{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:DBVJIH4F733GJ3JJ5DGUMYNTFG","short_pith_number":"pith:DBVJIH4F","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"},"canonical_sha256":"186a941f85fef664ed29e8cd4661b3299fb55f2b116eb33ce0fe6d4599e35ae1","source":{"kind":"arxiv","id":"1407.0969","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0969","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0969v2","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0969","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"DBVJIH4F733G","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DBVJIH4F733GJ3JJ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DBVJIH4F","created_at":"2026-05-18T12:28:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:DBVJIH4F733GJ3JJ5DGUMYNTFG","target":"record","payload":{"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"},"canonical_sha256":"186a941f85fef664ed29e8cd4661b3299fb55f2b116eb33ce0fe6d4599e35ae1","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"},"source_kind":"arxiv","source_id":"1407.0969","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CRFDJurZxI0SOogSMn2GdZS8Uvcl3etXuGv1UQeQhYU7mWXC8OL6DGUedUcoVMxLeWpzIQu1eDLx57qbMZ1eBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:46:33.107310Z"},"content_sha256":"1e30585ab09f76a241efd01c2e1cb724ae574e1822c4442f38f1da4e61287a72","schema_version":"1.0","event_id":"sha256:1e30585ab09f76a241efd01c2e1cb724ae574e1822c4442f38f1da4e61287a72"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:DBVJIH4F733GJ3JJ5DGUMYNTFG","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:21:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ofbMRTbju0XRtdQYUcT/ZEheg5QTQp/i6B6PHPzQNmIGbtVLkIJcXK68+7UbRY/ZC/drnANLA8YRR4INWfjpBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:46:33.108064Z"},"content_sha256":"74bc022822512b1851817b626fd77ee27dc09698ac98d6098cae55b205012338","schema_version":"1.0","event_id":"sha256:74bc022822512b1851817b626fd77ee27dc09698ac98d6098cae55b205012338"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/bundle.json","state_url":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-07T20:46:33Z","links":{"resolver":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG","bundle":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/bundle.json","state":"https://pith.science/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DBVJIH4F733GJ3JJ5DGUMYNTFG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:DBVJIH4F733GJ3JJ5DGUMYNTFG","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"285f34efa7e6f8e161c30d2886cc7a9a83cffdc8455648a26051afaa00498a2e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-02T19:06:06Z","title_canon_sha256":"38df6916b7b636dbd1a12f64556a849eee68e59d144c6bb604acb95ebff3aaff"},"schema_version":"1.0","source":{"id":"1407.0969","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.0969","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"arxiv_version","alias_value":"1407.0969v2","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.0969","created_at":"2026-05-18T01:21:38Z"},{"alias_kind":"pith_short_12","alias_value":"DBVJIH4F733G","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"DBVJIH4F733GJ3JJ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"DBVJIH4F","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:74bc022822512b1851817b626fd77ee27dc09698ac98d6098cae55b205012338","target":"graph","created_at":"2026-05-18T01:21:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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","authors_text":"F\\'elix Cabello S\\'anchez, Jes\\'us M. F. Castillo, Jes\\'us Su\\'arez, Stanislaw Goldstein","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-02T19:06:06Z","title":"Twisting non-commutative $L_p$ spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0969","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1e30585ab09f76a241efd01c2e1cb724ae574e1822c4442f38f1da4e61287a72","target":"record","created_at":"2026-05-18T01:21:38Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"285f34efa7e6f8e161c30d2886cc7a9a83cffdc8455648a26051afaa00498a2e","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-07-02T19:06:06Z","title_canon_sha256":"38df6916b7b636dbd1a12f64556a849eee68e59d144c6bb604acb95ebff3aaff"},"schema_version":"1.0","source":{"id":"1407.0969","kind":"arxiv","version":2}},"canonical_sha256":"186a941f85fef664ed29e8cd4661b3299fb55f2b116eb33ce0fe6d4599e35ae1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"186a941f85fef664ed29e8cd4661b3299fb55f2b116eb33ce0fe6d4599e35ae1","first_computed_at":"2026-05-18T01:21:38.025127Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:38.025127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tu8n3goPDiWyPZs62U1G6Sw1LeT0fC6QGxO0mrECPEMjTiDpjdC+67sgjb/XBeUdmqWCjAZw0uh99uNYCc02BQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:38.025735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.0969","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1e30585ab09f76a241efd01c2e1cb724ae574e1822c4442f38f1da4e61287a72","sha256:74bc022822512b1851817b626fd77ee27dc09698ac98d6098cae55b205012338"],"state_sha256":"f639af4e9551368311520b7d627992c529baff14ee8dc1ed48b71cfb0f091dfc"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hDyFZRAjWdRKAL87nI0ax5+nzMyPwhlKinxKDRBjjt6JxISuTEuPvxRxnOs3m2sd9YalM3SptWzy5tp68TLnAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:46:33.112079Z","bundle_sha256":"34ea9228de70b0f6101d54c4e0e2be644946ea4309cf2711eb274c4478f34522"}}