{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1998:W6WOOPKIH23UU6LBDTHGRKZW6Y","short_pith_number":"pith:W6WOOPKI","schema_version":"1.0","canonical_sha256":"b7ace73d483eb74a79611cce68ab36f601079e52131f4cff23c65c2d786de18d","source":{"kind":"arxiv","id":"math/9804148","version":1},"attestation_state":"computed","paper":{"title":"Approximation and support theorem for a two space-dimensional wave equation","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Annie Millet, Marta Sanz-Sol\\'e","submitted_at":"1998-04-03T00:00:00Z","abstract_excerpt":"We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, aproximation in the $L^p$ norm, for $p\\geq 1$ is also proved."},"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":"math/9804148","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.PR","submitted_at":"1998-04-03T00:00:00Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"66f9282d5186bf307ab78855a0499c718343ba515be855a62da768deca0df0cf","abstract_canon_sha256":"62c3334d3337abe8fb01a9dfd15b4bbd301e9bc20373a659c2810f8add021b23"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:34.076707Z","signature_b64":"erH1asLSIO1qnlfRE0Aomw5Z9kysFttJGXlUsA2bS/Uq9nU1dVn8hXi00DqEO1c1/SSJ45NMu3t4o3PbWNzABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b7ace73d483eb74a79611cce68ab36f601079e52131f4cff23c65c2d786de18d","last_reissued_at":"2026-05-18T01:05:34.076167Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:34.076167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Approximation and support theorem for a two space-dimensional wave equation","license":"","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Annie Millet, Marta Sanz-Sol\\'e","submitted_at":"1998-04-03T00:00:00Z","abstract_excerpt":"We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, aproximation in the $L^p$ norm, for $p\\geq 1$ is also proved."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9804148","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":"math/9804148","created_at":"2026-05-18T01:05:34.076263+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9804148v1","created_at":"2026-05-18T01:05:34.076263+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9804148","created_at":"2026-05-18T01:05:34.076263+00:00"},{"alias_kind":"pith_short_12","alias_value":"W6WOOPKIH23U","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_16","alias_value":"W6WOOPKIH23UU6LB","created_at":"2026-05-18T12:25:49.038998+00:00"},{"alias_kind":"pith_short_8","alias_value":"W6WOOPKI","created_at":"2026-05-18T12:25:49.038998+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/W6WOOPKIH23UU6LBDTHGRKZW6Y","json":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y.json","graph_json":"https://pith.science/api/pith-number/W6WOOPKIH23UU6LBDTHGRKZW6Y/graph.json","events_json":"https://pith.science/api/pith-number/W6WOOPKIH23UU6LBDTHGRKZW6Y/events.json","paper":"https://pith.science/paper/W6WOOPKI"},"agent_actions":{"view_html":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y","download_json":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y.json","view_paper":"https://pith.science/paper/W6WOOPKI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9804148&json=true","fetch_graph":"https://pith.science/api/pith-number/W6WOOPKIH23UU6LBDTHGRKZW6Y/graph.json","fetch_events":"https://pith.science/api/pith-number/W6WOOPKIH23UU6LBDTHGRKZW6Y/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y/action/timestamp_anchor","attest_storage":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y/action/storage_attestation","attest_author":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y/action/author_attestation","sign_citation":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y/action/citation_signature","submit_replication":"https://pith.science/pith/W6WOOPKIH23UU6LBDTHGRKZW6Y/action/replication_record"}},"created_at":"2026-05-18T01:05:34.076263+00:00","updated_at":"2026-05-18T01:05:34.076263+00:00"}