{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:HFBXPH6GUPS2ROVNWMFW6C7LSP","short_pith_number":"pith:HFBXPH6G","schema_version":"1.0","canonical_sha256":"3943779fc6a3e5a8baadb30b6f0beb93fe089ce22add1faa70ecd28502d0db72","source":{"kind":"arxiv","id":"1609.05443","version":1},"attestation_state":"computed","paper":{"title":"Cauchy and signaling problems for the time-fractional diffusion-wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.CV","math.MP"],"primary_cat":"math.AP","authors_text":"Francesco Mainardi, Yuri Luchko","submitted_at":"2016-09-18T08:16:28Z","abstract_excerpt":"In this paper, some known and novel properties of the Cauchy and signaling problems for the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional derivative of order $\\beta,\\ 1 \\le \\beta \\le 2$ are investigated. In particular, their response to a localized disturbance of the initial data is studied. It is known that whereas the diffusion equation describes a process where the disturbance spreads infinitely fast, the propagation velocity of the disturbance is a constant for the wave equation. We show that the time-fractional diffusion-wave equation interpolates betw"},"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":"1609.05443","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2016-09-18T08:16:28Z","cross_cats_sorted":["cond-mat.stat-mech","math-ph","math.CV","math.MP"],"title_canon_sha256":"ec569059e6c217abb42f2a9013c0cde3db1fe90261144d42a15d70724f95a934","abstract_canon_sha256":"126392d24b433149544a60d1de4780d2881292ee91bcc1e8afefd575a9c5ed69"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:26.388162Z","signature_b64":"w268TedxuaOCrWk4oofLamRP17WbJO04XDegFtTPJL0p2uJ0btVYeo0fk7pG1VaB1bs5j9sOMve+Ez3aXZesAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3943779fc6a3e5a8baadb30b6f0beb93fe089ce22add1faa70ecd28502d0db72","last_reissued_at":"2026-05-18T01:04:26.387591Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:26.387591Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cauchy and signaling problems for the time-fractional diffusion-wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math-ph","math.CV","math.MP"],"primary_cat":"math.AP","authors_text":"Francesco Mainardi, Yuri Luchko","submitted_at":"2016-09-18T08:16:28Z","abstract_excerpt":"In this paper, some known and novel properties of the Cauchy and signaling problems for the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional derivative of order $\\beta,\\ 1 \\le \\beta \\le 2$ are investigated. In particular, their response to a localized disturbance of the initial data is studied. It is known that whereas the diffusion equation describes a process where the disturbance spreads infinitely fast, the propagation velocity of the disturbance is a constant for the wave equation. We show that the time-fractional diffusion-wave equation interpolates betw"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05443","kind":"arxiv","version":1},"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":"1609.05443","created_at":"2026-05-18T01:04:26.387672+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.05443v1","created_at":"2026-05-18T01:04:26.387672+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.05443","created_at":"2026-05-18T01:04:26.387672+00:00"},{"alias_kind":"pith_short_12","alias_value":"HFBXPH6GUPS2","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"HFBXPH6GUPS2ROVN","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"HFBXPH6G","created_at":"2026-05-18T12:30:19.053100+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/HFBXPH6GUPS2ROVNWMFW6C7LSP","json":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP.json","graph_json":"https://pith.science/api/pith-number/HFBXPH6GUPS2ROVNWMFW6C7LSP/graph.json","events_json":"https://pith.science/api/pith-number/HFBXPH6GUPS2ROVNWMFW6C7LSP/events.json","paper":"https://pith.science/paper/HFBXPH6G"},"agent_actions":{"view_html":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP","download_json":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP.json","view_paper":"https://pith.science/paper/HFBXPH6G","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.05443&json=true","fetch_graph":"https://pith.science/api/pith-number/HFBXPH6GUPS2ROVNWMFW6C7LSP/graph.json","fetch_events":"https://pith.science/api/pith-number/HFBXPH6GUPS2ROVNWMFW6C7LSP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP/action/storage_attestation","attest_author":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP/action/author_attestation","sign_citation":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP/action/citation_signature","submit_replication":"https://pith.science/pith/HFBXPH6GUPS2ROVNWMFW6C7LSP/action/replication_record"}},"created_at":"2026-05-18T01:04:26.387672+00:00","updated_at":"2026-05-18T01:04:26.387672+00:00"}