{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:CDBBOGBMGCE7B65AVVHKRFXFW6","short_pith_number":"pith:CDBBOGBM","schema_version":"1.0","canonical_sha256":"10c217182c3089f0fba0ad4ea896e5b792c526712dd8275eb8c0d59f6ce15718","source":{"kind":"arxiv","id":"1707.08415","version":1},"attestation_state":"computed","paper":{"title":"Wave equation with a coloured stable noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Georgiy Shevchenko, Larysa Pryhara","submitted_at":"2017-07-26T12:57:54Z","abstract_excerpt":"We define a random measure generated by a real anisotropic harmonizable fractional stable field $Z^H$ with stability parameter $\\alpha\\in(1,2)$ and Hurst index $H\\in(1/2,1)$ and prove that the measure is $\\sigma$-additive in probability. An integral with respect to this measure is constructed, which enables us to consider a wave equation in $\\mathbb R^3$ with a random source generated by $Z^H$. We show that the solution to this equation, given by Kirchhoff's formula, has a modification, which is H\\\"older continuous of any order up to $(3H-1)\\wedge 1$. In the case where $H\\in(2/3,1)$, we show f"},"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":"1707.08415","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-07-26T12:57:54Z","cross_cats_sorted":[],"title_canon_sha256":"82c267f7304573123e510d5db8f5b800cb980318569cd7d4a46ecda3012ba315","abstract_canon_sha256":"2c1ed8e8366ebfc66758a9e50e437d83355b9c014cabe91e2590d93e8f07f963"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:24.302664Z","signature_b64":"A04K34Ecrchot7K3GzLX4mMxC7slOJvTrcSLmDSNqBXv+y2mFcCsnO11QRUs+UVrbIM97EW+oNKW1seozP3iAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10c217182c3089f0fba0ad4ea896e5b792c526712dd8275eb8c0d59f6ce15718","last_reissued_at":"2026-05-18T00:39:24.302061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:24.302061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Wave equation with a coloured stable noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Georgiy Shevchenko, Larysa Pryhara","submitted_at":"2017-07-26T12:57:54Z","abstract_excerpt":"We define a random measure generated by a real anisotropic harmonizable fractional stable field $Z^H$ with stability parameter $\\alpha\\in(1,2)$ and Hurst index $H\\in(1/2,1)$ and prove that the measure is $\\sigma$-additive in probability. An integral with respect to this measure is constructed, which enables us to consider a wave equation in $\\mathbb R^3$ with a random source generated by $Z^H$. We show that the solution to this equation, given by Kirchhoff's formula, has a modification, which is H\\\"older continuous of any order up to $(3H-1)\\wedge 1$. In the case where $H\\in(2/3,1)$, we show f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.08415","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":"1707.08415","created_at":"2026-05-18T00:39:24.302145+00:00"},{"alias_kind":"arxiv_version","alias_value":"1707.08415v1","created_at":"2026-05-18T00:39:24.302145+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1707.08415","created_at":"2026-05-18T00:39:24.302145+00:00"},{"alias_kind":"pith_short_12","alias_value":"CDBBOGBMGCE7","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_16","alias_value":"CDBBOGBMGCE7B65A","created_at":"2026-05-18T12:31:10.602751+00:00"},{"alias_kind":"pith_short_8","alias_value":"CDBBOGBM","created_at":"2026-05-18T12:31:10.602751+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/CDBBOGBMGCE7B65AVVHKRFXFW6","json":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6.json","graph_json":"https://pith.science/api/pith-number/CDBBOGBMGCE7B65AVVHKRFXFW6/graph.json","events_json":"https://pith.science/api/pith-number/CDBBOGBMGCE7B65AVVHKRFXFW6/events.json","paper":"https://pith.science/paper/CDBBOGBM"},"agent_actions":{"view_html":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6","download_json":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6.json","view_paper":"https://pith.science/paper/CDBBOGBM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1707.08415&json=true","fetch_graph":"https://pith.science/api/pith-number/CDBBOGBMGCE7B65AVVHKRFXFW6/graph.json","fetch_events":"https://pith.science/api/pith-number/CDBBOGBMGCE7B65AVVHKRFXFW6/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6/action/storage_attestation","attest_author":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6/action/author_attestation","sign_citation":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6/action/citation_signature","submit_replication":"https://pith.science/pith/CDBBOGBMGCE7B65AVVHKRFXFW6/action/replication_record"}},"created_at":"2026-05-18T00:39:24.302145+00:00","updated_at":"2026-05-18T00:39:24.302145+00:00"}