{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:CYUMD3IKGXWRRUALLRVUG5647K","short_pith_number":"pith:CYUMD3IK","canonical_record":{"source":{"id":"1305.0045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-30T22:38:26Z","cross_cats_sorted":[],"title_canon_sha256":"ed580e9361c0be3b995b094e91686b8614773f4faf6fddf34019f6c5be1a72c9","abstract_canon_sha256":"50580aa78e650dc58525ee2ff5e748d3232d9f32e803e4d994416b2135c7a49a"},"schema_version":"1.0"},"canonical_sha256":"1628c1ed0a35ed18d00b5c6b4377dcfa93a02e0b634d2a6b7178c279b948ca51","source":{"kind":"arxiv","id":"1305.0045","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0045","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0045v1","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0045","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"CYUMD3IKGXWR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CYUMD3IKGXWRRUAL","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CYUMD3IK","created_at":"2026-05-18T12:27:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:CYUMD3IKGXWRRUALLRVUG5647K","target":"record","payload":{"canonical_record":{"source":{"id":"1305.0045","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-30T22:38:26Z","cross_cats_sorted":[],"title_canon_sha256":"ed580e9361c0be3b995b094e91686b8614773f4faf6fddf34019f6c5be1a72c9","abstract_canon_sha256":"50580aa78e650dc58525ee2ff5e748d3232d9f32e803e4d994416b2135c7a49a"},"schema_version":"1.0"},"canonical_sha256":"1628c1ed0a35ed18d00b5c6b4377dcfa93a02e0b634d2a6b7178c279b948ca51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:26:42.169304Z","signature_b64":"wjEZn5QG7+uUSBAyL4jpbvBupihuIiBxBZT0T3e8PuAfEDvjhf4As26xL7Y24nqT7h/AQ5/VFdvIuAkLiEe7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1628c1ed0a35ed18d00b5c6b4377dcfa93a02e0b634d2a6b7178c279b948ca51","last_reissued_at":"2026-05-18T03:26:42.168705Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:26:42.168705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1305.0045","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":"2026-05-18T03:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5PY16sDJMH6umT8NmjhnRqNT/iY/m8sgeVxj3my8mShxeUjtCJUbkXxbcUNuc2VmNNQCNuetwmdpppVgDbGlDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:08:24.708519Z"},"content_sha256":"88db843f69a80301498e4d8e70dee4e29cff6c6496531ac33be9289dd0d570b1","schema_version":"1.0","event_id":"sha256:88db843f69a80301498e4d8e70dee4e29cff6c6496531ac33be9289dd0d570b1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:CYUMD3IKGXWRRUALLRVUG5647K","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Strict comparison of projections and positive combinations of projections in certain multiplier algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"P. W. Ng, Shuang Zhang, Victor Kaftal","submitted_at":"2013-04-30T22:38:26Z","abstract_excerpt":"In this paper we investigate whether positive elements in the multiplier algebras of certain finite C*-algebras can be written as finite linear combinations of projections with positive coefficients (PCP). Our focus is on the category of underlying C*-algebras that are separable, simple, with real rank zero, stable rank one, finitely many extreme traces, and strict comparison of projections by the traces. We prove that the strict comparison of projections holds also in the multiplier algebra of the stabilizer algebra. Based on this result and under the additional hypothesis that the multiplier"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0045","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":"2026-05-18T03:26:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ixLPfCo/HFvNp+tRDR1sexOiMedMHI+fncC4x4bc7Cz1C5IHc2bRSDPs0FlqbBmlaKtVJX9Qm50PpRfH67zDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T07:08:24.708864Z"},"content_sha256":"1d1ba0523ae83fa27dffbe4f3ad98d6f8fb52554004ac4355771300627bbdd66","schema_version":"1.0","event_id":"sha256:1d1ba0523ae83fa27dffbe4f3ad98d6f8fb52554004ac4355771300627bbdd66"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYUMD3IKGXWRRUALLRVUG5647K/bundle.json","state_url":"https://pith.science/pith/CYUMD3IKGXWRRUALLRVUG5647K/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYUMD3IKGXWRRUALLRVUG5647K/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":"2026-05-27T07:08:24Z","links":{"resolver":"https://pith.science/pith/CYUMD3IKGXWRRUALLRVUG5647K","bundle":"https://pith.science/pith/CYUMD3IKGXWRRUALLRVUG5647K/bundle.json","state":"https://pith.science/pith/CYUMD3IKGXWRRUALLRVUG5647K/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYUMD3IKGXWRRUALLRVUG5647K/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:CYUMD3IKGXWRRUALLRVUG5647K","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":"50580aa78e650dc58525ee2ff5e748d3232d9f32e803e4d994416b2135c7a49a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-30T22:38:26Z","title_canon_sha256":"ed580e9361c0be3b995b094e91686b8614773f4faf6fddf34019f6c5be1a72c9"},"schema_version":"1.0","source":{"id":"1305.0045","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0045","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0045v1","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0045","created_at":"2026-05-18T03:26:42Z"},{"alias_kind":"pith_short_12","alias_value":"CYUMD3IKGXWR","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"CYUMD3IKGXWRRUAL","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"CYUMD3IK","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:1d1ba0523ae83fa27dffbe4f3ad98d6f8fb52554004ac4355771300627bbdd66","target":"graph","created_at":"2026-05-18T03:26:42Z","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":"In this paper we investigate whether positive elements in the multiplier algebras of certain finite C*-algebras can be written as finite linear combinations of projections with positive coefficients (PCP). Our focus is on the category of underlying C*-algebras that are separable, simple, with real rank zero, stable rank one, finitely many extreme traces, and strict comparison of projections by the traces. We prove that the strict comparison of projections holds also in the multiplier algebra of the stabilizer algebra. Based on this result and under the additional hypothesis that the multiplier","authors_text":"P. W. Ng, Shuang Zhang, Victor Kaftal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-30T22:38:26Z","title":"Strict comparison of projections and positive combinations of projections in certain multiplier algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0045","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":"sha256:88db843f69a80301498e4d8e70dee4e29cff6c6496531ac33be9289dd0d570b1","target":"record","created_at":"2026-05-18T03:26:42Z","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":"50580aa78e650dc58525ee2ff5e748d3232d9f32e803e4d994416b2135c7a49a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-04-30T22:38:26Z","title_canon_sha256":"ed580e9361c0be3b995b094e91686b8614773f4faf6fddf34019f6c5be1a72c9"},"schema_version":"1.0","source":{"id":"1305.0045","kind":"arxiv","version":1}},"canonical_sha256":"1628c1ed0a35ed18d00b5c6b4377dcfa93a02e0b634d2a6b7178c279b948ca51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1628c1ed0a35ed18d00b5c6b4377dcfa93a02e0b634d2a6b7178c279b948ca51","first_computed_at":"2026-05-18T03:26:42.168705Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:42.168705Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wjEZn5QG7+uUSBAyL4jpbvBupihuIiBxBZT0T3e8PuAfEDvjhf4As26xL7Y24nqT7h/AQ5/VFdvIuAkLiEe7Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:42.169304Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0045","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88db843f69a80301498e4d8e70dee4e29cff6c6496531ac33be9289dd0d570b1","sha256:1d1ba0523ae83fa27dffbe4f3ad98d6f8fb52554004ac4355771300627bbdd66"],"state_sha256":"98ff6ab72eec7f3a332abddef574539d7f26794eb186750e438c3dc2fb67c8dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bhe8ILful08UZETTcNxxJpsCZzDTJeVrqZHkzBYXAHhkLQ+iC8d/C3BO+0MaMCexVXkF+PO45PWjfqtvv0woDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T07:08:24.711074Z","bundle_sha256":"1a98f795d25ceb2e3b16e9cd20c7d2424b936a43045e468beb4848a8ce8b94fa"}}