{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:YCSKLDKSMUNZP2UDNBK6NQL55Y","short_pith_number":"pith:YCSKLDKS","canonical_record":{"source":{"id":"1603.07199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-23T14:31:21Z","cross_cats_sorted":[],"title_canon_sha256":"d69a4f93508cf13d8b7897d096690cf37d69ac87efcc1bed9886f7f10d8fe07d","abstract_canon_sha256":"5af245f83ac4c512a22c210a91e52fd9dd4c096c95792d572cc9725081e09492"},"schema_version":"1.0"},"canonical_sha256":"c0a4a58d52651b97ea836855e6c17dee014125a149d62f5fe88a33c6b6f3625c","source":{"kind":"arxiv","id":"1603.07199","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07199","created_at":"2026-05-18T01:18:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07199v2","created_at":"2026-05-18T01:18:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07199","created_at":"2026-05-18T01:18:06Z"},{"alias_kind":"pith_short_12","alias_value":"YCSKLDKSMUNZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YCSKLDKSMUNZP2UD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YCSKLDKS","created_at":"2026-05-18T12:30:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:YCSKLDKSMUNZP2UDNBK6NQL55Y","target":"record","payload":{"canonical_record":{"source":{"id":"1603.07199","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-23T14:31:21Z","cross_cats_sorted":[],"title_canon_sha256":"d69a4f93508cf13d8b7897d096690cf37d69ac87efcc1bed9886f7f10d8fe07d","abstract_canon_sha256":"5af245f83ac4c512a22c210a91e52fd9dd4c096c95792d572cc9725081e09492"},"schema_version":"1.0"},"canonical_sha256":"c0a4a58d52651b97ea836855e6c17dee014125a149d62f5fe88a33c6b6f3625c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:18:06.245982Z","signature_b64":"cLs/Ngo/Q+M08JpTxYxNulNF7QFzbbyJkQ4nPV9ThetJE0Y52LswFaoHahMDHQjg4SiWyr2BMaGTh91fpHfNAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c0a4a58d52651b97ea836855e6c17dee014125a149d62f5fe88a33c6b6f3625c","last_reissued_at":"2026-05-18T01:18:06.245334Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:18:06.245334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.07199","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:18:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gtg43XXlL9JWILtM2cHtMoLkL7ntUP02gO7c56oRLlRZl4jrOMjt7wwb0/p7KeOTCmHYKev/A7ypj3Fc0O2LDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:36:30.567552Z"},"content_sha256":"bc742fcadad6b2895a6e2e0fe43e31ada8f6b6098a6a2c0b08d9a2aa4c55bc90","schema_version":"1.0","event_id":"sha256:bc742fcadad6b2895a6e2e0fe43e31ada8f6b6098a6a2c0b08d9a2aa4c55bc90"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:YCSKLDKSMUNZP2UDNBK6NQL55Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Comparison Properties of the Cuntz semigroup and applications to C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Henning Petzka, Joan Bosa","submitted_at":"2016-03-23T14:31:21Z","abstract_excerpt":"We study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $\\omega$-comparison. We show differences of all properties by providing examples, which suggest that the corona factorization property for C*-algebras might allow for both finite and infinite projections. In addition, we show that R{\\o}rdam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07199","kind":"arxiv","version":2},"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":"2026-05-18T01:18:06Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QPDTBIQDiDfs9Renk+GfzM5Sxe0PrEOqErLX2WeGg+3HfCdsSjf5YydbpWxE/BDiA1lVBKB4aCvbuk485rrECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-29T15:36:30.567894Z"},"content_sha256":"2bd63531781e4fdcb5f13d9b7b200da5085a4d1c4b94a91f0714380e12562082","schema_version":"1.0","event_id":"sha256:2bd63531781e4fdcb5f13d9b7b200da5085a4d1c4b94a91f0714380e12562082"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y/bundle.json","state_url":"https://pith.science/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y/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":"2026-06-29T15:36:30Z","links":{"resolver":"https://pith.science/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y","bundle":"https://pith.science/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y/bundle.json","state":"https://pith.science/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YCSKLDKSMUNZP2UDNBK6NQL55Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:YCSKLDKSMUNZP2UDNBK6NQL55Y","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":"5af245f83ac4c512a22c210a91e52fd9dd4c096c95792d572cc9725081e09492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-23T14:31:21Z","title_canon_sha256":"d69a4f93508cf13d8b7897d096690cf37d69ac87efcc1bed9886f7f10d8fe07d"},"schema_version":"1.0","source":{"id":"1603.07199","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.07199","created_at":"2026-05-18T01:18:06Z"},{"alias_kind":"arxiv_version","alias_value":"1603.07199v2","created_at":"2026-05-18T01:18:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.07199","created_at":"2026-05-18T01:18:06Z"},{"alias_kind":"pith_short_12","alias_value":"YCSKLDKSMUNZ","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_16","alias_value":"YCSKLDKSMUNZP2UD","created_at":"2026-05-18T12:30:53Z"},{"alias_kind":"pith_short_8","alias_value":"YCSKLDKS","created_at":"2026-05-18T12:30:53Z"}],"graph_snapshots":[{"event_id":"sha256:2bd63531781e4fdcb5f13d9b7b200da5085a4d1c4b94a91f0714380e12562082","target":"graph","created_at":"2026-05-18T01:18:06Z","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 study comparison properties in the category Cu aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $\\omega$-comparison. We show differences of all properties by providing examples, which suggest that the corona factorization property for C*-algebras might allow for both finite and infinite projections. In addition, we show that R{\\o}rdam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.","authors_text":"Henning Petzka, Joan Bosa","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-23T14:31:21Z","title":"Comparison Properties of the Cuntz semigroup and applications to C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.07199","kind":"arxiv","version":2},"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:bc742fcadad6b2895a6e2e0fe43e31ada8f6b6098a6a2c0b08d9a2aa4c55bc90","target":"record","created_at":"2026-05-18T01:18:06Z","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":"5af245f83ac4c512a22c210a91e52fd9dd4c096c95792d572cc9725081e09492","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-03-23T14:31:21Z","title_canon_sha256":"d69a4f93508cf13d8b7897d096690cf37d69ac87efcc1bed9886f7f10d8fe07d"},"schema_version":"1.0","source":{"id":"1603.07199","kind":"arxiv","version":2}},"canonical_sha256":"c0a4a58d52651b97ea836855e6c17dee014125a149d62f5fe88a33c6b6f3625c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c0a4a58d52651b97ea836855e6c17dee014125a149d62f5fe88a33c6b6f3625c","first_computed_at":"2026-05-18T01:18:06.245334Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:18:06.245334Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cLs/Ngo/Q+M08JpTxYxNulNF7QFzbbyJkQ4nPV9ThetJE0Y52LswFaoHahMDHQjg4SiWyr2BMaGTh91fpHfNAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:18:06.245982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.07199","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bc742fcadad6b2895a6e2e0fe43e31ada8f6b6098a6a2c0b08d9a2aa4c55bc90","sha256:2bd63531781e4fdcb5f13d9b7b200da5085a4d1c4b94a91f0714380e12562082"],"state_sha256":"177f246132f7db3dfee15078b6875a23a6dcb8d39e0db5abd174090b98d77c33"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ru8gNAfdaqj1ZtkoyssYXyrGQghn3ocmb0uhBaHkTizY8TEoXth0T5EK7k9lAW5nwo3058kjCtA2gpNsWxyEAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-29T15:36:30.569753Z","bundle_sha256":"feec389da1ef1000c05b77b8896f6f6ec03134f982505a2490b91c69ba6bc3a5"}}