{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:SBKO5RPX5LGGWYK2R2PZHZSEXI","short_pith_number":"pith:SBKO5RPX","schema_version":"1.0","canonical_sha256":"9054eec5f7eacc6b615a8e9f93e644ba370f2a9c58ff70e64b125b5ddefc4df8","source":{"kind":"arxiv","id":"1109.2419","version":1},"attestation_state":"computed","paper":{"title":"Embedding theorems for harmonic multifunctional spaces on R^n+1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Milos Arsenovic, Romi F. Shamoyan","submitted_at":"2011-09-12T09:55:12Z","abstract_excerpt":"We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function."},"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":"1109.2419","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-09-12T09:55:12Z","cross_cats_sorted":[],"title_canon_sha256":"b4315b57fb32415ff5a60ae435f1b0877da5f78fc914f76da4e10a8829b7e356","abstract_canon_sha256":"338e2a0fe79dc0d184ae981b252c23d01830ecacdc2e5b670372641cd9d4b9fd"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:37:09.097690Z","signature_b64":"wwNc8YSaD5KA5lGhXd/mugo2tgE7uEiz/rJidiNlwYrC+O8ITpWqMVJ7m7kJ2UvqFOZaQbwnLl2dvcgT8XkgDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9054eec5f7eacc6b615a8e9f93e644ba370f2a9c58ff70e64b125b5ddefc4df8","last_reissued_at":"2026-05-18T03:37:09.097036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:37:09.097036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Embedding theorems for harmonic multifunctional spaces on R^n+1","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Milos Arsenovic, Romi F. Shamoyan","submitted_at":"2011-09-12T09:55:12Z","abstract_excerpt":"We introduce and study properties of certain new multifunctional harmonic spaces in the upper halfspace.We prove several sharp embedding theorems for such multifunctional spaces,these results are new even in the case of a single function."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2419","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":"1109.2419","created_at":"2026-05-18T03:37:09.097154+00:00"},{"alias_kind":"arxiv_version","alias_value":"1109.2419v1","created_at":"2026-05-18T03:37:09.097154+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1109.2419","created_at":"2026-05-18T03:37:09.097154+00:00"},{"alias_kind":"pith_short_12","alias_value":"SBKO5RPX5LGG","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"SBKO5RPX5LGGWYK2","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"SBKO5RPX","created_at":"2026-05-18T12:26:41.206345+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/SBKO5RPX5LGGWYK2R2PZHZSEXI","json":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI.json","graph_json":"https://pith.science/api/pith-number/SBKO5RPX5LGGWYK2R2PZHZSEXI/graph.json","events_json":"https://pith.science/api/pith-number/SBKO5RPX5LGGWYK2R2PZHZSEXI/events.json","paper":"https://pith.science/paper/SBKO5RPX"},"agent_actions":{"view_html":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI","download_json":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI.json","view_paper":"https://pith.science/paper/SBKO5RPX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1109.2419&json=true","fetch_graph":"https://pith.science/api/pith-number/SBKO5RPX5LGGWYK2R2PZHZSEXI/graph.json","fetch_events":"https://pith.science/api/pith-number/SBKO5RPX5LGGWYK2R2PZHZSEXI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI/action/storage_attestation","attest_author":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI/action/author_attestation","sign_citation":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI/action/citation_signature","submit_replication":"https://pith.science/pith/SBKO5RPX5LGGWYK2R2PZHZSEXI/action/replication_record"}},"created_at":"2026-05-18T03:37:09.097154+00:00","updated_at":"2026-05-18T03:37:09.097154+00:00"}