{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:NCCG6VWXHUTSMAFUSCYG2VSFPF","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":"569b7506eb07001fda45868415601a52f69cb8120674eb7a788762f15494362f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-06-29T14:48:16Z","title_canon_sha256":"e37e9332808ed1739f0a274b80c6929964091b6bd276d51eb4041e48c6cd8960"},"schema_version":"1.0","source":{"id":"1307.0111","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0111","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0111v1","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0111","created_at":"2026-05-18T00:51:03Z"},{"alias_kind":"pith_short_12","alias_value":"NCCG6VWXHUTS","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_16","alias_value":"NCCG6VWXHUTSMAFU","created_at":"2026-05-18T12:27:52Z"},{"alias_kind":"pith_short_8","alias_value":"NCCG6VWX","created_at":"2026-05-18T12:27:52Z"}],"graph_snapshots":[{"event_id":"sha256:764146f783f4c975cca72986c62560a07f41f1d33200a268a4e74e4dbc8fc2f5","target":"graph","created_at":"2026-05-18T00:51:03Z","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":"Our motivating question was whether all traces on a U-ultrapower of a C*-algebra A, where U is a non-principal ultrafilter on N, are necessarily U-limits of traces on A. We show that this is false so long as A has infinitely many extremal traces, and even exhibit a 2^c size family of such traces on the ultrapower. For this to fail even when A has finitely many traces implies that A contains operators that can be expressed as sums of n+1 but not n *-commutators, for arbitrarily large n. We show that this happens for a direct sum of Pedersen-Petersen C*-algebras, and analyze some other interesti","authors_text":"Ilijas Farah, Tristan Bice","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-06-29T14:48:16Z","title":"Traces, Ultrapowers and the Pedersen-Petersen C*-Algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0111","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:f589e1cae9868bce08d214204b1a5bd39656ff8a46cc4a11b33779390a3e5a6f","target":"record","created_at":"2026-05-18T00:51:03Z","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":"569b7506eb07001fda45868415601a52f69cb8120674eb7a788762f15494362f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-06-29T14:48:16Z","title_canon_sha256":"e37e9332808ed1739f0a274b80c6929964091b6bd276d51eb4041e48c6cd8960"},"schema_version":"1.0","source":{"id":"1307.0111","kind":"arxiv","version":1}},"canonical_sha256":"68846f56d73d272600b490b06d5645796a42fc9ff6c52526b0c674ec8a294ab2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68846f56d73d272600b490b06d5645796a42fc9ff6c52526b0c674ec8a294ab2","first_computed_at":"2026-05-18T00:51:03.606485Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:03.606485Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mik554iRGk8sWOlOl6u1bxkQeksDtUL2f4t8o+DEL7RcRki002LtDPfGRCU6r0bXA0jT/JUm8nzx//ByOSgiBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:03.606926Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0111","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f589e1cae9868bce08d214204b1a5bd39656ff8a46cc4a11b33779390a3e5a6f","sha256:764146f783f4c975cca72986c62560a07f41f1d33200a268a4e74e4dbc8fc2f5"],"state_sha256":"832ae9242cdf2d74830d994e08c2e6a277b2cf80ecfbbddf64c8760f29576a9c"}