{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ACJCXLO6ZDRPAQQN6EKFVYZ5D5","short_pith_number":"pith:ACJCXLO6","schema_version":"1.0","canonical_sha256":"00922baddec8e2f0420df1145ae33d1f5e087deb105e726465f0ee922bca12b5","source":{"kind":"arxiv","id":"1308.2139","version":2},"attestation_state":"computed","paper":{"title":"Fractional Klein-Gordon equations and related stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Federico Polito, Roberto Garra","submitted_at":"2013-08-09T14:36:10Z","abstract_excerpt":"This paper presents finite-velocity random motions driven by fractional Klein-Gordon equations of order $\\alpha \\in (0,1]$. A key tool in the analysis is played by the McBride's theory which converts fractional hyper-Bessel operators into Erdelyi-Kober integral operators. Special attention is payed to the fractional telegraph process whose space-dependent distribution solves a non-homogeneous fractional Klein-Gordon equation. The distribution of the fractional telegraph process for $\\alpha = 1$ coincides with that of the classical telegraph process and its driving equation converts into the ho"},"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":"1308.2139","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-09T14:36:10Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"a4db131fcb1e1c9c6d3b65259f12ad04941e68d704c7055ef55c74dcf49d265f","abstract_canon_sha256":"34ae1510b429f25a54bd21bdad54e49e2d72c2a19b71d9fdfdf1fe2050e4d4dc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:48:46.863929Z","signature_b64":"t9RF6PJimVUZbw/4akPIg5X2QmB1X4m9UAJPjP/CWIeuiAbQVnH3uyiW7/VUe07LLRmHxuLRIVcqGRO+pOa8AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"00922baddec8e2f0420df1145ae33d1f5e087deb105e726465f0ee922bca12b5","last_reissued_at":"2026-05-18T02:48:46.863356Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:48:46.863356Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Fractional Klein-Gordon equations and related stochastic processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Enzo Orsingher, Federico Polito, Roberto Garra","submitted_at":"2013-08-09T14:36:10Z","abstract_excerpt":"This paper presents finite-velocity random motions driven by fractional Klein-Gordon equations of order $\\alpha \\in (0,1]$. A key tool in the analysis is played by the McBride's theory which converts fractional hyper-Bessel operators into Erdelyi-Kober integral operators. Special attention is payed to the fractional telegraph process whose space-dependent distribution solves a non-homogeneous fractional Klein-Gordon equation. The distribution of the fractional telegraph process for $\\alpha = 1$ coincides with that of the classical telegraph process and its driving equation converts into the ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2139","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":"1308.2139","created_at":"2026-05-18T02:48:46.863449+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.2139v2","created_at":"2026-05-18T02:48:46.863449+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.2139","created_at":"2026-05-18T02:48:46.863449+00:00"},{"alias_kind":"pith_short_12","alias_value":"ACJCXLO6ZDRP","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"ACJCXLO6ZDRPAQQN","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"ACJCXLO6","created_at":"2026-05-18T12:27:38.830355+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/ACJCXLO6ZDRPAQQN6EKFVYZ5D5","json":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5.json","graph_json":"https://pith.science/api/pith-number/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/graph.json","events_json":"https://pith.science/api/pith-number/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/events.json","paper":"https://pith.science/paper/ACJCXLO6"},"agent_actions":{"view_html":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5","download_json":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5.json","view_paper":"https://pith.science/paper/ACJCXLO6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.2139&json=true","fetch_graph":"https://pith.science/api/pith-number/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/graph.json","fetch_events":"https://pith.science/api/pith-number/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/action/storage_attestation","attest_author":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/action/author_attestation","sign_citation":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/action/citation_signature","submit_replication":"https://pith.science/pith/ACJCXLO6ZDRPAQQN6EKFVYZ5D5/action/replication_record"}},"created_at":"2026-05-18T02:48:46.863449+00:00","updated_at":"2026-05-18T02:48:46.863449+00:00"}