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The assumed regularity for the data is almost optimal with respect to scaling as $r \\to 1$ . This closes the gap between what is known in the case $r=2$ , namely $s > \\frac{3}{4}$ , and the critical value $s_c = \\frac{1}{2}$ with respect to scaling."},"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":"1908.05651","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-08-15T17:48:04Z","cross_cats_sorted":[],"title_canon_sha256":"611f14e8f023221e534dba82d2e360a4cdac378424cfa16cbe00a0c50d0b419f","abstract_canon_sha256":"17c7beeae1b6928a74dff23d809135a6ce2d26a06aca7967033ecb17766e81e6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:18:26.820479Z","signature_b64":"dpEF0V0qpUcIHbJJrg19brhVd755zI+t0Xngg/Ul0CkRFDRmH0EXuN7GIEDRZo7hrfXPInmAG5OpV3IBPKr9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b73b0394c5e48f8bea7f0f840e48b95b38981afeee7271c7fe981197598bb482","last_reissued_at":"2026-07-05T00:18:26.820109Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:18:26.820109Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost optimal local well-posedness for the Maxwell-Klein-Gordon system with data in Fourier-Lebesgue spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Hartmut Pecher","submitted_at":"2019-08-15T17:48:04Z","abstract_excerpt":"We prove a low regularity local well-posedness result for the Maxwell-Klein-Gordon system in three space dimensions for data in Fourier - Lebesgue spaces $\\widehat{H}^{s,r}$ , where $\\|f\\|_{\\widehat{H}^{s,r}} = \\|\\langle \\xi \\rangle^s \\widehat{f}(\\xi)\\|_{\\widehat{L}^{r'}}$ , $\\frac{1}{r}+\\frac{1}{r'} = 1$ . The assumed regularity for the data is almost optimal with respect to scaling as $r \\to 1$ . 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