{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HFIRQJOAOQXM2EST55THQCSL43","short_pith_number":"pith:HFIRQJOA","schema_version":"1.0","canonical_sha256":"39511825c0742ecd1253ef66780a4be6c5fc7d6bd611c3f45762770ea91b9179","source":{"kind":"arxiv","id":"1503.01560","version":1},"attestation_state":"computed","paper":{"title":"Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Tataru, Sung-Jin Oh","submitted_at":"2015-03-05T07:15:45Z","abstract_excerpt":"This paper is the first part of a trilogy dedicated to a proof of global well-posedness and scattering of the (4+1)-dimensional mass-less Maxwell-Klein-Gordon equation (MKG) for any finite energy initial data. The main result of the present paper is a large energy local well-posedness theorem for MKG in the global Coulomb gauge, where the lifespan is bounded from below by the energy concentration scale of the data. Hence the proof of global well-posedness is reduced to establishing non-concentration of energy. To deal with non-local features of MKG we develop initial data excision and gluing t"},"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":"1503.01560","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2015-03-05T07:15:45Z","cross_cats_sorted":[],"title_canon_sha256":"c66a1e6f6cf3be1ce24f6b9751e23eb2823ca2b9962de980701d5fa7a76618c1","abstract_canon_sha256":"c2513fd27e5aea5cd61c8d1e23f9ba88fee08afdedf9495384063cb3b18a5a26"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:33.359305Z","signature_b64":"bQ4kFH/Bu0GYN38nNgvyFh3uJjmEkIYlbKfYYFgiT6yOLm8+UG5Y/4SuYhROTJB8+uquexH5CQzcwyoShWnHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39511825c0742ecd1253ef66780a4be6c5fc7d6bd611c3f45762770ea91b9179","last_reissued_at":"2026-05-18T02:25:33.358914Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:33.358914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Daniel Tataru, Sung-Jin Oh","submitted_at":"2015-03-05T07:15:45Z","abstract_excerpt":"This paper is the first part of a trilogy dedicated to a proof of global well-posedness and scattering of the (4+1)-dimensional mass-less Maxwell-Klein-Gordon equation (MKG) for any finite energy initial data. The main result of the present paper is a large energy local well-posedness theorem for MKG in the global Coulomb gauge, where the lifespan is bounded from below by the energy concentration scale of the data. Hence the proof of global well-posedness is reduced to establishing non-concentration of energy. To deal with non-local features of MKG we develop initial data excision and gluing t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.01560","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.01560","created_at":"2026-05-18T02:25:33.358974+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.01560v1","created_at":"2026-05-18T02:25:33.358974+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.01560","created_at":"2026-05-18T02:25:33.358974+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFIRQJOAOQXM","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFIRQJOAOQXM2EST","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFIRQJOA","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/HFIRQJOAOQXM2EST55THQCSL43","json":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43.json","graph_json":"https://pith.science/api/pith-number/HFIRQJOAOQXM2EST55THQCSL43/graph.json","events_json":"https://pith.science/api/pith-number/HFIRQJOAOQXM2EST55THQCSL43/events.json","paper":"https://pith.science/paper/HFIRQJOA"},"agent_actions":{"view_html":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43","download_json":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43.json","view_paper":"https://pith.science/paper/HFIRQJOA","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.01560&json=true","fetch_graph":"https://pith.science/api/pith-number/HFIRQJOAOQXM2EST55THQCSL43/graph.json","fetch_events":"https://pith.science/api/pith-number/HFIRQJOAOQXM2EST55THQCSL43/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43/action/storage_attestation","attest_author":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43/action/author_attestation","sign_citation":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43/action/citation_signature","submit_replication":"https://pith.science/pith/HFIRQJOAOQXM2EST55THQCSL43/action/replication_record"}},"created_at":"2026-05-18T02:25:33.358974+00:00","updated_at":"2026-05-18T02:25:33.358974+00:00"}