{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4QKDQ2DBEAWQA4IQQFDFNIQ2D4","short_pith_number":"pith:4QKDQ2DB","schema_version":"1.0","canonical_sha256":"e414386861202d007110814656a21a1f2e2b510fd6bfc5a043b281c8a56a7dba","source":{"kind":"arxiv","id":"1702.02488","version":2},"attestation_state":"computed","paper":{"title":"Local time of Levy random walks: a path integral approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Vaclav Zatloukal","submitted_at":"2017-02-08T16:01:35Z","abstract_excerpt":"Local time of a stochastic process quantifies the amount of time that sample trajectories $x(\\tau)$ spend in the vicinity of an arbitrary point $x$. For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on local times of Levy random walks (or Levy flights), which correspond to fractional diffusion equations."},"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":"1702.02488","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-02-08T16:01:35Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"d19809fbfa1acdd29e26d405c8c9135e141beb27fef3c7a08674565ad52ccb6e","abstract_canon_sha256":"0461bcf3b75c96ab0c7ca0a23f71ed9e4dfd6f4703872d526b0448f1d8675d43"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:26.798989Z","signature_b64":"NdhPrb59FMIiGx852QBQU7HGoL9yHo/3bnthFzjiGB4rvaIETpF1fDFf5Is2Zb+nDQSZyK9aQOzI24MODQ9GBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e414386861202d007110814656a21a1f2e2b510fd6bfc5a043b281c8a56a7dba","last_reissued_at":"2026-05-18T00:43:26.798282Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:26.798282Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Local time of Levy random walks: a path integral approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Vaclav Zatloukal","submitted_at":"2017-02-08T16:01:35Z","abstract_excerpt":"Local time of a stochastic process quantifies the amount of time that sample trajectories $x(\\tau)$ spend in the vicinity of an arbitrary point $x$. For a generic Hamiltonian, we employ the phase-space path-integral representation of random walk transition probabilities in order to quantify the properties of the local time. For time-independent systems, the resolvent of the Hamiltonian operator proves to be a central tool for this purpose. In particular, we focus on local times of Levy random walks (or Levy flights), which correspond to fractional diffusion equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02488","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1702.02488","created_at":"2026-05-18T00:43:26.798389+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.02488v2","created_at":"2026-05-18T00:43:26.798389+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.02488","created_at":"2026-05-18T00:43:26.798389+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QKDQ2DBEAWQ","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QKDQ2DBEAWQA4IQ","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QKDQ2DB","created_at":"2026-05-18T12:31:00.734936+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/4QKDQ2DBEAWQA4IQQFDFNIQ2D4","json":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4.json","graph_json":"https://pith.science/api/pith-number/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/graph.json","events_json":"https://pith.science/api/pith-number/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/events.json","paper":"https://pith.science/paper/4QKDQ2DB"},"agent_actions":{"view_html":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4","download_json":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4.json","view_paper":"https://pith.science/paper/4QKDQ2DB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.02488&json=true","fetch_graph":"https://pith.science/api/pith-number/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/graph.json","fetch_events":"https://pith.science/api/pith-number/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/action/storage_attestation","attest_author":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/action/author_attestation","sign_citation":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/action/citation_signature","submit_replication":"https://pith.science/pith/4QKDQ2DBEAWQA4IQQFDFNIQ2D4/action/replication_record"}},"created_at":"2026-05-18T00:43:26.798389+00:00","updated_at":"2026-05-18T00:43:26.798389+00:00"}