAT7YUJN4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F5B5XZYR","created_at":"2026-05-18T12:32:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:F5B5XZYRAT7YUJN4SXPKJHKYYF","target":"record","payload":{"canonical_record":{"source":{"id":"1805.06616","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-05-17T06:41:18Z","cross_cats_sorted":[],"title_canon_sha256":"20d316a4b2f0dd683e196e84282aa289de0f46fe95f1f8fde75a212576a35563","abstract_canon_sha256":"64f8e113e26d423d01166b7702ef6be5bc26b4ee51c03eb315be7297f84aa98f"},"schema_version":"1.0"},"canonical_sha256":"2f43dbe71104ff8a25bc95dea49d58c165127fdecf849256e7f20e82a23ce0dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:15:43.902152Z","signature_b64":"s1RTedC6rOZJbntv0ACEUaXQDafn1pmoEI46e15jQOonJNw+91v1MED0PApqRdvY9Ly7Or1KAE3PkntSdHn1Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f43dbe71104ff8a25bc95dea49d58c165127fdecf849256e7f20e82a23ce0dd","last_reissued_at":"2026-05-18T00:15:43.901614Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:15:43.901614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.06616","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":"2026-05-18T00:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"og/lkO1nN0prvwtFyS2OzXiLbgUM+HTxTrQrR/GRddefc1Xq1jOot1npIBxHRvCtq0Z8cD9NqmnZR9Ng8WeoCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:36:09.582603Z"},"content_sha256":"bd38e1fba3d38400aca053f00aa2fbf75498f109750dae5b9a5178a5f987e765","schema_version":"1.0","event_id":"sha256:bd38e1fba3d38400aca053f00aa2fbf75498f109750dae5b9a5178a5f987e765"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:F5B5XZYRAT7YUJN4SXPKJHKYYF","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of type I blowup solutions for a higher order semilinear parabolic equation","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hatem Zaag, Tej-Eddine Ghoul, Van Tien Nguyen","submitted_at":"2018-05-17T06:41:18Z","abstract_excerpt":"We consider the higher-order semilinear parabolic equation $$ \\partial_t u = -(-\\Delta)^{m} u + u|u|^{p-1}, $$ in the whole space $\\mathbb{R}^N$, where $p > 1$ and $m \\geq 1$ is an odd integer. We exhibit type I non self-similar blowup solutions for this equation and obtain a sharp description of its asymptotic behavior. The method of construction relies on the spectral analysis of a non self-adjoint linearized operator in an appropriate scaled variables setting. In view of known spectral and sectorial properties of the linearized operator obtained by [Galaktionov, rspa2011], we revisit the te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06616","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:15:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FIolsteS3gs8F9joaQjxYibVOQxREpfUpyAxUHjN5c23aT2XT6uqEfIcC6AW8vLskcMDoxV/4Riqwv0jHaBmAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T04:36:09.582941Z"},"content_sha256":"0baa0f5eb118719b736c2edd3ca3aac07777a27b0867290bf9fee10c4b50fbf3","schema_version":"1.0","event_id":"sha256:0baa0f5eb118719b736c2edd3ca3aac07777a27b0867290bf9fee10c4b50fbf3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF/bundle.json","state_url":"https://pith.science/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF/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":"2026-06-24T04:36:09Z","links":{"resolver":"https://pith.science/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF","bundle":"https://pith.science/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF/bundle.json","state":"https://pith.science/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F5B5XZYRAT7YUJN4SXPKJHKYYF/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:F5B5XZYRAT7YUJN4SXPKJHKYYF","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":"64f8e113e26d423d01166b7702ef6be5bc26b4ee51c03eb315be7297f84aa98f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-05-17T06:41:18Z","title_canon_sha256":"20d316a4b2f0dd683e196e84282aa289de0f46fe95f1f8fde75a212576a35563"},"schema_version":"1.0","source":{"id":"1805.06616","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.06616","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"arxiv_version","alias_value":"1805.06616v1","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.06616","created_at":"2026-05-18T00:15:43Z"},{"alias_kind":"pith_short_12","alias_value":"F5B5XZYRAT7Y","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_16","alias_value":"F5B5XZYRAT7YUJN4","created_at":"2026-05-18T12:32:22Z"},{"alias_kind":"pith_short_8","alias_value":"F5B5XZYR","created_at":"2026-05-18T12:32:22Z"}],"graph_snapshots":[{"event_id":"sha256:0baa0f5eb118719b736c2edd3ca3aac07777a27b0867290bf9fee10c4b50fbf3","target":"graph","created_at":"2026-05-18T00:15:43Z","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 consider the higher-order semilinear parabolic equation $$ \\partial_t u = -(-\\Delta)^{m} u + u|u|^{p-1}, $$ in the whole space $\\mathbb{R}^N$, where $p > 1$ and $m \\geq 1$ is an odd integer. We exhibit type I non self-similar blowup solutions for this equation and obtain a sharp description of its asymptotic behavior. The method of construction relies on the spectral analysis of a non self-adjoint linearized operator in an appropriate scaled variables setting. In view of known spectral and sectorial properties of the linearized operator obtained by [Galaktionov, rspa2011], we revisit the te","authors_text":"Hatem Zaag, Tej-Eddine Ghoul, Van Tien Nguyen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-05-17T06:41:18Z","title":"Construction of type I blowup solutions for a higher order semilinear parabolic equation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06616","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:bd38e1fba3d38400aca053f00aa2fbf75498f109750dae5b9a5178a5f987e765","target":"record","created_at":"2026-05-18T00:15:43Z","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":"64f8e113e26d423d01166b7702ef6be5bc26b4ee51c03eb315be7297f84aa98f","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AP","submitted_at":"2018-05-17T06:41:18Z","title_canon_sha256":"20d316a4b2f0dd683e196e84282aa289de0f46fe95f1f8fde75a212576a35563"},"schema_version":"1.0","source":{"id":"1805.06616","kind":"arxiv","version":1}},"canonical_sha256":"2f43dbe71104ff8a25bc95dea49d58c165127fdecf849256e7f20e82a23ce0dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2f43dbe71104ff8a25bc95dea49d58c165127fdecf849256e7f20e82a23ce0dd","first_computed_at":"2026-05-18T00:15:43.901614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:43.901614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s1RTedC6rOZJbntv0ACEUaXQDafn1pmoEI46e15jQOonJNw+91v1MED0PApqRdvY9Ly7Or1KAE3PkntSdHn1Ag==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:43.902152Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.06616","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd38e1fba3d38400aca053f00aa2fbf75498f109750dae5b9a5178a5f987e765","sha256:0baa0f5eb118719b736c2edd3ca3aac07777a27b0867290bf9fee10c4b50fbf3"],"state_sha256":"943fe14c9ddd0f6d2ae9bd79a5f1ad73bd4810f7c784a3e2ef378cd0d9be9204"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"96VZw5S/6hLu72kPGXhcCYbWjho6Gj4WqIDu5GJjNnm39ks7ZYOBtQfk280kz8wC36bSCc0UnZm8WMu0iZ6uBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T04:36:09.584773Z","bundle_sha256":"fbc890d92385e0a9d4c1cd43da4fdcb5fbb84fb4f62941a5d124ec84c2148f88"}}