{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PXK3XYD4NBR7Y23FR4I2RH3Q6H","short_pith_number":"pith:PXK3XYD4","canonical_record":{"source":{"id":"1201.4844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-23T20:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"cf7a181c06ebb51712ec0347d26627a6e36f29d36f624e479f5669009c4e3979","abstract_canon_sha256":"89d5eebe0ebd0513d398ad581678b3bd9661f2dfbe4a30019d8afafdf88f12fd"},"schema_version":"1.0"},"canonical_sha256":"7dd5bbe07c6863fc6b658f11a89f70f1fa3784ac6957142f9486d09a2a6a2f70","source":{"kind":"arxiv","id":"1201.4844","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4844","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4844v1","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4844","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"PXK3XYD4NBR7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PXK3XYD4NBR7Y23F","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PXK3XYD4","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PXK3XYD4NBR7Y23FR4I2RH3Q6H","target":"record","payload":{"canonical_record":{"source":{"id":"1201.4844","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-23T20:10:35Z","cross_cats_sorted":[],"title_canon_sha256":"cf7a181c06ebb51712ec0347d26627a6e36f29d36f624e479f5669009c4e3979","abstract_canon_sha256":"89d5eebe0ebd0513d398ad581678b3bd9661f2dfbe4a30019d8afafdf88f12fd"},"schema_version":"1.0"},"canonical_sha256":"7dd5bbe07c6863fc6b658f11a89f70f1fa3784ac6957142f9486d09a2a6a2f70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:04:05.132219Z","signature_b64":"B+Syjqx5oDH/UlkzOVzvQ65fjmWszIAPgLvoHxGPM2jOGo6O5fH5NnI8vBVw/5k9PHhw9x81JKvV52K8fsuHCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dd5bbe07c6863fc6b658f11a89f70f1fa3784ac6957142f9486d09a2a6a2f70","last_reissued_at":"2026-05-18T04:04:05.131717Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:04:05.131717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.4844","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":"2026-05-18T04:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3aavBzs+CepJdzawU6HE/fD8o8RsacFavO7CZETqHREf6A2utZad9/kA5VraQmeKixmHUlzQ+l9R0lFMkVQSAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:08:56.641638Z"},"content_sha256":"a714d22eea449b1849311ab50746d0c9b1fa60e4e03da7b72d1f44e602fff320","schema_version":"1.0","event_id":"sha256:a714d22eea449b1849311ab50746d0c9b1fa60e4e03da7b72d1f44e602fff320"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PXK3XYD4NBR7Y23FR4I2RH3Q6H","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"P. W. Ng, S. Zhang, V. Kaftal","submitted_at":"2012-01-23T20:10:35Z","abstract_excerpt":"We give an overview of the question: which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive elements can be written as a sum of finitely many projections. We focus on von Neumann algebras, on purely infinite simple C*-algebras, and on their associated multiplier algebras."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4844","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":"2026-05-18T04:04:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbMm95N0dioo1cD3q0l61/52QoPtri/MEDTk8S+Htwj3lqjpqUocAHKitjrl6Snj+/4jeSbxLjQO9CqJFSaqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:08:56.642377Z"},"content_sha256":"e3e6ea1884df02edf4df578e601e29ab9191f4b46b353daac499a7f1e02f2b7d","schema_version":"1.0","event_id":"sha256:e3e6ea1884df02edf4df578e601e29ab9191f4b46b353daac499a7f1e02f2b7d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H/bundle.json","state_url":"https://pith.science/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H/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":"2026-05-31T21:08:56Z","links":{"resolver":"https://pith.science/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H","bundle":"https://pith.science/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H/bundle.json","state":"https://pith.science/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXK3XYD4NBR7Y23FR4I2RH3Q6H/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PXK3XYD4NBR7Y23FR4I2RH3Q6H","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":"89d5eebe0ebd0513d398ad581678b3bd9661f2dfbe4a30019d8afafdf88f12fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-23T20:10:35Z","title_canon_sha256":"cf7a181c06ebb51712ec0347d26627a6e36f29d36f624e479f5669009c4e3979"},"schema_version":"1.0","source":{"id":"1201.4844","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.4844","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"arxiv_version","alias_value":"1201.4844v1","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.4844","created_at":"2026-05-18T04:04:05Z"},{"alias_kind":"pith_short_12","alias_value":"PXK3XYD4NBR7","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PXK3XYD4NBR7Y23F","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PXK3XYD4","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:e3e6ea1884df02edf4df578e601e29ab9191f4b46b353daac499a7f1e02f2b7d","target":"graph","created_at":"2026-05-18T04:04:05Z","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 give an overview of the question: which positive elements in an operator algebra can be written as a linear combination of projections with positive coefficients. A special case of independent interest is the question of which positive elements can be written as a sum of finitely many projections. We focus on von Neumann algebras, on purely infinite simple C*-algebras, and on their associated multiplier algebras.","authors_text":"P. W. Ng, S. Zhang, V. Kaftal","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-23T20:10:35Z","title":"Positive combinations of projections in von Neumann algebras and purely infinite simple C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.4844","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:a714d22eea449b1849311ab50746d0c9b1fa60e4e03da7b72d1f44e602fff320","target":"record","created_at":"2026-05-18T04:04:05Z","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":"89d5eebe0ebd0513d398ad581678b3bd9661f2dfbe4a30019d8afafdf88f12fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-01-23T20:10:35Z","title_canon_sha256":"cf7a181c06ebb51712ec0347d26627a6e36f29d36f624e479f5669009c4e3979"},"schema_version":"1.0","source":{"id":"1201.4844","kind":"arxiv","version":1}},"canonical_sha256":"7dd5bbe07c6863fc6b658f11a89f70f1fa3784ac6957142f9486d09a2a6a2f70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dd5bbe07c6863fc6b658f11a89f70f1fa3784ac6957142f9486d09a2a6a2f70","first_computed_at":"2026-05-18T04:04:05.131717Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:04:05.131717Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"B+Syjqx5oDH/UlkzOVzvQ65fjmWszIAPgLvoHxGPM2jOGo6O5fH5NnI8vBVw/5k9PHhw9x81JKvV52K8fsuHCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:04:05.132219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.4844","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a714d22eea449b1849311ab50746d0c9b1fa60e4e03da7b72d1f44e602fff320","sha256:e3e6ea1884df02edf4df578e601e29ab9191f4b46b353daac499a7f1e02f2b7d"],"state_sha256":"388a8d65da2d722504892ce4be14a2b309201f06ed40b6c46b034516b7bda86b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"okUI47FqONNSMOGNdNPuaW72cpQeD0hfPkaNJyhDCNQzd2lzFqwJVHwkssu+P3sP9Ir8E8jVGhzEqKYNJkjRAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:08:56.646463Z","bundle_sha256":"924bff677f0c440766e860d480884dea15b5a23757ce588425f6e9012e32ae69"}}