{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:IV7WK76DBHDNE7GEJSGUNDP3QN","short_pith_number":"pith:IV7WK76D","schema_version":"1.0","canonical_sha256":"457f657fc309c6d27cc44c8d468dfb8379fe2d7a0791271bbbb3b602e98dda55","source":{"kind":"arxiv","id":"1303.7346","version":1},"attestation_state":"computed","paper":{"title":"Sharp extensions for convoluted solutions of wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pedro J. Miana, Ver\\'onica Poblete","submitted_at":"2013-03-29T10:06:44Z","abstract_excerpt":"In this paper we give sharp extensions of convoluted solutions of wave equations in abstract Banach spaces. The main technique is to use the algebraic structure, for convolution products $\\ast$ and $\\ast_c$, of these solutions which are defined by a version of the Duhamel's formula. We define algebra homomorphisms, for the convolution product $\\ast_c$, from a certain set of test-functions and apply our results to concrete examples of abstract wave equations."},"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":"1303.7346","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-03-29T10:06:44Z","cross_cats_sorted":[],"title_canon_sha256":"4c22fd37fbac24d47bc8656f8aa5664340bc4aa01c4d5f38a65e59969df3b11c","abstract_canon_sha256":"91962807db5466ecbfc26bc9baf39d8e565b3053a680154ab6fee67815f27e0a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:29:28.728969Z","signature_b64":"+kHT5OhlMS3IG3F+qqy48Lk8C4VPXYXFDGf/fP6nIWtflJiePT7Wvs+lqO/2irbi8y6MydRKIn8d7XL1bDfjDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"457f657fc309c6d27cc44c8d468dfb8379fe2d7a0791271bbbb3b602e98dda55","last_reissued_at":"2026-05-18T03:29:28.728252Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:29:28.728252Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp extensions for convoluted solutions of wave equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pedro J. Miana, Ver\\'onica Poblete","submitted_at":"2013-03-29T10:06:44Z","abstract_excerpt":"In this paper we give sharp extensions of convoluted solutions of wave equations in abstract Banach spaces. The main technique is to use the algebraic structure, for convolution products $\\ast$ and $\\ast_c$, of these solutions which are defined by a version of the Duhamel's formula. We define algebra homomorphisms, for the convolution product $\\ast_c$, from a certain set of test-functions and apply our results to concrete examples of abstract wave equations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.7346","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":"1303.7346","created_at":"2026-05-18T03:29:28.728366+00:00"},{"alias_kind":"arxiv_version","alias_value":"1303.7346v1","created_at":"2026-05-18T03:29:28.728366+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1303.7346","created_at":"2026-05-18T03:29:28.728366+00:00"},{"alias_kind":"pith_short_12","alias_value":"IV7WK76DBHDN","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_16","alias_value":"IV7WK76DBHDNE7GE","created_at":"2026-05-18T12:27:49.015174+00:00"},{"alias_kind":"pith_short_8","alias_value":"IV7WK76D","created_at":"2026-05-18T12:27:49.015174+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/IV7WK76DBHDNE7GEJSGUNDP3QN","json":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN.json","graph_json":"https://pith.science/api/pith-number/IV7WK76DBHDNE7GEJSGUNDP3QN/graph.json","events_json":"https://pith.science/api/pith-number/IV7WK76DBHDNE7GEJSGUNDP3QN/events.json","paper":"https://pith.science/paper/IV7WK76D"},"agent_actions":{"view_html":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN","download_json":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN.json","view_paper":"https://pith.science/paper/IV7WK76D","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1303.7346&json=true","fetch_graph":"https://pith.science/api/pith-number/IV7WK76DBHDNE7GEJSGUNDP3QN/graph.json","fetch_events":"https://pith.science/api/pith-number/IV7WK76DBHDNE7GEJSGUNDP3QN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN/action/storage_attestation","attest_author":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN/action/author_attestation","sign_citation":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN/action/citation_signature","submit_replication":"https://pith.science/pith/IV7WK76DBHDNE7GEJSGUNDP3QN/action/replication_record"}},"created_at":"2026-05-18T03:29:28.728366+00:00","updated_at":"2026-05-18T03:29:28.728366+00:00"}