{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1993:6QMIY77H2LRNBDJQCETVYFKLW4","short_pith_number":"pith:6QMIY77H","canonical_record":{"source":{"id":"math/9308208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1993-08-24T18:14:54Z","cross_cats_sorted":[],"title_canon_sha256":"b75b01a586c9b68c39258af46188cd8ce2fbd6c17bd462795d133fbd8db980f0","abstract_canon_sha256":"17133b10c21beab3da8fdfccb0c047848467509900dabfa95005193e2bb4b92d"},"schema_version":"1.0"},"canonical_sha256":"f4188c7fe7d2e2d08d3011275c154bb702adec9dcc0fccab7c5d3be711c0f362","source":{"kind":"arxiv","id":"math/9308208","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9308208","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9308208v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9308208","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"6QMIY77H2LRN","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"6QMIY77H2LRNBDJQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"6QMIY77H","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1993:6QMIY77H2LRNBDJQCETVYFKLW4","target":"record","payload":{"canonical_record":{"source":{"id":"math/9308208","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1993-08-24T18:14:54Z","cross_cats_sorted":[],"title_canon_sha256":"b75b01a586c9b68c39258af46188cd8ce2fbd6c17bd462795d133fbd8db980f0","abstract_canon_sha256":"17133b10c21beab3da8fdfccb0c047848467509900dabfa95005193e2bb4b92d"},"schema_version":"1.0"},"canonical_sha256":"f4188c7fe7d2e2d08d3011275c154bb702adec9dcc0fccab7c5d3be711c0f362","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:51.999139Z","signature_b64":"9TqjC/H0iIbdFdeaoSA3ubrIQpJT5t3Ar3njWKz/bStLugNHujaCFXVBxFw7xG08r2zKftyxZmCPrgx2hwgpDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4188c7fe7d2e2d08d3011275c154bb702adec9dcc0fccab7c5d3be711c0f362","last_reissued_at":"2026-05-18T01:05:51.998747Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:51.998747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9308208","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"X49vviye0+To2t5YOm8BF7UxlVe1FkW0Hsfc3Ou4rtvv2ejZH9NTO4C2wnrohpYX/Dsi0KaRXipjCnL/9r6AAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:43:20.798939Z"},"content_sha256":"f2887b45f02350e2fd1f3de85b492f924d637f50a41a585fb6c9dde570ff2aed","schema_version":"1.0","event_id":"sha256:f2887b45f02350e2fd1f3de85b492f924d637f50a41a585fb6c9dde570ff2aed"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1993:6QMIY77H2LRNBDJQCETVYFKLW4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bilinear forms on exact operator spaces and B(H)\\otimes B(H)","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Gilles Pisier, Marius Junge","submitted_at":"1993-08-24T18:14:54Z","abstract_excerpt":"Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra $K(H)$ of all the compact operators on an infinite dimensional Hilbert space $H$). We study a class of bounded linear maps $u\\colon E\\to F^*$ which we call tracially bounded. In particular, we prove that every completely bounded (in short $c.b.$) map $u\\colon E\\to F^*$ factors boundedly through a Hilbert space. This is used to show that the set $OS_n$ of all $n$-dimensional operator spaces equipped with the $c.b.$ version of the Banach Mazur distance is not separable if $n>2$.\n  As an application we show that there is mor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9308208","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zw9lG6N4QtphGS5T18D9kge1qn7W+F0EhZkGeDjZaNP24Y5pNQYAh1oU3Vfer3MNskFmkiHKLR7GlCfcN+kLBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T09:43:20.799287Z"},"content_sha256":"33ad09cd5a92d8ef67c8d640a1f022f47ecbbb37d05fc0a3fc6b8429a862954f","schema_version":"1.0","event_id":"sha256:33ad09cd5a92d8ef67c8d640a1f022f47ecbbb37d05fc0a3fc6b8429a862954f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6QMIY77H2LRNBDJQCETVYFKLW4/bundle.json","state_url":"https://pith.science/pith/6QMIY77H2LRNBDJQCETVYFKLW4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6QMIY77H2LRNBDJQCETVYFKLW4/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":"2026-06-05T09:43:20Z","links":{"resolver":"https://pith.science/pith/6QMIY77H2LRNBDJQCETVYFKLW4","bundle":"https://pith.science/pith/6QMIY77H2LRNBDJQCETVYFKLW4/bundle.json","state":"https://pith.science/pith/6QMIY77H2LRNBDJQCETVYFKLW4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6QMIY77H2LRNBDJQCETVYFKLW4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1993:6QMIY77H2LRNBDJQCETVYFKLW4","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":"17133b10c21beab3da8fdfccb0c047848467509900dabfa95005193e2bb4b92d","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1993-08-24T18:14:54Z","title_canon_sha256":"b75b01a586c9b68c39258af46188cd8ce2fbd6c17bd462795d133fbd8db980f0"},"schema_version":"1.0","source":{"id":"math/9308208","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9308208","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"arxiv_version","alias_value":"math/9308208v1","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9308208","created_at":"2026-05-18T01:05:51Z"},{"alias_kind":"pith_short_12","alias_value":"6QMIY77H2LRN","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"6QMIY77H2LRNBDJQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"6QMIY77H","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:33ad09cd5a92d8ef67c8d640a1f022f47ecbbb37d05fc0a3fc6b8429a862954f","target":"graph","created_at":"2026-05-18T01:05:51Z","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":"Let $E,F$ be exact operators (For example subspaces of the $C^*$-algebra $K(H)$ of all the compact operators on an infinite dimensional Hilbert space $H$). We study a class of bounded linear maps $u\\colon E\\to F^*$ which we call tracially bounded. In particular, we prove that every completely bounded (in short $c.b.$) map $u\\colon E\\to F^*$ factors boundedly through a Hilbert space. This is used to show that the set $OS_n$ of all $n$-dimensional operator spaces equipped with the $c.b.$ version of the Banach Mazur distance is not separable if $n>2$.\n  As an application we show that there is mor","authors_text":"Gilles Pisier, Marius Junge","cross_cats":[],"headline":"","license":"","primary_cat":"math.FA","submitted_at":"1993-08-24T18:14:54Z","title":"Bilinear forms on exact operator spaces and B(H)\\otimes B(H)"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9308208","kind":"arxiv","version":1},"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:f2887b45f02350e2fd1f3de85b492f924d637f50a41a585fb6c9dde570ff2aed","target":"record","created_at":"2026-05-18T01:05:51Z","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":"17133b10c21beab3da8fdfccb0c047848467509900dabfa95005193e2bb4b92d","cross_cats_sorted":[],"license":"","primary_cat":"math.FA","submitted_at":"1993-08-24T18:14:54Z","title_canon_sha256":"b75b01a586c9b68c39258af46188cd8ce2fbd6c17bd462795d133fbd8db980f0"},"schema_version":"1.0","source":{"id":"math/9308208","kind":"arxiv","version":1}},"canonical_sha256":"f4188c7fe7d2e2d08d3011275c154bb702adec9dcc0fccab7c5d3be711c0f362","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4188c7fe7d2e2d08d3011275c154bb702adec9dcc0fccab7c5d3be711c0f362","first_computed_at":"2026-05-18T01:05:51.998747Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:51.998747Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9TqjC/H0iIbdFdeaoSA3ubrIQpJT5t3Ar3njWKz/bStLugNHujaCFXVBxFw7xG08r2zKftyxZmCPrgx2hwgpDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:51.999139Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9308208","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f2887b45f02350e2fd1f3de85b492f924d637f50a41a585fb6c9dde570ff2aed","sha256:33ad09cd5a92d8ef67c8d640a1f022f47ecbbb37d05fc0a3fc6b8429a862954f"],"state_sha256":"b9bb559ee964e7b4db28395fc13f953363109a7ee56dc2638130d80c27d19495"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tqouMroKgUDimv6M0wyQKzkq6dzeXXhvPX8kTsKISBgmTXJknBlHr3zmRjY8pWYKiFdlfniYwevMF5UXDg5cCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T09:43:20.801230Z","bundle_sha256":"1b87e5ab9b791203b2a6c3638d27de47b21801e8642ea979275e77ca70ca7b55"}}