{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:CGC2Q4MKKX6X5TKVNVHAVGT6HM","short_pith_number":"pith:CGC2Q4MK","schema_version":"1.0","canonical_sha256":"1185a8718a55fd7ecd556d4e0a9a7e3b0acf5fe7cbd8649a324d7b9b5239ee2f","source":{"kind":"arxiv","id":"1905.03343","version":1},"attestation_state":"computed","paper":{"title":"An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fernando Olivar-Romero, Oscar Rosas-Ortiz","submitted_at":"2019-05-08T21:05:37Z","abstract_excerpt":"We solve the Cauchy problem defined by the fractional partial differential equation $[\\partial_{tt}-\\kappa\\mathbb{D}]u=0$, with $\\mathbb{D}$ the pseudo-differential Riesz operator of first order, and the initial conditions $u(x,0)=\\mu(\\sqrt{\\pi}x_0)^{-1}e^{-(x/x_0)^2}$, $u_t(x,0)=0$. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse $u(x,0)$ by the Dirac delta distribution $\\varphi(x)=\\mu\\delta(x)$ is obtained as corollary."},"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":"1905.03343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-05-08T21:05:37Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"bd7ce626aa9337e5942a9a4c2ad50246d87f3dff0501171742d68eba54f78e21","abstract_canon_sha256":"e9688a9474c93953a2ff83cb86d142508a3e4d9049f03c913f2f787e4659ee79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:38.800737Z","signature_b64":"F83/qNHzJRfCN34EA44oepoRoKhMmJk1zlYjcDNcBiTCakHAqE62dHFL94pY/XSsuE1mIPiSpWi0Jgmau+L2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1185a8718a55fd7ecd556d4e0a9a7e3b0acf5fe7cbd8649a324d7b9b5239ee2f","last_reissued_at":"2026-05-17T23:40:38.800221Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:38.800221Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Integro-Differential Equation of the Fractional Form: Cauchy Problem and Solution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fernando Olivar-Romero, Oscar Rosas-Ortiz","submitted_at":"2019-05-08T21:05:37Z","abstract_excerpt":"We solve the Cauchy problem defined by the fractional partial differential equation $[\\partial_{tt}-\\kappa\\mathbb{D}]u=0$, with $\\mathbb{D}$ the pseudo-differential Riesz operator of first order, and the initial conditions $u(x,0)=\\mu(\\sqrt{\\pi}x_0)^{-1}e^{-(x/x_0)^2}$, $u_t(x,0)=0$. The solution of the Cauchy problem resulting from the substitution of the Gaussian pulse $u(x,0)$ by the Dirac delta distribution $\\varphi(x)=\\mu\\delta(x)$ is obtained as corollary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.03343","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":"1905.03343","created_at":"2026-05-17T23:40:38.800310+00:00"},{"alias_kind":"arxiv_version","alias_value":"1905.03343v1","created_at":"2026-05-17T23:40:38.800310+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1905.03343","created_at":"2026-05-17T23:40:38.800310+00:00"},{"alias_kind":"pith_short_12","alias_value":"CGC2Q4MKKX6X","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_16","alias_value":"CGC2Q4MKKX6X5TKV","created_at":"2026-05-18T12:33:12.712433+00:00"},{"alias_kind":"pith_short_8","alias_value":"CGC2Q4MK","created_at":"2026-05-18T12:33:12.712433+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/CGC2Q4MKKX6X5TKVNVHAVGT6HM","json":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM.json","graph_json":"https://pith.science/api/pith-number/CGC2Q4MKKX6X5TKVNVHAVGT6HM/graph.json","events_json":"https://pith.science/api/pith-number/CGC2Q4MKKX6X5TKVNVHAVGT6HM/events.json","paper":"https://pith.science/paper/CGC2Q4MK"},"agent_actions":{"view_html":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM","download_json":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM.json","view_paper":"https://pith.science/paper/CGC2Q4MK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1905.03343&json=true","fetch_graph":"https://pith.science/api/pith-number/CGC2Q4MKKX6X5TKVNVHAVGT6HM/graph.json","fetch_events":"https://pith.science/api/pith-number/CGC2Q4MKKX6X5TKVNVHAVGT6HM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM/action/storage_attestation","attest_author":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM/action/author_attestation","sign_citation":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM/action/citation_signature","submit_replication":"https://pith.science/pith/CGC2Q4MKKX6X5TKVNVHAVGT6HM/action/replication_record"}},"created_at":"2026-05-17T23:40:38.800310+00:00","updated_at":"2026-05-17T23:40:38.800310+00:00"}