{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:7VOOL5BGUGKKV3N7YPRB6QCYBK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c0945fc747e29242ab8b837aa32f83db922cf5ba65eaa210fd9d916bdc031315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T17:30:59Z","title_canon_sha256":"738c593524351ec2fcbf1755bb6ce22093eb1c32225e33475c76f69d9480012a"},"schema_version":"1.0","source":{"id":"2606.06427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.06427","created_at":"2026-06-05T01:15:45Z"},{"alias_kind":"arxiv_version","alias_value":"2606.06427v1","created_at":"2026-06-05T01:15:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.06427","created_at":"2026-06-05T01:15:45Z"},{"alias_kind":"pith_short_12","alias_value":"7VOOL5BGUGKK","created_at":"2026-06-05T01:15:45Z"},{"alias_kind":"pith_short_16","alias_value":"7VOOL5BGUGKKV3N7","created_at":"2026-06-05T01:15:45Z"},{"alias_kind":"pith_short_8","alias_value":"7VOOL5BG","created_at":"2026-06-05T01:15:45Z"}],"graph_snapshots":[{"event_id":"sha256:78ee5252bade3fb3e7ddf4d9f7078035bc65138e31015b9798e08002844e9820","target":"graph","created_at":"2026-06-05T01:15:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.06427/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Yi-Hsuan Lin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T17:30:59Z","title":"Recovering stable kernels from exterior measurements"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06427","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:dc53331832b4a01dc2379967ec94ba0065d583005fb4cc38938c2a817547068d","target":"record","created_at":"2026-06-05T01:15:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"c0945fc747e29242ab8b837aa32f83db922cf5ba65eaa210fd9d916bdc031315","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2026-06-04T17:30:59Z","title_canon_sha256":"738c593524351ec2fcbf1755bb6ce22093eb1c32225e33475c76f69d9480012a"},"schema_version":"1.0","source":{"id":"2606.06427","kind":"arxiv","version":1}},"canonical_sha256":"fd5ce5f426a194aaedbfc3e21f40580aa73b08910c1ca4f088fc9e312bbff948","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd5ce5f426a194aaedbfc3e21f40580aa73b08910c1ca4f088fc9e312bbff948","first_computed_at":"2026-06-05T01:15:45.268515Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-05T01:15:45.268515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ttI9jGyMu6ncEKFnMycXk90PAI8Adspl18fVt+fWrgIEtua0AeCoUyLJm0P4ccWIEEO/PMAqoPk8BXr0FIeoBg==","signature_status":"signed_v1","signed_at":"2026-06-05T01:15:45.268905Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.06427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc53331832b4a01dc2379967ec94ba0065d583005fb4cc38938c2a817547068d","sha256:78ee5252bade3fb3e7ddf4d9f7078035bc65138e31015b9798e08002844e9820"],"state_sha256":"77a16506de0286dc6efbf393108ca7e5684952ebd9e52e116704118c6399046a"}