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For a bounded open set $\\Omega\\subset\\mathbb R^n$, with $\\Omega_e=\\mathbb R^n\\setminus\\overline\\Omega$, we consider restricted exterior Dirichlet-to-Neumann maps $\\Lambda_a^{W_1,W_2}$, where exterior data are supported in $W_1\\Subset\\Omega_e$ and the nonlocal Neumann data are observed on $W"},"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":"2606.06427","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T17:30:59Z","cross_cats_sorted":[],"title_canon_sha256":"738c593524351ec2fcbf1755bb6ce22093eb1c32225e33475c76f69d9480012a","abstract_canon_sha256":"c0945fc747e29242ab8b837aa32f83db922cf5ba65eaa210fd9d916bdc031315"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-05T01:15:45.268905Z","signature_b64":"ttI9jGyMu6ncEKFnMycXk90PAI8Adspl18fVt+fWrgIEtua0AeCoUyLJm0P4ccWIEEO/PMAqoPk8BXr0FIeoBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fd5ce5f426a194aaedbfc3e21f40580aa73b08910c1ca4f088fc9e312bbff948","last_reissued_at":"2026-06-05T01:15:45.268515Z","signature_status":"signed_v1","first_computed_at":"2026-06-05T01:15:45.268515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Recovering stable kernels from exterior measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi-Hsuan Lin","submitted_at":"2026-06-04T17:30:59Z","abstract_excerpt":"We study an inverse problem for translation-invariant symmetric stable operators of the form\n  \\begin{equation*}\n  L_a u(x)=\\mathrm{P.V.}\\int_{\\mathbb R^n}(u(x)-u(y))\\frac{a((x-y)/|x-y|)}{|x-y|^{n+2s}}\\,dy,\n  \\quad 0<s<1,\n  \\end{equation*}\n  where the unknown is the even angular density $a$ on $\\mathbb Sn$. For a bounded open set $\\Omega\\subset\\mathbb R^n$, with $\\Omega_e=\\mathbb R^n\\setminus\\overline\\Omega$, we consider restricted exterior Dirichlet-to-Neumann maps $\\Lambda_a^{W_1,W_2}$, where exterior data are supported in $W_1\\Subset\\Omega_e$ and the nonlocal Neumann data are observed on $W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06427/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":"2606.06427","created_at":"2026-06-05T01:15:45.268579+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.06427v1","created_at":"2026-06-05T01:15:45.268579+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06427","created_at":"2026-06-05T01:15:45.268579+00:00"},{"alias_kind":"pith_short_12","alias_value":"7VOOL5BGUGKK","created_at":"2026-06-05T01:15:45.268579+00:00"},{"alias_kind":"pith_short_16","alias_value":"7VOOL5BGUGKKV3N7","created_at":"2026-06-05T01:15:45.268579+00:00"},{"alias_kind":"pith_short_8","alias_value":"7VOOL5BG","created_at":"2026-06-05T01:15:45.268579+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/7VOOL5BGUGKKV3N7YPRB6QCYBK","json":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK.json","graph_json":"https://pith.science/api/pith-number/7VOOL5BGUGKKV3N7YPRB6QCYBK/graph.json","events_json":"https://pith.science/api/pith-number/7VOOL5BGUGKKV3N7YPRB6QCYBK/events.json","paper":"https://pith.science/paper/7VOOL5BG"},"agent_actions":{"view_html":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK","download_json":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK.json","view_paper":"https://pith.science/paper/7VOOL5BG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.06427&json=true","fetch_graph":"https://pith.science/api/pith-number/7VOOL5BGUGKKV3N7YPRB6QCYBK/graph.json","fetch_events":"https://pith.science/api/pith-number/7VOOL5BGUGKKV3N7YPRB6QCYBK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK/action/storage_attestation","attest_author":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK/action/author_attestation","sign_citation":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK/action/citation_signature","submit_replication":"https://pith.science/pith/7VOOL5BGUGKKV3N7YPRB6QCYBK/action/replication_record"}},"created_at":"2026-06-05T01:15:45.268579+00:00","updated_at":"2026-06-05T01:15:45.268579+00:00"}