{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:GE2TB6HEW3MXJYQ53WXIGZAG7V","short_pith_number":"pith:GE2TB6HE","schema_version":"1.0","canonical_sha256":"313530f8e4b6d974e21dddae836406fd6dd3f0656941539b8460cc660c5998b7","source":{"kind":"arxiv","id":"1004.3986","version":2},"attestation_state":"computed","paper":{"title":"Transient anomalous sub-diffusion on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mark M. Meerschaert, Palaniappan Vellaisamy","submitted_at":"2010-04-22T19:00:04Z","abstract_excerpt":"This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and eigenfunction expansions in time and space, are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator."},"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":"1004.3986","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-04-22T19:00:04Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"f16b182fc654c921917a67dcc45e3ceff31427150e1c1ce885b7db2ae9c6cbd1","abstract_canon_sha256":"56bf18c73dd35163e5767219ec085142e11198c4b277a8121e6854c3d65cc0a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:38.513691Z","signature_b64":"zSZTosaO9QdVPELlnIJ1B41VlcN24kK0JEHZVFvX1wSIMlGqKncZiVG7bDtW9m4HGhxuy/BkD2r3J40Dt8QUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"313530f8e4b6d974e21dddae836406fd6dd3f0656941539b8460cc660c5998b7","last_reissued_at":"2026-05-18T00:56:38.513086Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:38.513086Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Transient anomalous sub-diffusion on bounded domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Erkan Nane, Mark M. Meerschaert, Palaniappan Vellaisamy","submitted_at":"2010-04-22T19:00:04Z","abstract_excerpt":"This paper develops strong solutions and stochastic solutions for the tempered fractional diffusion equation on bounded domains. First the eigenvalue problem for tempered fractional derivatives is solved. Then a separation of variables, and eigenfunction expansions in time and space, are used to write strong solutions. Finally, stochastic solutions are written in terms of an inverse subordinator."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.3986","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":"1004.3986","created_at":"2026-05-18T00:56:38.513158+00:00"},{"alias_kind":"arxiv_version","alias_value":"1004.3986v2","created_at":"2026-05-18T00:56:38.513158+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.3986","created_at":"2026-05-18T00:56:38.513158+00:00"},{"alias_kind":"pith_short_12","alias_value":"GE2TB6HEW3MX","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_16","alias_value":"GE2TB6HEW3MXJYQ5","created_at":"2026-05-18T12:26:07.630475+00:00"},{"alias_kind":"pith_short_8","alias_value":"GE2TB6HE","created_at":"2026-05-18T12:26:07.630475+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/GE2TB6HEW3MXJYQ53WXIGZAG7V","json":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V.json","graph_json":"https://pith.science/api/pith-number/GE2TB6HEW3MXJYQ53WXIGZAG7V/graph.json","events_json":"https://pith.science/api/pith-number/GE2TB6HEW3MXJYQ53WXIGZAG7V/events.json","paper":"https://pith.science/paper/GE2TB6HE"},"agent_actions":{"view_html":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V","download_json":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V.json","view_paper":"https://pith.science/paper/GE2TB6HE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1004.3986&json=true","fetch_graph":"https://pith.science/api/pith-number/GE2TB6HEW3MXJYQ53WXIGZAG7V/graph.json","fetch_events":"https://pith.science/api/pith-number/GE2TB6HEW3MXJYQ53WXIGZAG7V/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V/action/storage_attestation","attest_author":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V/action/author_attestation","sign_citation":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V/action/citation_signature","submit_replication":"https://pith.science/pith/GE2TB6HEW3MXJYQ53WXIGZAG7V/action/replication_record"}},"created_at":"2026-05-18T00:56:38.513158+00:00","updated_at":"2026-05-18T00:56:38.513158+00:00"}