{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:U52IH2QUWXPOTVVFIGZA3NFNEM","short_pith_number":"pith:U52IH2QU","canonical_record":{"source":{"id":"1703.01543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-05T01:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"6bd5bcfdadbdc77d2efed68b647133482a4175ab102abf7d26985b701f1df3d1","abstract_canon_sha256":"43d9a35a3484d53b1adba296e32e3db6f40b2b60ff577f83e9ee45a3a0abd0f4"},"schema_version":"1.0"},"canonical_sha256":"a77483ea14b5dee9d6a541b20db4ad2318c3a6dfc8a8deaa6844c4115fb1e175","source":{"kind":"arxiv","id":"1703.01543","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01543","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01543v1","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01543","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"U52IH2QUWXPO","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U52IH2QUWXPOTVVF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U52IH2QU","created_at":"2026-05-18T12:31:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:U52IH2QUWXPOTVVFIGZA3NFNEM","target":"record","payload":{"canonical_record":{"source":{"id":"1703.01543","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-05T01:40:28Z","cross_cats_sorted":[],"title_canon_sha256":"6bd5bcfdadbdc77d2efed68b647133482a4175ab102abf7d26985b701f1df3d1","abstract_canon_sha256":"43d9a35a3484d53b1adba296e32e3db6f40b2b60ff577f83e9ee45a3a0abd0f4"},"schema_version":"1.0"},"canonical_sha256":"a77483ea14b5dee9d6a541b20db4ad2318c3a6dfc8a8deaa6844c4115fb1e175","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:49:30.362796Z","signature_b64":"sTS/VgRtX4GRzKJgDqVPl7+YM8DDHsiy9LgUk3hZJcqXUZvWgn+fKvGMPVL2gPJXo+x067oeEQILXoBGr94UCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a77483ea14b5dee9d6a541b20db4ad2318c3a6dfc8a8deaa6844c4115fb1e175","last_reissued_at":"2026-05-18T00:49:30.362110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:49:30.362110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1703.01543","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":"2026-05-18T00:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oAbRVrhnzHJF3NamJwfcrkux8E3GyU/87CPdug68mCGgGQJWqkrlHNroe76Qy10JywhvFEZVuEvqfxqTFLTjBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T13:46:32.038266Z"},"content_sha256":"7430dc5d85ac2d47529c06ff1ba0f214637bdc9ed5102d5f563489748c952499","schema_version":"1.0","event_id":"sha256:7430dc5d85ac2d47529c06ff1ba0f214637bdc9ed5102d5f563489748c952499"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:U52IH2QUWXPOTVVFIGZA3NFNEM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometries of perfect norm ideals of compact operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Behzod Aminov, Vladimir Chilin","submitted_at":"2017-03-05T01:40:28Z","abstract_excerpt":"It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $\\mathcal C_E\\neq \\mathcal C_2$ of compact operators, acting in a complex separable infnite-dimensional Hilbert space $\\mathcal H$ there exist unitary operators $u$ and $v$ on $\\mathcal H$ such that $V(x)=uxv$ or $V(x) = ux^tv$ for all $x\\in \\mathcal C_E$, where $x^t$ is the transpose of an operator $x$ with respect to a fixed orthonormal basis in $\\mathcal H$. In addition, it is shown that any surjective 2-local isometry on a perfect Banach symmetric ideal $\\mathcal C_E \\neq \\mathcal C_2$ is a linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01543","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":"2026-05-18T00:49:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"spgq1NyHH4N29Id18aBRgk7fupM2o3s7gSIxu9g+CZHpuoP1od19YvpXqaZ8Z1S9uXpBaoVLnQYDjsi+c2FwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T13:46:32.038628Z"},"content_sha256":"ce27080151c504b33115454b35a610cdf22dac49db523c9592c91280e4ba3d97","schema_version":"1.0","event_id":"sha256:ce27080151c504b33115454b35a610cdf22dac49db523c9592c91280e4ba3d97"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/U52IH2QUWXPOTVVFIGZA3NFNEM/bundle.json","state_url":"https://pith.science/pith/U52IH2QUWXPOTVVFIGZA3NFNEM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/U52IH2QUWXPOTVVFIGZA3NFNEM/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":"2026-06-28T13:46:32Z","links":{"resolver":"https://pith.science/pith/U52IH2QUWXPOTVVFIGZA3NFNEM","bundle":"https://pith.science/pith/U52IH2QUWXPOTVVFIGZA3NFNEM/bundle.json","state":"https://pith.science/pith/U52IH2QUWXPOTVVFIGZA3NFNEM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/U52IH2QUWXPOTVVFIGZA3NFNEM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:U52IH2QUWXPOTVVFIGZA3NFNEM","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":"43d9a35a3484d53b1adba296e32e3db6f40b2b60ff577f83e9ee45a3a0abd0f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-05T01:40:28Z","title_canon_sha256":"6bd5bcfdadbdc77d2efed68b647133482a4175ab102abf7d26985b701f1df3d1"},"schema_version":"1.0","source":{"id":"1703.01543","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.01543","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"arxiv_version","alias_value":"1703.01543v1","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.01543","created_at":"2026-05-18T00:49:30Z"},{"alias_kind":"pith_short_12","alias_value":"U52IH2QUWXPO","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_16","alias_value":"U52IH2QUWXPOTVVF","created_at":"2026-05-18T12:31:46Z"},{"alias_kind":"pith_short_8","alias_value":"U52IH2QU","created_at":"2026-05-18T12:31:46Z"}],"graph_snapshots":[{"event_id":"sha256:ce27080151c504b33115454b35a610cdf22dac49db523c9592c91280e4ba3d97","target":"graph","created_at":"2026-05-18T00:49:30Z","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":"It is proved that for every surjective linear isometry $V$ on a perfect Banach symmetric ideal $\\mathcal C_E\\neq \\mathcal C_2$ of compact operators, acting in a complex separable infnite-dimensional Hilbert space $\\mathcal H$ there exist unitary operators $u$ and $v$ on $\\mathcal H$ such that $V(x)=uxv$ or $V(x) = ux^tv$ for all $x\\in \\mathcal C_E$, where $x^t$ is the transpose of an operator $x$ with respect to a fixed orthonormal basis in $\\mathcal H$. In addition, it is shown that any surjective 2-local isometry on a perfect Banach symmetric ideal $\\mathcal C_E \\neq \\mathcal C_2$ is a linea","authors_text":"Behzod Aminov, Vladimir Chilin","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-05T01:40:28Z","title":"Isometries of perfect norm ideals of compact operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.01543","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":"sha256:7430dc5d85ac2d47529c06ff1ba0f214637bdc9ed5102d5f563489748c952499","target":"record","created_at":"2026-05-18T00:49:30Z","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":"43d9a35a3484d53b1adba296e32e3db6f40b2b60ff577f83e9ee45a3a0abd0f4","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-03-05T01:40:28Z","title_canon_sha256":"6bd5bcfdadbdc77d2efed68b647133482a4175ab102abf7d26985b701f1df3d1"},"schema_version":"1.0","source":{"id":"1703.01543","kind":"arxiv","version":1}},"canonical_sha256":"a77483ea14b5dee9d6a541b20db4ad2318c3a6dfc8a8deaa6844c4115fb1e175","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a77483ea14b5dee9d6a541b20db4ad2318c3a6dfc8a8deaa6844c4115fb1e175","first_computed_at":"2026-05-18T00:49:30.362110Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:49:30.362110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sTS/VgRtX4GRzKJgDqVPl7+YM8DDHsiy9LgUk3hZJcqXUZvWgn+fKvGMPVL2gPJXo+x067oeEQILXoBGr94UCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:49:30.362796Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.01543","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7430dc5d85ac2d47529c06ff1ba0f214637bdc9ed5102d5f563489748c952499","sha256:ce27080151c504b33115454b35a610cdf22dac49db523c9592c91280e4ba3d97"],"state_sha256":"25877624ee4e39ff3a91f18d49f575ef0e92a77f4e3071280fca0e1676394544"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vTlTdw5T1O+Ij3BcTw3Q7vUoIl+PwovztdNgPsSkgAyIuCPrlueQWv/SqZjoLcyUpTRtGbR16BXUHAL6EZfNCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T13:46:32.040478Z","bundle_sha256":"cded2068746f45e4633bbcf5fe48bb3f82c885ffd014ef40a4162868f902856e"}}