{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:3SFQSKJBVIXSHPFVGYJ4FNTGOA","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":"1682896f30c4462538300eec3741c72ccb89cd3bfedd411d4642a2acd772476a","cross_cats_sorted":["math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-25T17:05:45Z","title_canon_sha256":"d0ca9dcbb74074a8c791ade2147ab76f951cb396ac1098e6b1e631de5a2ccaac"},"schema_version":"1.0","source":{"id":"1503.07458","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1503.07458","created_at":"2026-05-18T01:09:48Z"},{"alias_kind":"arxiv_version","alias_value":"1503.07458v1","created_at":"2026-05-18T01:09:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.07458","created_at":"2026-05-18T01:09:48Z"},{"alias_kind":"pith_short_12","alias_value":"3SFQSKJBVIXS","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"3SFQSKJBVIXSHPFV","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"3SFQSKJB","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:f8fe2cf4db9db01fc4fb30e3d8e8771c50d7c31e6b9973ec7b93283255a27578","target":"graph","created_at":"2026-05-18T01:09:48Z","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"},"paper":{"abstract_excerpt":"Fractional (L\\'{e}vy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral properties of the prototype example of the Cauchy operator $(-\\Delta )^{1/2}$ in the interval $D=(-1,1) \\subset R$, with a focus on functional shapes of lowest eigenfunctions and their fall-off at the boundaries of $D$. New high accuracy formulas are deduced for approximate eigenfunctions. We analyze how their shape reproduction fidelity is correlated with the evaluation finesse of the corresponding eigenvalues.","authors_text":"Mariusz \\.Zaba, Piotr Garbaczewski","cross_cats":["math.MP","math.SP","quant-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-25T17:05:45Z","title":"Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.07458","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:c9222d2af136c9b21d20f41fbd60eea37ce099535ea21e2fb1406c25a7b297c6","target":"record","created_at":"2026-05-18T01:09:48Z","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":"1682896f30c4462538300eec3741c72ccb89cd3bfedd411d4642a2acd772476a","cross_cats_sorted":["math.MP","math.SP","quant-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-03-25T17:05:45Z","title_canon_sha256":"d0ca9dcbb74074a8c791ade2147ab76f951cb396ac1098e6b1e631de5a2ccaac"},"schema_version":"1.0","source":{"id":"1503.07458","kind":"arxiv","version":1}},"canonical_sha256":"dc8b092921aa2f23bcb53613c2b6667009617e6cf63a78fbb20e2965bc430dff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc8b092921aa2f23bcb53613c2b6667009617e6cf63a78fbb20e2965bc430dff","first_computed_at":"2026-05-18T01:09:48.910364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:09:48.910364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gCh0P32JtZldHmgMe417V6ySxSD2Vxw3c3LzsFq419O6dNA+f+X5DxW5q4ms+Eq24Kdmcy1G7LqRlO1WDLKXAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:09:48.910936Z","signed_message":"canonical_sha256_bytes"},"source_id":"1503.07458","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c9222d2af136c9b21d20f41fbd60eea37ce099535ea21e2fb1406c25a7b297c6","sha256:f8fe2cf4db9db01fc4fb30e3d8e8771c50d7c31e6b9973ec7b93283255a27578"],"state_sha256":"22c44ad50d5ae5b6ed41deefe05a8e82850e7812dcece9174dd2d3c1bc3383f9"}