{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:Y2YWFJHTTGEAF77YHV2ZM3UEQL","short_pith_number":"pith:Y2YWFJHT","canonical_record":{"source":{"id":"math/0609604","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-09-21T14:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"bdaeb05554ecd177c0b5e9670756c100608b3faf7800df1535dc0e3440ecf82b","abstract_canon_sha256":"cd85f1ab74b9a5295690178250b5c261dee6b04020adfea35325a39b3e5171e0"},"schema_version":"1.0"},"canonical_sha256":"c6b162a4f3998802fff83d75966e8482e33b48506cd2365339a1413dedab60df","source":{"kind":"arxiv","id":"math/0609604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609604","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609604v1","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609604","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y2YWFJHTTGEA","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"Y2YWFJHTTGEAF77Y","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"Y2YWFJHT","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:Y2YWFJHTTGEAF77YHV2ZM3UEQL","target":"record","payload":{"canonical_record":{"source":{"id":"math/0609604","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.OA","submitted_at":"2006-09-21T14:09:32Z","cross_cats_sorted":[],"title_canon_sha256":"bdaeb05554ecd177c0b5e9670756c100608b3faf7800df1535dc0e3440ecf82b","abstract_canon_sha256":"cd85f1ab74b9a5295690178250b5c261dee6b04020adfea35325a39b3e5171e0"},"schema_version":"1.0"},"canonical_sha256":"c6b162a4f3998802fff83d75966e8482e33b48506cd2365339a1413dedab60df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:14:59.160966Z","signature_b64":"XaPqLhWqVbDn/k2duBiVqrcfbvC56t7CzJlmxqsZ7E0ZdEZNGNKaka1ihHEAY642dKv45qiUG0II/tmemn0dBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6b162a4f3998802fff83d75966e8482e33b48506cd2365339a1413dedab60df","last_reissued_at":"2026-05-18T01:14:59.160519Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:14:59.160519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0609604","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":"2026-05-18T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mo+4HaefP7ZpbEjG92VGzQ+EVN9/0AQJJQ0NpCElj6Qmv7PW12iMKPHgQLroX8Q6NXn91bsk3EFxztGQQ+pDDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:17:52.271985Z"},"content_sha256":"61c165c479d2ee90cb6562f2e48344fde31d5c8e7feda273f536c613ecee6f17","schema_version":"1.0","event_id":"sha256:61c165c479d2ee90cb6562f2e48344fde31d5c8e7feda273f536c613ecee6f17"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:Y2YWFJHTTGEAF77YHV2ZM3UEQL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras","license":"","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"David R. Pitts","submitted_at":"2006-09-21T14:09:32Z","abstract_excerpt":"We combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison's Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C*-algebra is similar to a *-representation precisely when the image operator algebra \\lamb"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609604","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":"2026-05-18T01:14:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JAAWtMeLTTbja6r2zrhcGk6J5h/kZEOPCh7HOu90NlBdHP5R/T45CGk5LDlxSZbIC4ekn08WbGCkddJusyY0BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T11:17:52.272717Z"},"content_sha256":"4ad4fdcf30ca4a2bdbf9ae083d49f69c70c080ba1289e2637c2f1d64cd363f57","schema_version":"1.0","event_id":"sha256:4ad4fdcf30ca4a2bdbf9ae083d49f69c70c080ba1289e2637c2f1d64cd363f57"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL/bundle.json","state_url":"https://pith.science/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL/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":"2026-06-11T11:17:52Z","links":{"resolver":"https://pith.science/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL","bundle":"https://pith.science/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL/bundle.json","state":"https://pith.science/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Y2YWFJHTTGEAF77YHV2ZM3UEQL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:Y2YWFJHTTGEAF77YHV2ZM3UEQL","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":"cd85f1ab74b9a5295690178250b5c261dee6b04020adfea35325a39b3e5171e0","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2006-09-21T14:09:32Z","title_canon_sha256":"bdaeb05554ecd177c0b5e9670756c100608b3faf7800df1535dc0e3440ecf82b"},"schema_version":"1.0","source":{"id":"math/0609604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0609604","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0609604v1","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0609604","created_at":"2026-05-18T01:14:59Z"},{"alias_kind":"pith_short_12","alias_value":"Y2YWFJHTTGEA","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"Y2YWFJHTTGEAF77Y","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"Y2YWFJHT","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:4ad4fdcf30ca4a2bdbf9ae083d49f69c70c080ba1289e2637c2f1d64cd363f57","target":"graph","created_at":"2026-05-18T01:14:59Z","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 combine the notion of norming algebra introduced by Pop, Sinclair and Smith with a result of Pisier to show that if A_1 and A_2 are operator algebras, then any bounded epimorphism of A_1 onto A_2 is completely bounded provided that A_2 contains a norming C*-subalgebra. We use this result to give some insights into Kadison's Similarity Problem: we show that every faithful bounded homomorphism of a C*-algebra on a Hilbert space has completely bounded inverse, and show that a bounded representation of a C*-algebra is similar to a *-representation precisely when the image operator algebra \\lamb","authors_text":"David R. Pitts","cross_cats":[],"headline":"","license":"","primary_cat":"math.OA","submitted_at":"2006-09-21T14:09:32Z","title":"Norming Algebras and Automatic Complete Boundedness of Isomorphisms of Operator Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609604","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":"sha256:61c165c479d2ee90cb6562f2e48344fde31d5c8e7feda273f536c613ecee6f17","target":"record","created_at":"2026-05-18T01:14:59Z","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":"cd85f1ab74b9a5295690178250b5c261dee6b04020adfea35325a39b3e5171e0","cross_cats_sorted":[],"license":"","primary_cat":"math.OA","submitted_at":"2006-09-21T14:09:32Z","title_canon_sha256":"bdaeb05554ecd177c0b5e9670756c100608b3faf7800df1535dc0e3440ecf82b"},"schema_version":"1.0","source":{"id":"math/0609604","kind":"arxiv","version":1}},"canonical_sha256":"c6b162a4f3998802fff83d75966e8482e33b48506cd2365339a1413dedab60df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6b162a4f3998802fff83d75966e8482e33b48506cd2365339a1413dedab60df","first_computed_at":"2026-05-18T01:14:59.160519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:14:59.160519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"XaPqLhWqVbDn/k2duBiVqrcfbvC56t7CzJlmxqsZ7E0ZdEZNGNKaka1ihHEAY642dKv45qiUG0II/tmemn0dBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:14:59.160966Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0609604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61c165c479d2ee90cb6562f2e48344fde31d5c8e7feda273f536c613ecee6f17","sha256:4ad4fdcf30ca4a2bdbf9ae083d49f69c70c080ba1289e2637c2f1d64cd363f57"],"state_sha256":"882ccf8c24519962ffef9d30a7481cd2b1320b796beb2b1ec99a5029576a55b6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"taUbEtL2DZCIvCmc7KmtdY2Es8TX/0kv1JffynfPoA8VXO/AFRxdtFMc2Pt0Lhotv1uFnWnOXBq2WdR4F2scAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T11:17:52.276715Z","bundle_sha256":"d267179b01f205ab4adeeb63b9fdd5aeee7aed5d56f45649c4b0238aa0114ce1"}}