{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:XQQ6DJOKLTRS74R7OFBSYTKFW6","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":"ac5dcc1524864547f787ae7f8cd9b7507b912538a0c1cc99deee19c2fb319fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-17T09:59:45Z","title_canon_sha256":"005af0631a0b4c7f4c46fbcd66276bed41248a2a8fef531f2f4a8d5fb43cfd30"},"schema_version":"1.0","source":{"id":"1711.06476","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06476","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06476v1","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06476","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"XQQ6DJOKLTRS","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"XQQ6DJOKLTRS74R7","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"XQQ6DJOK","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:d252fcbb68c025d3967dedf94bb10b3799c08fab91edd1c5a46a79855ca2c451","target":"graph","created_at":"2026-05-18T00:30:20Z","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 study m-corotational solutions to the Harmonic Map Heat Flow from $\\mathbb{R}^2$ to $\\mathbb{S}^2$. We first consider maps of zero topological degree, with initial energy below the threshold given by twice the energy of the harmonic map solutions. For $m \\geq 2$, we establish the smooth global existence and decay of such solutions via the {\\it concentration-compactness} approach of Kenig-Merle, recovering classical results of Struwe by this alternate method. The proof relies on a profile decomposition, and the energy dissipation relation. We then consider maps of degree $m$ and initial ener","authors_text":"Dimitrios Roxanas, Stephen Gustafson","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-17T09:59:45Z","title":"Global solutions for the critical, higher-degree corotational harmonic map heat flow to $\\mathbb{S}^2$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06476","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":"sha256:47a19afb3dd334136ec3bd663af1677d1102f592d658d80bb3759712677b1b3b","target":"record","created_at":"2026-05-18T00:30:20Z","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":"ac5dcc1524864547f787ae7f8cd9b7507b912538a0c1cc99deee19c2fb319fc0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-17T09:59:45Z","title_canon_sha256":"005af0631a0b4c7f4c46fbcd66276bed41248a2a8fef531f2f4a8d5fb43cfd30"},"schema_version":"1.0","source":{"id":"1711.06476","kind":"arxiv","version":1}},"canonical_sha256":"bc21e1a5ca5ce32ff23f71432c4d45b781440870b73bbcc05f7c52b7015dd1ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bc21e1a5ca5ce32ff23f71432c4d45b781440870b73bbcc05f7c52b7015dd1ff","first_computed_at":"2026-05-18T00:30:20.993823Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:20.993823Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zDv+BpgrFQibXNej1kQgiyQ7dHmqnS7c4jVrugW5k5krvZXSWxupynQIg1xgRKTouT/RDkj93w1cPvucVH5DAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:20.994502Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06476","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47a19afb3dd334136ec3bd663af1677d1102f592d658d80bb3759712677b1b3b","sha256:d252fcbb68c025d3967dedf94bb10b3799c08fab91edd1c5a46a79855ca2c451"],"state_sha256":"f35b871302ba580a6007de719c95dab1549f44485b2020987733974bc8f86d56"}