{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AB4LXUFM65FBWX7SMEYZRZI67N","short_pith_number":"pith:AB4LXUFM","canonical_record":{"source":{"id":"1712.05285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-14T15:30:16Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"8b655e5754b6a987dd8a54c6e9fc55b0b99b3e4d8d552fdbf4d0a713dfa40bc7","abstract_canon_sha256":"244375dfd30df9b5f572d918b7dcb5e0097ec318428c2ec6866be4f4a8b4b141"},"schema_version":"1.0"},"canonical_sha256":"0078bbd0acf74a1b5ff2613198e51efb73ee3db1cb4e6b219843d7e7c930be94","source":{"kind":"arxiv","id":"1712.05285","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05285","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05285v3","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05285","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"AB4LXUFM65FB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AB4LXUFM65FBWX7S","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AB4LXUFM","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AB4LXUFM65FBWX7SMEYZRZI67N","target":"record","payload":{"canonical_record":{"source":{"id":"1712.05285","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-14T15:30:16Z","cross_cats_sorted":["math-ph","math.MP","math.QA"],"title_canon_sha256":"8b655e5754b6a987dd8a54c6e9fc55b0b99b3e4d8d552fdbf4d0a713dfa40bc7","abstract_canon_sha256":"244375dfd30df9b5f572d918b7dcb5e0097ec318428c2ec6866be4f4a8b4b141"},"schema_version":"1.0"},"canonical_sha256":"0078bbd0acf74a1b5ff2613198e51efb73ee3db1cb4e6b219843d7e7c930be94","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.217868Z","signature_b64":"gmZULeWwAu+sLKMJgXY+fhSSbXNPftioBv2WvgdVdmnmwhbOM16EVsPNOHTYpenEn0+8TTxz1qfAtDGGaUHJAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0078bbd0acf74a1b5ff2613198e51efb73ee3db1cb4e6b219843d7e7c930be94","last_reissued_at":"2026-05-18T00:01:15.217443Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.217443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.05285","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:01:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"D2oWxaa5JWVmJtuYGatnFepVXTxeaWdZ4ou0JmUjUxQW3BpAJSk/Pflzr3B4ETmL4l8oLDbtyEBDmJyiFslFAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:23:32.176942Z"},"content_sha256":"fc9049894538e4bab898314d624cb542641f1b66812854c0a069ad5c97f35551","schema_version":"1.0","event_id":"sha256:fc9049894538e4bab898314d624cb542641f1b66812854c0a069ad5c97f35551"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AB4LXUFM65FBWX7SMEYZRZI67N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the complete boundedness of the Schur block product","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.QA"],"primary_cat":"math.OA","authors_text":"Erik Christensen","submitted_at":"2017-12-14T15:30:16Z","abstract_excerpt":"We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_{ij}), B:= (b_{ij}): A (*) B := (a_{ij}b_{ij}) = V* pi(A) F pi(B) V, such that V is an isometry, pi is a *-representation and F is a self-adjoint unitary. This implies an inequality due to Livshits and two apparently new ones on diagonals of matrices. ||A (*) B|| \\leq ||A||_r ||B||_c operator, row and column norm; - diag(A*A) \\leq A* (*) A \\leq diag(A*A), and for all vectors f, g: |<A(*)B f,g> |^2 \\leq < "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05285","kind":"arxiv","version":3},"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":"2026-05-18T00:01:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c8Ig7akDPS8Q1afg0qstgmzUMCDxGCLqP0ynBCqnxR9Mk2IKN1Lqo1pO9zqvVRdGwMCQ3QcsGTJ8pb10PzwZDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-25T21:23:32.177621Z"},"content_sha256":"1a0658a1d1685d340c448f86221e1ba51ad2ac1d86480d8a9102bbc95e41e43e","schema_version":"1.0","event_id":"sha256:1a0658a1d1685d340c448f86221e1ba51ad2ac1d86480d8a9102bbc95e41e43e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/bundle.json","state_url":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AB4LXUFM65FBWX7SMEYZRZI67N/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":"2026-05-25T21:23:32Z","links":{"resolver":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N","bundle":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/bundle.json","state":"https://pith.science/pith/AB4LXUFM65FBWX7SMEYZRZI67N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AB4LXUFM65FBWX7SMEYZRZI67N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AB4LXUFM65FBWX7SMEYZRZI67N","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":"244375dfd30df9b5f572d918b7dcb5e0097ec318428c2ec6866be4f4a8b4b141","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-14T15:30:16Z","title_canon_sha256":"8b655e5754b6a987dd8a54c6e9fc55b0b99b3e4d8d552fdbf4d0a713dfa40bc7"},"schema_version":"1.0","source":{"id":"1712.05285","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.05285","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1712.05285v3","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.05285","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"AB4LXUFM65FB","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AB4LXUFM65FBWX7S","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AB4LXUFM","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:1a0658a1d1685d340c448f86221e1ba51ad2ac1d86480d8a9102bbc95e41e43e","target":"graph","created_at":"2026-05-18T00:01:15Z","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":"We give a Stinespring representation of the Schur block product, say (*), on pairs of square matrices with entries in a C*-algebra as a completely bounded bilinear operator of the form: A:=(a_{ij}), B:= (b_{ij}): A (*) B := (a_{ij}b_{ij}) = V* pi(A) F pi(B) V, such that V is an isometry, pi is a *-representation and F is a self-adjoint unitary. This implies an inequality due to Livshits and two apparently new ones on diagonals of matrices. ||A (*) B|| \\leq ||A||_r ||B||_c operator, row and column norm; - diag(A*A) \\leq A* (*) A \\leq diag(A*A), and for all vectors f, g: |<A(*)B f,g> |^2 \\leq < ","authors_text":"Erik Christensen","cross_cats":["math-ph","math.MP","math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-14T15:30:16Z","title":"On the complete boundedness of the Schur block product"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.05285","kind":"arxiv","version":3},"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:fc9049894538e4bab898314d624cb542641f1b66812854c0a069ad5c97f35551","target":"record","created_at":"2026-05-18T00:01:15Z","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":"244375dfd30df9b5f572d918b7dcb5e0097ec318428c2ec6866be4f4a8b4b141","cross_cats_sorted":["math-ph","math.MP","math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-12-14T15:30:16Z","title_canon_sha256":"8b655e5754b6a987dd8a54c6e9fc55b0b99b3e4d8d552fdbf4d0a713dfa40bc7"},"schema_version":"1.0","source":{"id":"1712.05285","kind":"arxiv","version":3}},"canonical_sha256":"0078bbd0acf74a1b5ff2613198e51efb73ee3db1cb4e6b219843d7e7c930be94","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0078bbd0acf74a1b5ff2613198e51efb73ee3db1cb4e6b219843d7e7c930be94","first_computed_at":"2026-05-18T00:01:15.217443Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:15.217443Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gmZULeWwAu+sLKMJgXY+fhSSbXNPftioBv2WvgdVdmnmwhbOM16EVsPNOHTYpenEn0+8TTxz1qfAtDGGaUHJAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:15.217868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.05285","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fc9049894538e4bab898314d624cb542641f1b66812854c0a069ad5c97f35551","sha256:1a0658a1d1685d340c448f86221e1ba51ad2ac1d86480d8a9102bbc95e41e43e"],"state_sha256":"dbe0551f4ef34ecf24f4446f17abd2999a124ac358b04a6876c7f9c809fd04ff"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bv5LKCuLzUHSUAS/w5aKFNZUth+k3O3+TfA7EnWKWRcK6FhjRNf7ev6wMzYl265a1YwMPFfpGwuRk/Oba576AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-25T21:23:32.181486Z","bundle_sha256":"c81825cbb161f4662ab8284a2e22baab40bb0219b151df2dbd64939d112ea47f"}}