{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:DBVJIH4F733GJ3JJ5DGUMYNTFG","short_pith_number":"pith:DBVJIH4F","schema_version":"1.0","canonical_sha256":"186a941f85fef664ed29e8cd4661b3299fb55f2b116eb33ce0fe6d4599e35ae1","source":{"kind":"arxiv","id":"1407.0969","version":2},"attestation_state":"computed","paper":{"title":"Twisting non-commutative $L_p$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Jes\\'us Su\\'arez, Stanislaw Goldstein","submitted_at":"2014-07-02T19:06:06Z","abstract_excerpt":"The paper makes the first steps into the study of extensions (\"twisted sums\") of noncommutative $L^p$-spaces regarded as Banach modules over the underlying von Neumann algebra $\\mathcal M$.\n  Our approach combines Kalton's description of extensions by centralizers (these are certain maps which are, in general, neither linear nor bounded) with a general principle, due to Rochberg and Weiss saying that whenever one finds a given Banach space $Y$ as an intermediate space in a (complex) interpolation scale, one automatically gets a self-extension $ 0\\longrightarrow Y\\longrightarrow X\\longrightarro"},"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":"1407.0969","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-02T19:06:06Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"38df6916b7b636dbd1a12f64556a849eee68e59d144c6bb604acb95ebff3aaff","abstract_canon_sha256":"285f34efa7e6f8e161c30d2886cc7a9a83cffdc8455648a26051afaa00498a2e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:38.025735Z","signature_b64":"tu8n3goPDiWyPZs62U1G6Sw1LeT0fC6QGxO0mrECPEMjTiDpjdC+67sgjb/XBeUdmqWCjAZw0uh99uNYCc02BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"186a941f85fef664ed29e8cd4661b3299fb55f2b116eb33ce0fe6d4599e35ae1","last_reissued_at":"2026-05-18T01:21:38.025127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:38.025127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twisting non-commutative $L_p$ spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Jes\\'us Su\\'arez, Stanislaw Goldstein","submitted_at":"2014-07-02T19:06:06Z","abstract_excerpt":"The paper makes the first steps into the study of extensions (\"twisted sums\") of noncommutative $L^p$-spaces regarded as Banach modules over the underlying von Neumann algebra $\\mathcal M$.\n  Our approach combines Kalton's description of extensions by centralizers (these are certain maps which are, in general, neither linear nor bounded) with a general principle, due to Rochberg and Weiss saying that whenever one finds a given Banach space $Y$ as an intermediate space in a (complex) interpolation scale, one automatically gets a self-extension $ 0\\longrightarrow Y\\longrightarrow X\\longrightarro"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0969","kind":"arxiv","version":2},"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":"1407.0969","created_at":"2026-05-18T01:21:38.025229+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.0969v2","created_at":"2026-05-18T01:21:38.025229+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0969","created_at":"2026-05-18T01:21:38.025229+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBVJIH4F733G","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBVJIH4F733GJ3JJ","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBVJIH4F","created_at":"2026-05-18T12:28:25.294606+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/DBVJIH4F733GJ3JJ5DGUMYNTFG","json":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG.json","graph_json":"https://pith.science/api/pith-number/DBVJIH4F733GJ3JJ5DGUMYNTFG/graph.json","events_json":"https://pith.science/api/pith-number/DBVJIH4F733GJ3JJ5DGUMYNTFG/events.json","paper":"https://pith.science/paper/DBVJIH4F"},"agent_actions":{"view_html":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG","download_json":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG.json","view_paper":"https://pith.science/paper/DBVJIH4F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.0969&json=true","fetch_graph":"https://pith.science/api/pith-number/DBVJIH4F733GJ3JJ5DGUMYNTFG/graph.json","fetch_events":"https://pith.science/api/pith-number/DBVJIH4F733GJ3JJ5DGUMYNTFG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/action/storage_attestation","attest_author":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/action/author_attestation","sign_citation":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/action/citation_signature","submit_replication":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/action/replication_record"}},"created_at":"2026-05-18T01:21:38.025229+00:00","updated_at":"2026-05-18T01:21:38.025229+00:00"}