{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4MOCKMCDZQJ5NDVLRGUEKBPH76","short_pith_number":"pith:4MOCKMCD","canonical_record":{"source":{"id":"1008.3733","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-23T00:52:28Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0cc5cc997d4209c05cf73c6b3d5890f913ae64c88d103fa6894929c034f4e057","abstract_canon_sha256":"0b0ea98ba41225d3ccd76489b3c776f1686bdd763b4da62e03653e5e2b5c2999"},"schema_version":"1.0"},"canonical_sha256":"e31c253043cc13d68eab89a84505e7ff817776dfe68a3bbdbbe6a9879c32cb0a","source":{"kind":"arxiv","id":"1008.3733","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3733","created_at":"2026-05-18T04:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3733v4","created_at":"2026-05-18T04:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3733","created_at":"2026-05-18T04:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"4MOCKMCDZQJ5","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4MOCKMCDZQJ5NDVL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4MOCKMCD","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4MOCKMCDZQJ5NDVLRGUEKBPH76","target":"record","payload":{"canonical_record":{"source":{"id":"1008.3733","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-23T00:52:28Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"0cc5cc997d4209c05cf73c6b3d5890f913ae64c88d103fa6894929c034f4e057","abstract_canon_sha256":"0b0ea98ba41225d3ccd76489b3c776f1686bdd763b4da62e03653e5e2b5c2999"},"schema_version":"1.0"},"canonical_sha256":"e31c253043cc13d68eab89a84505e7ff817776dfe68a3bbdbbe6a9879c32cb0a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:43.665090Z","signature_b64":"exXD29j2f+qh16STYLkQo5u1sXV62xuU31gbb1YAJoiTfav2gkUygszEYDq6Ak177DPC6x3HjNA3UB9PRcPxDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e31c253043cc13d68eab89a84505e7ff817776dfe68a3bbdbbe6a9879c32cb0a","last_reissued_at":"2026-05-18T04:06:43.664580Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:43.664580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.3733","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BQEwFngZSAZ99RT3+1mKWrGjmkMTJgV0RWPhihVZr0IYSMDbsQ+jOLA7/QBUJSPsktSBSDcBVlGjSYqpUlPcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:23:12.115265Z"},"content_sha256":"87b2b523c4f889b94fa72ff5ee18072ba3bfef603fcc30a429841f65926aa562","schema_version":"1.0","event_id":"sha256:87b2b523c4f889b94fa72ff5ee18072ba3bfef603fcc30a429841f65926aa562"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4MOCKMCDZQJ5NDVLRGUEKBPH76","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Leibniz Seminorms and Best Approximation from C*-subalgebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Marc A. Rieffel (U. C. Berkeley)","submitted_at":"2010-08-23T00:52:28Z","abstract_excerpt":"We show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3733","kind":"arxiv","version":4},"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":"2026-05-18T04:06:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B9SgbM2ZbWp6r6FIEu4bmYrcDuoq7r/BFy90YO4HjtLxLHhxkhgPVncyDaAOjUWltpSkUjjdfkkidoz68S88Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-08T21:23:12.115790Z"},"content_sha256":"74a47758941fc94fb4c8e72bff05d9e92099297263ebba0d18c56870718cb16d","schema_version":"1.0","event_id":"sha256:74a47758941fc94fb4c8e72bff05d9e92099297263ebba0d18c56870718cb16d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76/bundle.json","state_url":"https://pith.science/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76/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":"2026-08-08T21:23:12Z","links":{"resolver":"https://pith.science/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76","bundle":"https://pith.science/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76/bundle.json","state":"https://pith.science/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4MOCKMCDZQJ5NDVLRGUEKBPH76/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4MOCKMCDZQJ5NDVLRGUEKBPH76","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":"0b0ea98ba41225d3ccd76489b3c776f1686bdd763b4da62e03653e5e2b5c2999","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-23T00:52:28Z","title_canon_sha256":"0cc5cc997d4209c05cf73c6b3d5890f913ae64c88d103fa6894929c034f4e057"},"schema_version":"1.0","source":{"id":"1008.3733","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.3733","created_at":"2026-05-18T04:06:43Z"},{"alias_kind":"arxiv_version","alias_value":"1008.3733v4","created_at":"2026-05-18T04:06:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.3733","created_at":"2026-05-18T04:06:43Z"},{"alias_kind":"pith_short_12","alias_value":"4MOCKMCDZQJ5","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4MOCKMCDZQJ5NDVL","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4MOCKMCD","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:74a47758941fc94fb4c8e72bff05d9e92099297263ebba0d18c56870718cb16d","target":"graph","created_at":"2026-05-18T04:06:43Z","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 show that if B is a C*-subalgebra of a C*-algebra A such that B contains a bounded approximate identity for A, and if L is the pull-back to A of the quotient norm on A/B, then L is strongly Leibniz. In connection with this situation we study certain aspects of best approximation of elements of a unital C*-algebra by elements of a unital C*-subalgebra.","authors_text":"Marc A. Rieffel (U. C. Berkeley)","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-23T00:52:28Z","title":"Leibniz Seminorms and Best Approximation from C*-subalgebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.3733","kind":"arxiv","version":4},"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":"sha256:87b2b523c4f889b94fa72ff5ee18072ba3bfef603fcc30a429841f65926aa562","target":"record","created_at":"2026-05-18T04:06:43Z","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":"0b0ea98ba41225d3ccd76489b3c776f1686bdd763b4da62e03653e5e2b5c2999","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2010-08-23T00:52:28Z","title_canon_sha256":"0cc5cc997d4209c05cf73c6b3d5890f913ae64c88d103fa6894929c034f4e057"},"schema_version":"1.0","source":{"id":"1008.3733","kind":"arxiv","version":4}},"canonical_sha256":"e31c253043cc13d68eab89a84505e7ff817776dfe68a3bbdbbe6a9879c32cb0a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e31c253043cc13d68eab89a84505e7ff817776dfe68a3bbdbbe6a9879c32cb0a","first_computed_at":"2026-05-18T04:06:43.664580Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:43.664580Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"exXD29j2f+qh16STYLkQo5u1sXV62xuU31gbb1YAJoiTfav2gkUygszEYDq6Ak177DPC6x3HjNA3UB9PRcPxDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:43.665090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.3733","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:87b2b523c4f889b94fa72ff5ee18072ba3bfef603fcc30a429841f65926aa562","sha256:74a47758941fc94fb4c8e72bff05d9e92099297263ebba0d18c56870718cb16d"],"state_sha256":"0305ff95e2594c4e283a89b644a8a1baedf24c10f5c11568615755e20cbc4199"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pXqX3ddek9qOGswqYBa3I9R4UG/lgNLBKJV/ENf8DoSBAB7ITvUcRtDjbS9R9+w1xgh5da7DVZle5T4Zh6h2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-08T21:23:12.119899Z","bundle_sha256":"0f50614767cf7c91ef08cf2f62f360d5e00a8906bf430aa13eb70ff7edba6ae5"}}