{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:TRZRLVB2J623E2KTQZF7BLHKJB","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":"c542fc2c2f7e9a7ae9b67806ea9251afc38465bab4ed7d0895d3f60d5a45830f","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-02T23:42:03Z","title_canon_sha256":"62e67760b5595e38d7bff19202ef4b96dc481fe8145e76b5f0b1297f5c668ec2"},"schema_version":"1.0","source":{"id":"1006.0524","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.0524","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"arxiv_version","alias_value":"1006.0524v4","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.0524","created_at":"2026-05-18T04:06:55Z"},{"alias_kind":"pith_short_12","alias_value":"TRZRLVB2J623","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_16","alias_value":"TRZRLVB2J623E2KT","created_at":"2026-05-18T12:26:15Z"},{"alias_kind":"pith_short_8","alias_value":"TRZRLVB2","created_at":"2026-05-18T12:26:15Z"}],"graph_snapshots":[{"event_id":"sha256:221bd15d9ef76dae1d291a9201fde1fe2a0fe82aeb98a615d6a18b06cdb2461e","target":"graph","created_at":"2026-05-18T04:06:55Z","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":"We study one-dimensional Levy processes with Levy-Khintchine exponent psi(xi^2), where psi is a complete Bernstein function. These processes are subordinate Brownian motions corresponding to subordinators, whose Levy measure has completely monotone density; or, equivalently, symmetric Levy processes whose Levy measure has completely monotone density on the positive half-line. Examples include symmetric stable processes and relativistic processes. The main result is a formula for the generalized eigenfunctions of transition operators of the process killed after exiting the half-line. A generali","authors_text":"Mateusz Kwasnicki","cross_cats":["math.SP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-02T23:42:03Z","title":"Spectral analysis of subordinate Brownian motions in half-line"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.0524","kind":"arxiv","version":4},"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":"sha256:127c12d5e1421f7f28b13965dde437b65aebb1d42b2f5483b67fc82f6a45c512","target":"record","created_at":"2026-05-18T04:06:55Z","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":"c542fc2c2f7e9a7ae9b67806ea9251afc38465bab4ed7d0895d3f60d5a45830f","cross_cats_sorted":["math.SP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-06-02T23:42:03Z","title_canon_sha256":"62e67760b5595e38d7bff19202ef4b96dc481fe8145e76b5f0b1297f5c668ec2"},"schema_version":"1.0","source":{"id":"1006.0524","kind":"arxiv","version":4}},"canonical_sha256":"9c7315d43a4fb5b26953864bf0acea4872b0237ac7271a89c344f898df6ec77a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9c7315d43a4fb5b26953864bf0acea4872b0237ac7271a89c344f898df6ec77a","first_computed_at":"2026-05-18T04:06:55.188184Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:55.188184Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vIbXQllmy7Ibn/jVQKU8ONQ8/8FVwKr9qDQFZ5UEhO96qnSDxQrSwciVUkwZG/+m/OKv8L5NKnv9Ef6dakk5Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:55.188769Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.0524","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:127c12d5e1421f7f28b13965dde437b65aebb1d42b2f5483b67fc82f6a45c512","sha256:221bd15d9ef76dae1d291a9201fde1fe2a0fe82aeb98a615d6a18b06cdb2461e"],"state_sha256":"2fdded6feec7d9c43c5e52fc52aa91b5549fa1154fa1f72ec80e21d779e7d166"}