{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HUK2EFDOCPUTTYDOQJ6LLHKFBK","short_pith_number":"pith:HUK2EFDO","schema_version":"1.0","canonical_sha256":"3d15a2146e13e939e06e827cb59d450aafc327c5a9c1145764358dfc4c1d8e1c","source":{"kind":"arxiv","id":"1504.05051","version":2},"attestation_state":"computed","paper":{"title":"A class of large global solutions for the Wave--Map equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisabetta Chiodaroli, Joachim Krieger","submitted_at":"2015-04-20T13:30:34Z","abstract_excerpt":"In this paper we consider the equation for equivariant wave maps from $R^{3+1}$ to $S^3$ and we prove global in forward time existence of certain $C^\\infty$-smooth solutions which have infinite critical Sobolev norm $\\dot{H}^{\\frac{3}{2}}(R^3)\\times \\dot{H}^{\\frac{1}{2}}(R^3)$. Our construction provides solutions which can moreover satisfy the additional size condition $\\|u(0, \\cdot)\\|_{L^\\infty(|x|\\geq 1)}>M$ for arbitrarily chosen $M>0$. These solutions are also stable under suitable perturbations. Our method is based on a perturbative approach around suitably constructed approximate self--s"},"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":"1504.05051","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-04-20T13:30:34Z","cross_cats_sorted":[],"title_canon_sha256":"12af73ec649c321a2320d8783b337d15f5ee2ff354317b46e1945204a3f347c9","abstract_canon_sha256":"b7101ca14273fe6b6d7c55c9bce4f16485c1321338bf740e828bce29f8c80fae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:10:18.443191Z","signature_b64":"j+St4QyRjafejpe7YhlD8FKM64H6PDOzadE9OYC8/OFToH7em54T/qaTXNSH3Cft9InlzEc3Ne/39Hm/6s1bDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d15a2146e13e939e06e827cb59d450aafc327c5a9c1145764358dfc4c1d8e1c","last_reissued_at":"2026-05-18T01:10:18.442519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:10:18.442519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A class of large global solutions for the Wave--Map equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Elisabetta Chiodaroli, Joachim Krieger","submitted_at":"2015-04-20T13:30:34Z","abstract_excerpt":"In this paper we consider the equation for equivariant wave maps from $R^{3+1}$ to $S^3$ and we prove global in forward time existence of certain $C^\\infty$-smooth solutions which have infinite critical Sobolev norm $\\dot{H}^{\\frac{3}{2}}(R^3)\\times \\dot{H}^{\\frac{1}{2}}(R^3)$. Our construction provides solutions which can moreover satisfy the additional size condition $\\|u(0, \\cdot)\\|_{L^\\infty(|x|\\geq 1)}>M$ for arbitrarily chosen $M>0$. These solutions are also stable under suitable perturbations. Our method is based on a perturbative approach around suitably constructed approximate self--s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05051","kind":"arxiv","version":2},"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":"1504.05051","created_at":"2026-05-18T01:10:18.442620+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.05051v2","created_at":"2026-05-18T01:10:18.442620+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05051","created_at":"2026-05-18T01:10:18.442620+00:00"},{"alias_kind":"pith_short_12","alias_value":"HUK2EFDOCPUT","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HUK2EFDOCPUTTYDO","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HUK2EFDO","created_at":"2026-05-18T12:29:25.134429+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/HUK2EFDOCPUTTYDOQJ6LLHKFBK","json":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK.json","graph_json":"https://pith.science/api/pith-number/HUK2EFDOCPUTTYDOQJ6LLHKFBK/graph.json","events_json":"https://pith.science/api/pith-number/HUK2EFDOCPUTTYDOQJ6LLHKFBK/events.json","paper":"https://pith.science/paper/HUK2EFDO"},"agent_actions":{"view_html":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK","download_json":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK.json","view_paper":"https://pith.science/paper/HUK2EFDO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.05051&json=true","fetch_graph":"https://pith.science/api/pith-number/HUK2EFDOCPUTTYDOQJ6LLHKFBK/graph.json","fetch_events":"https://pith.science/api/pith-number/HUK2EFDOCPUTTYDOQJ6LLHKFBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK/action/storage_attestation","attest_author":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK/action/author_attestation","sign_citation":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK/action/citation_signature","submit_replication":"https://pith.science/pith/HUK2EFDOCPUTTYDOQJ6LLHKFBK/action/replication_record"}},"created_at":"2026-05-18T01:10:18.442620+00:00","updated_at":"2026-05-18T01:10:18.442620+00:00"}