{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:22BUOUAWWNURLWLOKHHRJOTMHS","short_pith_number":"pith:22BUOUAW","schema_version":"1.0","canonical_sha256":"d683475016b36915d96e51cf14ba6c3c85ad193c4f89853d92ea51f65df2828d","source":{"kind":"arxiv","id":"1509.06100","version":1},"attestation_state":"computed","paper":{"title":"Beurling-Lax type theorems in the complex and quaternionic setting: the half-space case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Alpay, Irene Sabadini","submitted_at":"2015-09-21T03:08:50Z","abstract_excerpt":"We give a generalization of the Beurling-Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting."},"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":"1509.06100","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-09-21T03:08:50Z","cross_cats_sorted":[],"title_canon_sha256":"09055e9f381630b8f61347f7710aa1d3d9e61407720f988711fb33da4bebe3ad","abstract_canon_sha256":"a798a8ccb52c78c88d3007c1da6a730c2cc5370fc4eb4646a7439e8e996c8c18"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:35.831453Z","signature_b64":"etET4EhzG2RX1q1yu+OeNHq59VJ+sVNW0YiT6W57SeghyCpYH89OZmRekts28V5UZQqzinm5VO8JCADDxG02BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d683475016b36915d96e51cf14ba6c3c85ad193c4f89853d92ea51f65df2828d","last_reissued_at":"2026-05-18T01:32:35.831041Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:35.831041Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Beurling-Lax type theorems in the complex and quaternionic setting: the half-space case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Daniel Alpay, Irene Sabadini","submitted_at":"2015-09-21T03:08:50Z","abstract_excerpt":"We give a generalization of the Beurling-Lax theorem both in the complex and quaternionic settings. We consider in the first case functions meromorphic in the right complex half-plane, and functions slice hypermeromorphic in the right quaternionic half-space in the second case. In both settings we also discuss a unified framework, which includes both the disk and the half-plane for the complex case and the open unit ball and the half-space in the quaternionic setting."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06100","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":"1509.06100","created_at":"2026-05-18T01:32:35.831099+00:00"},{"alias_kind":"arxiv_version","alias_value":"1509.06100v1","created_at":"2026-05-18T01:32:35.831099+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.06100","created_at":"2026-05-18T01:32:35.831099+00:00"},{"alias_kind":"pith_short_12","alias_value":"22BUOUAWWNUR","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"22BUOUAWWNURLWLO","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"22BUOUAW","created_at":"2026-05-18T12:28:59.999130+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/22BUOUAWWNURLWLOKHHRJOTMHS","json":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS.json","graph_json":"https://pith.science/api/pith-number/22BUOUAWWNURLWLOKHHRJOTMHS/graph.json","events_json":"https://pith.science/api/pith-number/22BUOUAWWNURLWLOKHHRJOTMHS/events.json","paper":"https://pith.science/paper/22BUOUAW"},"agent_actions":{"view_html":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS","download_json":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS.json","view_paper":"https://pith.science/paper/22BUOUAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1509.06100&json=true","fetch_graph":"https://pith.science/api/pith-number/22BUOUAWWNURLWLOKHHRJOTMHS/graph.json","fetch_events":"https://pith.science/api/pith-number/22BUOUAWWNURLWLOKHHRJOTMHS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS/action/storage_attestation","attest_author":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS/action/author_attestation","sign_citation":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS/action/citation_signature","submit_replication":"https://pith.science/pith/22BUOUAWWNURLWLOKHHRJOTMHS/action/replication_record"}},"created_at":"2026-05-18T01:32:35.831099+00:00","updated_at":"2026-05-18T01:32:35.831099+00:00"}