{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:64ZLCS2RC4M25ZOOPZLPPIS336","short_pith_number":"pith:64ZLCS2R","canonical_record":{"source":{"id":"2412.16087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-20T17:33:54Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"a65966f24d4b7f6778e81fa29eb83f8dc132ac48ee2f3f6bea2230148233fea1","abstract_canon_sha256":"475b00474b3fc2538f6915cee57d93e824765858ae9cf3cdc947fe51a5d39c9f"},"schema_version":"1.0"},"canonical_sha256":"f732b14b511719aee5ce7e56f7a25bdfbcbdd27caf143afc05ce544ed5bf8c1a","source":{"kind":"arxiv","id":"2412.16087","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16087","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16087v2","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16087","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"64ZLCS2RC4M2","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"64ZLCS2RC4M25ZOO","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"64ZLCS2R","created_at":"2026-07-05T11:20:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:64ZLCS2RC4M25ZOOPZLPPIS336","target":"record","payload":{"canonical_record":{"source":{"id":"2412.16087","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-20T17:33:54Z","cross_cats_sorted":["math.RA"],"title_canon_sha256":"a65966f24d4b7f6778e81fa29eb83f8dc132ac48ee2f3f6bea2230148233fea1","abstract_canon_sha256":"475b00474b3fc2538f6915cee57d93e824765858ae9cf3cdc947fe51a5d39c9f"},"schema_version":"1.0"},"canonical_sha256":"f732b14b511719aee5ce7e56f7a25bdfbcbdd27caf143afc05ce544ed5bf8c1a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:20:49.174207Z","signature_b64":"srLQD6dEoKU7jhqn3sjaVcPwXttdJnFO9iTiyXWh4WjtiPiFM6yT/poIqbrRhcIdKtdshyPq/tTaAj17gwQKBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f732b14b511719aee5ce7e56f7a25bdfbcbdd27caf143afc05ce544ed5bf8c1a","last_reissued_at":"2026-07-05T11:20:49.173761Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:20:49.173761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2412.16087","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":"2026-07-05T11:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wROwpFXjfWL3aJsu+DjYVEZ9Oh2SSyM4w8Tx/gURJtP9KB+al+UL8Cf133ljCUWtGQsNmqhlkNdXeiYw4pgqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:12:23.148385Z"},"content_sha256":"88ebbce2367246532f165a06fec433ae7b9ba35153e2574032dfffb348fb4f77","schema_version":"1.0","event_id":"sha256:88ebbce2367246532f165a06fec433ae7b9ba35153e2574032dfffb348fb4f77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:64ZLCS2RC4M25ZOOPZLPPIS336","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lie ideals in properly infinite C*-algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.OA","authors_text":"Hannes Thiel","submitted_at":"2024-12-20T17:33:54Z","abstract_excerpt":"We show that every Lie ideal in a unital, properly infinite C*-algebra is commutator equivalent to a unique two-sided ideal. It follows that the Lie ideal structure of such a C*-algebra is concisely encoded by its lattice of two-sided ideals. This answers a question of Robert in this setting.\n  We obtain similar structure results for Lie ideals in unital, real rank zero C*-algebras without characters. As an application, we show that every Lie ideal in a von Neumann algebra is related to a unique two-sided ideal, which solves a problem of Bre\\v{s}ar, Kissin, and Shulman."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16087","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.16087/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T11:20:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9u9LEMH4FTchSL5mNVW3limQgpWeJqMAgRQcprxNAcAKHw0hl4GvGOfeNMkkKP6sZyxaUa2JZ6UjFYzA3kWyCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T23:12:23.148894Z"},"content_sha256":"240e80d96d2d0a0ecf893903fddce27d3c07622bff44e90421c05857846be145","schema_version":"1.0","event_id":"sha256:240e80d96d2d0a0ecf893903fddce27d3c07622bff44e90421c05857846be145"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64ZLCS2RC4M25ZOOPZLPPIS336/bundle.json","state_url":"https://pith.science/pith/64ZLCS2RC4M25ZOOPZLPPIS336/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64ZLCS2RC4M25ZOOPZLPPIS336/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":"2026-08-14T23:12:23Z","links":{"resolver":"https://pith.science/pith/64ZLCS2RC4M25ZOOPZLPPIS336","bundle":"https://pith.science/pith/64ZLCS2RC4M25ZOOPZLPPIS336/bundle.json","state":"https://pith.science/pith/64ZLCS2RC4M25ZOOPZLPPIS336/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64ZLCS2RC4M25ZOOPZLPPIS336/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:64ZLCS2RC4M25ZOOPZLPPIS336","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":"475b00474b3fc2538f6915cee57d93e824765858ae9cf3cdc947fe51a5d39c9f","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-20T17:33:54Z","title_canon_sha256":"a65966f24d4b7f6778e81fa29eb83f8dc132ac48ee2f3f6bea2230148233fea1"},"schema_version":"1.0","source":{"id":"2412.16087","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2412.16087","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"arxiv_version","alias_value":"2412.16087v2","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2412.16087","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"pith_short_12","alias_value":"64ZLCS2RC4M2","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"pith_short_16","alias_value":"64ZLCS2RC4M25ZOO","created_at":"2026-07-05T11:20:49Z"},{"alias_kind":"pith_short_8","alias_value":"64ZLCS2R","created_at":"2026-07-05T11:20:49Z"}],"graph_snapshots":[{"event_id":"sha256:240e80d96d2d0a0ecf893903fddce27d3c07622bff44e90421c05857846be145","target":"graph","created_at":"2026-07-05T11:20:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2412.16087/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that every Lie ideal in a unital, properly infinite C*-algebra is commutator equivalent to a unique two-sided ideal. It follows that the Lie ideal structure of such a C*-algebra is concisely encoded by its lattice of two-sided ideals. This answers a question of Robert in this setting.\n  We obtain similar structure results for Lie ideals in unital, real rank zero C*-algebras without characters. As an application, we show that every Lie ideal in a von Neumann algebra is related to a unique two-sided ideal, which solves a problem of Bre\\v{s}ar, Kissin, and Shulman.","authors_text":"Hannes Thiel","cross_cats":["math.RA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-20T17:33:54Z","title":"Lie ideals in properly infinite C*-algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.16087","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":"sha256:88ebbce2367246532f165a06fec433ae7b9ba35153e2574032dfffb348fb4f77","target":"record","created_at":"2026-07-05T11:20:49Z","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":"475b00474b3fc2538f6915cee57d93e824765858ae9cf3cdc947fe51a5d39c9f","cross_cats_sorted":["math.RA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-12-20T17:33:54Z","title_canon_sha256":"a65966f24d4b7f6778e81fa29eb83f8dc132ac48ee2f3f6bea2230148233fea1"},"schema_version":"1.0","source":{"id":"2412.16087","kind":"arxiv","version":2}},"canonical_sha256":"f732b14b511719aee5ce7e56f7a25bdfbcbdd27caf143afc05ce544ed5bf8c1a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f732b14b511719aee5ce7e56f7a25bdfbcbdd27caf143afc05ce544ed5bf8c1a","first_computed_at":"2026-07-05T11:20:49.173761Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:20:49.173761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"srLQD6dEoKU7jhqn3sjaVcPwXttdJnFO9iTiyXWh4WjtiPiFM6yT/poIqbrRhcIdKtdshyPq/tTaAj17gwQKBA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:20:49.174207Z","signed_message":"canonical_sha256_bytes"},"source_id":"2412.16087","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:88ebbce2367246532f165a06fec433ae7b9ba35153e2574032dfffb348fb4f77","sha256:240e80d96d2d0a0ecf893903fddce27d3c07622bff44e90421c05857846be145"],"state_sha256":"16467115e7e10863b5afd2bb32b212cc6bc2eb256dc985f18045c691f20b536d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WAAgoT1zSSLLO+uStd/8jJ62GjndaIFjym28j92ujhLoBsrE34+qw6eC+NP8MxwKPrlRjnap6k5W4dOpX0xfBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T23:12:23.152664Z","bundle_sha256":"2ef35be1b2c19fe236e2fb22acedb511b91c6da2733bc1fba8442a163ab8c000"}}