{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OLYSDWXCOQ5IMPRQWNKQIYRIBF","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":"073832d4187d4d1756d1c3c3fc625cf09e302f02a82dbe09d38c7695e393545a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-21T20:02:54Z","title_canon_sha256":"9ecf55e6e91baa79cc9800ffc5c5557cb4d5590666a2cca807e822c4d647a44f"},"schema_version":"1.0","source":{"id":"1103.4136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.4136","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"arxiv_version","alias_value":"1103.4136v2","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4136","created_at":"2026-05-18T04:08:34Z"},{"alias_kind":"pith_short_12","alias_value":"OLYSDWXCOQ5I","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OLYSDWXCOQ5IMPRQ","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OLYSDWXC","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:c0848b3ed310368eda7870d3f752ad59448b2b255043d67f37ca796e22e21d79","target":"graph","created_at":"2026-05-18T04:08:34Z","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 show precompactness results for solutions to parabolic fourth order geometric evolution equations. As part of the proof we obtain smoothing estimates for these flows in the presence of a curvature bound, an improvement on prior results which also require a Sobolev constant bound. As consequences of these results we show that for any solution with a finite time singularity, the $L^{\\infty}$ norm of the curvature must go to infinity. Furthermore, we characterize the behavior at infinity of solutions with bounded curvature.","authors_text":"Jeffrey Streets","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-21T20:02:54Z","title":"The long time behavior of fourth-order curvature flows"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4136","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":"sha256:3dcd533f064d68107fcff45390d84a0c6c9a4468941df8e08583be9cb1c3a012","target":"record","created_at":"2026-05-18T04:08:34Z","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":"073832d4187d4d1756d1c3c3fc625cf09e302f02a82dbe09d38c7695e393545a","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-03-21T20:02:54Z","title_canon_sha256":"9ecf55e6e91baa79cc9800ffc5c5557cb4d5590666a2cca807e822c4d647a44f"},"schema_version":"1.0","source":{"id":"1103.4136","kind":"arxiv","version":2}},"canonical_sha256":"72f121dae2743a863e30b355046228096e8ebd82380d98402d62abe34f22daf0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72f121dae2743a863e30b355046228096e8ebd82380d98402d62abe34f22daf0","first_computed_at":"2026-05-18T04:08:34.743602Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:08:34.743602Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"68MHIi49lt8459SK/+/HKHcrK7Nn7gkuAwglN6SBpXV5AaOVtNGj358ZnvapqF9YT6I91y21/hp88BkBc2S0Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:08:34.744244Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.4136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3dcd533f064d68107fcff45390d84a0c6c9a4468941df8e08583be9cb1c3a012","sha256:c0848b3ed310368eda7870d3f752ad59448b2b255043d67f37ca796e22e21d79"],"state_sha256":"e878f10e59d0af4c7bc12a18f99d51aba66c57b7a6c37772d1df712b3fffdac5"}