{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:342EYB62ZNLSYKR4U6Z42VH4LP","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":"7eba4005e6a9d879f1dbbd224abf1935fc796d6ce90b7fa78bf3becc42780728","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-17T17:41:34Z","title_canon_sha256":"ea2ff10ee65efef874581f64d30cf6ebb07372d51e91515a95dd09c8591c61ae"},"schema_version":"1.0","source":{"id":"2412.13118","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.13118","created_at":"2026-07-05T09:50:40Z"},{"alias_kind":"arxiv_version","alias_value":"2412.13118v1","created_at":"2026-07-05T09:50:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.13118","created_at":"2026-07-05T09:50:40Z"},{"alias_kind":"pith_short_12","alias_value":"342EYB62ZNLS","created_at":"2026-07-05T09:50:40Z"},{"alias_kind":"pith_short_16","alias_value":"342EYB62ZNLSYKR4","created_at":"2026-07-05T09:50:40Z"},{"alias_kind":"pith_short_8","alias_value":"342EYB62","created_at":"2026-07-05T09:50:40Z"}],"graph_snapshots":[{"event_id":"sha256:4d17c9c97066b42fd619c92ac47efe1474187b2501cab1e381a6c3d7329afd88","target":"graph","created_at":"2026-07-05T09:50:40Z","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/2412.13118/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We prove an entanglement principle for fractional Laplace operators on $\\mathbb R^n$ for $n\\geq 2$ as follows; if different fractional powers of the Laplace operator acting on several distinct functions on $\\mathbb R^n$, which vanish on some nonempty open set $O$, are known to be linearly dependent on $O$, then all the functions must be globally zero. This remarkable principle was recently discovered to be true for smooth functions on compact Riemannian manifolds without boundary \\cite{FKU24}. Our main result extends the principle to the noncompact Euclidean space stated for tempered distribut","authors_text":"Ali Feizmohammadi, Yi-Hsuan Lin","cross_cats":["math.CV"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-17T17:41:34Z","title":"Entanglement principle for the fractional Laplacian with applications to inverse problems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.13118","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":"sha256:8e8e3601f622df66c3df17aad29bd422f1b56fbbbc5e97c86e3e625d63d054c2","target":"record","created_at":"2026-07-05T09:50:40Z","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":"7eba4005e6a9d879f1dbbd224abf1935fc796d6ce90b7fa78bf3becc42780728","cross_cats_sorted":["math.CV"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2024-12-17T17:41:34Z","title_canon_sha256":"ea2ff10ee65efef874581f64d30cf6ebb07372d51e91515a95dd09c8591c61ae"},"schema_version":"1.0","source":{"id":"2412.13118","kind":"arxiv","version":1}},"canonical_sha256":"df344c07dacb572c2a3ca7b3cd54fc5bf862aca01e04f2589983374fd8b1a858","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"df344c07dacb572c2a3ca7b3cd54fc5bf862aca01e04f2589983374fd8b1a858","first_computed_at":"2026-07-05T09:50:40.484760Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:50:40.484760Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cZtU5wvbRVdFqg58RHv47KNZ0wiKHuInJsfOcXt6UkGUoCF9O9DYIPgq6pD4S0WoZpDZPk0aVv9DFBKwJcFlDg==","signature_status":"signed_v1","signed_at":"2026-07-05T09:50:40.485244Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.13118","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8e8e3601f622df66c3df17aad29bd422f1b56fbbbc5e97c86e3e625d63d054c2","sha256:4d17c9c97066b42fd619c92ac47efe1474187b2501cab1e381a6c3d7329afd88"],"state_sha256":"d284dcd8391f1fd464623c6183e5f801db84582f06c770d6878b21f243e304bb"}