{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:SBXQVI75SJVQHNXZXIGFD535GU","short_pith_number":"pith:SBXQVI75","canonical_record":{"source":{"id":"1409.8099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-09-29T12:45:10Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"d62850068cffdca549b578d53dbedf816689dcd67eadadc189256409f3cf9f11","abstract_canon_sha256":"8ce6fae064008451c57f560fb4d57e2ce01d8fdbeeaa74df2a2dde8d57502d11"},"schema_version":"1.0"},"canonical_sha256":"906f0aa3fd926b03b6f9ba0c51f77d35124df1343fc870adddf3ec37b36a8aad","source":{"kind":"arxiv","id":"1409.8099","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8099","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8099v2","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8099","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"SBXQVI75SJVQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SBXQVI75SJVQHNXZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SBXQVI75","created_at":"2026-05-18T12:28:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:SBXQVI75SJVQHNXZXIGFD535GU","target":"record","payload":{"canonical_record":{"source":{"id":"1409.8099","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-09-29T12:45:10Z","cross_cats_sorted":["math.DS","math.GR"],"title_canon_sha256":"d62850068cffdca549b578d53dbedf816689dcd67eadadc189256409f3cf9f11","abstract_canon_sha256":"8ce6fae064008451c57f560fb4d57e2ce01d8fdbeeaa74df2a2dde8d57502d11"},"schema_version":"1.0"},"canonical_sha256":"906f0aa3fd926b03b6f9ba0c51f77d35124df1343fc870adddf3ec37b36a8aad","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:41:03.179574Z","signature_b64":"AiazodZSdcSWvloQkF0lB4aCIeNKf0Gs0AbiZpyo0s8Z9tf889BaNWeqGDSEcXszeTlBw3ZTWqycBO/87cTSCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"906f0aa3fd926b03b6f9ba0c51f77d35124df1343fc870adddf3ec37b36a8aad","last_reissued_at":"2026-05-18T02:41:03.179063Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:41:03.179063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.8099","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":"2026-05-18T02:41:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JQvEfuX+LQ26Uz8pceStSPIZL0+9urD4u6i3O7TnFuIhKOhUPbRReuoxTsjYNXAksgOW2c9DFpxHXiX0cCX7Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:49:24.574570Z"},"content_sha256":"192c75c52322db59dc40e237b4d13d8d8f0fbb5be039fdb45ecc9a4a68cb6995","schema_version":"1.0","event_id":"sha256:192c75c52322db59dc40e237b4d13d8d8f0fbb5be039fdb45ecc9a4a68cb6995"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:SBXQVI75SJVQHNXZXIGFD535GU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Ideal structure of the C*-algebra of Thompson group T","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Collin Bleak, Kate Juschenko","submitted_at":"2014-09-29T12:45:10Z","abstract_excerpt":"In a recent paper Uffe Haagerup and Kristian Knudsen Olesen show that for Richard Thompson's group $T$, if there exists a finite set $H$ which can be decomposed as disjoint union of sets $H_1$ and $H_2$ with $\\sum_{g\\in H_1}\\pi(g)=\\sum_{h\\in H_2}\\pi(h)$ and such that the closed ideal generated by $\\sum_{g\\in H_1}\\lambda(g)-\\sum_{h\\in H_2}\\lambda(h)$ coincides with $C^*_\\lambda(T)$, then the Richard Thompson group $F$ is not amenable. In particular, if $C_{\\lambda}^*(T)$ is simple then $F$ is not amenable. Here we prove the converse, namely, if $F$ is not amenable then we can find two sets $H_1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8099","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":"2026-05-18T02:41:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1S4qU0v6qGilXDwr9kCNfHFfSP35pun2czuS0JTCb1kGCQB8hRXsrlWf4geoEaoS0YxRa8PHxs2kqvpACx4vCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-20T11:49:24.577320Z"},"content_sha256":"7b580a2453e77667bcce8a9a298e0d4d81ed768006ce2ea3265ed721736df05a","schema_version":"1.0","event_id":"sha256:7b580a2453e77667bcce8a9a298e0d4d81ed768006ce2ea3265ed721736df05a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SBXQVI75SJVQHNXZXIGFD535GU/bundle.json","state_url":"https://pith.science/pith/SBXQVI75SJVQHNXZXIGFD535GU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SBXQVI75SJVQHNXZXIGFD535GU/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":"2026-05-20T11:49:24Z","links":{"resolver":"https://pith.science/pith/SBXQVI75SJVQHNXZXIGFD535GU","bundle":"https://pith.science/pith/SBXQVI75SJVQHNXZXIGFD535GU/bundle.json","state":"https://pith.science/pith/SBXQVI75SJVQHNXZXIGFD535GU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SBXQVI75SJVQHNXZXIGFD535GU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:SBXQVI75SJVQHNXZXIGFD535GU","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":"8ce6fae064008451c57f560fb4d57e2ce01d8fdbeeaa74df2a2dde8d57502d11","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-09-29T12:45:10Z","title_canon_sha256":"d62850068cffdca549b578d53dbedf816689dcd67eadadc189256409f3cf9f11"},"schema_version":"1.0","source":{"id":"1409.8099","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.8099","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"arxiv_version","alias_value":"1409.8099v2","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.8099","created_at":"2026-05-18T02:41:03Z"},{"alias_kind":"pith_short_12","alias_value":"SBXQVI75SJVQ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_16","alias_value":"SBXQVI75SJVQHNXZ","created_at":"2026-05-18T12:28:49Z"},{"alias_kind":"pith_short_8","alias_value":"SBXQVI75","created_at":"2026-05-18T12:28:49Z"}],"graph_snapshots":[{"event_id":"sha256:7b580a2453e77667bcce8a9a298e0d4d81ed768006ce2ea3265ed721736df05a","target":"graph","created_at":"2026-05-18T02:41:03Z","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":"In a recent paper Uffe Haagerup and Kristian Knudsen Olesen show that for Richard Thompson's group $T$, if there exists a finite set $H$ which can be decomposed as disjoint union of sets $H_1$ and $H_2$ with $\\sum_{g\\in H_1}\\pi(g)=\\sum_{h\\in H_2}\\pi(h)$ and such that the closed ideal generated by $\\sum_{g\\in H_1}\\lambda(g)-\\sum_{h\\in H_2}\\lambda(h)$ coincides with $C^*_\\lambda(T)$, then the Richard Thompson group $F$ is not amenable. In particular, if $C_{\\lambda}^*(T)$ is simple then $F$ is not amenable. Here we prove the converse, namely, if $F$ is not amenable then we can find two sets $H_1","authors_text":"Collin Bleak, Kate Juschenko","cross_cats":["math.DS","math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-09-29T12:45:10Z","title":"Ideal structure of the C*-algebra of Thompson group T"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.8099","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":"sha256:192c75c52322db59dc40e237b4d13d8d8f0fbb5be039fdb45ecc9a4a68cb6995","target":"record","created_at":"2026-05-18T02:41:03Z","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":"8ce6fae064008451c57f560fb4d57e2ce01d8fdbeeaa74df2a2dde8d57502d11","cross_cats_sorted":["math.DS","math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-09-29T12:45:10Z","title_canon_sha256":"d62850068cffdca549b578d53dbedf816689dcd67eadadc189256409f3cf9f11"},"schema_version":"1.0","source":{"id":"1409.8099","kind":"arxiv","version":2}},"canonical_sha256":"906f0aa3fd926b03b6f9ba0c51f77d35124df1343fc870adddf3ec37b36a8aad","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"906f0aa3fd926b03b6f9ba0c51f77d35124df1343fc870adddf3ec37b36a8aad","first_computed_at":"2026-05-18T02:41:03.179063Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:41:03.179063Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AiazodZSdcSWvloQkF0lB4aCIeNKf0Gs0AbiZpyo0s8Z9tf889BaNWeqGDSEcXszeTlBw3ZTWqycBO/87cTSCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:41:03.179574Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.8099","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:192c75c52322db59dc40e237b4d13d8d8f0fbb5be039fdb45ecc9a4a68cb6995","sha256:7b580a2453e77667bcce8a9a298e0d4d81ed768006ce2ea3265ed721736df05a"],"state_sha256":"fdc20fb1c282f17cf0db12ccebdc151bb39b9011a3fd319478e84123d39bf985"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VD04qHFViVRYq9VfKNzdt7PSfjK4flXCG91vlXGDMUCzUnOQm2DTrX1mVTawXKpcrKAVREe8SfY3eu7+LjzECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-20T11:49:24.579417Z","bundle_sha256":"f79c2fd56c2757626c57acca9fe58b6146697392fd094adddb4ce4cf06c0a481"}}