{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:LCQZ4RKIB7SDU43B5SKIPAAXHC","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":"91d57624e78e65e8585b84dec16e1e930049d7d1f7e7578e9a0a017a2204c406","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-24T05:31:58Z","title_canon_sha256":"31c5a23ffc21205d9cde30da61f46d262949bc13af40a7ec96a0a4b19d371b29"},"schema_version":"1.0","source":{"id":"1207.5591","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.5591","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"arxiv_version","alias_value":"1207.5591v1","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.5591","created_at":"2026-05-18T03:50:22Z"},{"alias_kind":"pith_short_12","alias_value":"LCQZ4RKIB7SD","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_16","alias_value":"LCQZ4RKIB7SDU43B","created_at":"2026-05-18T12:27:14Z"},{"alias_kind":"pith_short_8","alias_value":"LCQZ4RKI","created_at":"2026-05-18T12:27:14Z"}],"graph_snapshots":[{"event_id":"sha256:4d26682c64c395f1addad7cc7dffbdc82f06cac465a5a713fadac9d2df45ec43","target":"graph","created_at":"2026-05-18T03:50:22Z","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":"For 2 + 1 dimensional wave maps with $\\mathbb{S}^2$ as the target, we show that for all positive numbers $T_0 > 0$ and $E_0 > 0$, there exist Cauchy initial data with energy at least $E_0$, so that the solution's life-span is at least $[0,T_0]$. We assume neither symmetry nor closeness to harmonic maps.","authors_text":"Jinhua Wang, Pin Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-24T05:31:58Z","title":"Long time solutions for wave maps with large data"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5591","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":"sha256:5a7db2256b474ea6331f6ae76a64d34f50abd04ca7e1eda95cee163609330cb4","target":"record","created_at":"2026-05-18T03:50:22Z","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":"91d57624e78e65e8585b84dec16e1e930049d7d1f7e7578e9a0a017a2204c406","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2012-07-24T05:31:58Z","title_canon_sha256":"31c5a23ffc21205d9cde30da61f46d262949bc13af40a7ec96a0a4b19d371b29"},"schema_version":"1.0","source":{"id":"1207.5591","kind":"arxiv","version":1}},"canonical_sha256":"58a19e45480fe43a7361ec9487801738b7748cdf95ea765e127518c46c9cb080","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58a19e45480fe43a7361ec9487801738b7748cdf95ea765e127518c46c9cb080","first_computed_at":"2026-05-18T03:50:22.476783Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:22.476783Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HWhq8CGy17BXLvghSXj4S7qbDW2AZfVMNg1b+QNnOvy+sNCVe61t8DEbxlOu7els+RNpswi9n4rFXqrT+pJtBg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:22.477695Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.5591","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a7db2256b474ea6331f6ae76a64d34f50abd04ca7e1eda95cee163609330cb4","sha256:4d26682c64c395f1addad7cc7dffbdc82f06cac465a5a713fadac9d2df45ec43"],"state_sha256":"c972ffbd60a52416e3db2a676bb513f62df0e8af8695ad7cf04547e61bf37860"}