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We further show that the minimiser $u_\\infty$ satisfies the (fractional) PDE $$ (-\\Delta)^s u_\\infty=E_\\infty(u_\\infty)\\,\\mathrm{sgn}f_\\infty \\qquad\\mbox{in }\\Omega, $$ for some analytic function $f_\\infty\\in L^1(\\Omega)$ obtained as the restriction of an $s$"},"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":"2510.14476","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2025-10-16T09:20:37Z","cross_cats_sorted":[],"title_canon_sha256":"e31f721a453faf3d277d984795f6d484c576b6285a836f2e8c27c2987e0114a7","abstract_canon_sha256":"81d4f487419646efcbccb65f5af335c99a56a2348c06b4ad07783db3388136f8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T02:04:37.248691Z","signature_b64":"bvclGxrJoT5K5oYDELX/J64xSlJwQAQGsWJ2LjCpsMutS8Q+0v2IkTlAaVmX4W7zAMPrXNcd1sXSnA9PeINIAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7d236280a01062027ec319bd25cbb7c5982719a86ff2de4aa9c7dc954807d3d","last_reissued_at":"2026-05-22T02:04:37.247757Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T02:04:37.247757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An $L^\\infty$-variational problem involving the Fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Roger Moser, Simone Carano","submitted_at":"2025-10-16T09:20:37Z","abstract_excerpt":"For $s\\in(0,1)$ and an open bounded set $\\Omega\\subset\\mathbb R^n$, we prove existence and uniqueness of absolute minimisers of the supremal functional $$E_\\infty(u)=\\|(-\\Delta)^s u\\|_{L^\\infty(\\mathbb R^n)},$$ where $(-\\Delta)^s$ is the Fractional Laplacian of order $s$ and $u$ has prescribed Dirichlet data in the complement of $\\Omega$. We further show that the minimiser $u_\\infty$ satisfies the (fractional) PDE $$ (-\\Delta)^s u_\\infty=E_\\infty(u_\\infty)\\,\\mathrm{sgn}f_\\infty \\qquad\\mbox{in }\\Omega, $$ for some analytic function $f_\\infty\\in L^1(\\Omega)$ obtained as the restriction of an $s$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2510.14476","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2510.14476/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2510.14476","created_at":"2026-05-22T02:04:37.247886+00:00"},{"alias_kind":"arxiv_version","alias_value":"2510.14476v2","created_at":"2026-05-22T02:04:37.247886+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2510.14476","created_at":"2026-05-22T02:04:37.247886+00:00"},{"alias_kind":"pith_short_12","alias_value":"W7JDMKAKAEDC","created_at":"2026-05-22T02:04:37.247886+00:00"},{"alias_kind":"pith_short_16","alias_value":"W7JDMKAKAEDCAJ7M","created_at":"2026-05-22T02:04:37.247886+00:00"},{"alias_kind":"pith_short_8","alias_value":"W7JDMKAK","created_at":"2026-05-22T02:04:37.247886+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/W7JDMKAKAEDCAJ7MGGN5EXF3PR","json":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR.json","graph_json":"https://pith.science/api/pith-number/W7JDMKAKAEDCAJ7MGGN5EXF3PR/graph.json","events_json":"https://pith.science/api/pith-number/W7JDMKAKAEDCAJ7MGGN5EXF3PR/events.json","paper":"https://pith.science/paper/W7JDMKAK"},"agent_actions":{"view_html":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR","download_json":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR.json","view_paper":"https://pith.science/paper/W7JDMKAK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2510.14476&json=true","fetch_graph":"https://pith.science/api/pith-number/W7JDMKAKAEDCAJ7MGGN5EXF3PR/graph.json","fetch_events":"https://pith.science/api/pith-number/W7JDMKAKAEDCAJ7MGGN5EXF3PR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR/action/storage_attestation","attest_author":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR/action/author_attestation","sign_citation":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR/action/citation_signature","submit_replication":"https://pith.science/pith/W7JDMKAKAEDCAJ7MGGN5EXF3PR/action/replication_record"}},"created_at":"2026-05-22T02:04:37.247886+00:00","updated_at":"2026-05-22T02:04:37.247886+00:00"}