{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:AXHIPPJW3CRUXGBFERLFQRL4SK","short_pith_number":"pith:AXHIPPJW","canonical_record":{"source":{"id":"1205.4649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-21T16:23:48Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"50492a30266ddab65b034a9e9a5c60d99cd2e595ddb358f680d665d10a8d27f5","abstract_canon_sha256":"c671f2aaf230f4a5abc16f648400e4c7c71d59ca6d713ac8f30a6a1334a1dd75"},"schema_version":"1.0"},"canonical_sha256":"05ce87bd36d8a34b9825245658457c928aec9b9414ba341ce7fecf71808eb4b3","source":{"kind":"arxiv","id":"1205.4649","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4649","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4649v1","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4649","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"AXHIPPJW3CRU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AXHIPPJW3CRUXGBF","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AXHIPPJW","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:AXHIPPJW3CRUXGBFERLFQRL4SK","target":"record","payload":{"canonical_record":{"source":{"id":"1205.4649","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-21T16:23:48Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"50492a30266ddab65b034a9e9a5c60d99cd2e595ddb358f680d665d10a8d27f5","abstract_canon_sha256":"c671f2aaf230f4a5abc16f648400e4c7c71d59ca6d713ac8f30a6a1334a1dd75"},"schema_version":"1.0"},"canonical_sha256":"05ce87bd36d8a34b9825245658457c928aec9b9414ba341ce7fecf71808eb4b3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:57:53.546160Z","signature_b64":"ucwLhtSsJGATt9IdG5Odr3etUhz+yWtUSurVJZKZz8ac571QC9ENVHI7u3f5SZnP5jF4gVkXgAEkflf5ntQuAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05ce87bd36d8a34b9825245658457c928aec9b9414ba341ce7fecf71808eb4b3","last_reissued_at":"2026-05-18T02:57:53.545644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:57:53.545644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.4649","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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LGUsX9P9Yb/MTtTMpK/3hA4uBEpKnFVpDNYdU1zyeQ+cW7cllM3g3flmRRKOS9EW6ku/FnRO7HXIV+FSNzFCCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:37:10.098001Z"},"content_sha256":"1bb10548f0c24b4387ddf3bedc9d62d932edf89d465ab089a237544e38f6c470","schema_version":"1.0","event_id":"sha256:1bb10548f0c24b4387ddf3bedc9d62d932edf89d465ab089a237544e38f6c470"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:AXHIPPJW3CRUXGBFERLFQRL4SK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"New C*-completions of discrete groups and related spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Erik Guentner, Nathanial P. Brown","submitted_at":"2012-05-21T16:23:48Z","abstract_excerpt":"Let $\\Gamma$ be a discrete group. To every ideal in $\\ell^{\\infty}(\\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general framework we develop unifies some classical results and leads to new insights. For example, we give the first C$^*$-algebraic characterization of a-T-menability; a new characterization of property (T); new examples of \"exotic\" quantum groups; and, after extending our construction to transformation groupoids, we improve and simplify a recent result of Douglas an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4649","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":"2026-05-18T02:57:53Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DHNFo40ahesry83bsup4njSpfDOtCwkAeJENqi8dpfy2TkvzTIpi8LEnSMTg/eQ2LiNV7AxqVoov9dLYAO11CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T00:37:10.098419Z"},"content_sha256":"d6763e6285c313d1b1eee9f72b67eb2566bc783b15265018233d481822be6afe","schema_version":"1.0","event_id":"sha256:d6763e6285c313d1b1eee9f72b67eb2566bc783b15265018233d481822be6afe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AXHIPPJW3CRUXGBFERLFQRL4SK/bundle.json","state_url":"https://pith.science/pith/AXHIPPJW3CRUXGBFERLFQRL4SK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AXHIPPJW3CRUXGBFERLFQRL4SK/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":"2026-06-23T00:37:10Z","links":{"resolver":"https://pith.science/pith/AXHIPPJW3CRUXGBFERLFQRL4SK","bundle":"https://pith.science/pith/AXHIPPJW3CRUXGBFERLFQRL4SK/bundle.json","state":"https://pith.science/pith/AXHIPPJW3CRUXGBFERLFQRL4SK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AXHIPPJW3CRUXGBFERLFQRL4SK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:AXHIPPJW3CRUXGBFERLFQRL4SK","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":"c671f2aaf230f4a5abc16f648400e4c7c71d59ca6d713ac8f30a6a1334a1dd75","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-21T16:23:48Z","title_canon_sha256":"50492a30266ddab65b034a9e9a5c60d99cd2e595ddb358f680d665d10a8d27f5"},"schema_version":"1.0","source":{"id":"1205.4649","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4649","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4649v1","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4649","created_at":"2026-05-18T02:57:53Z"},{"alias_kind":"pith_short_12","alias_value":"AXHIPPJW3CRU","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"AXHIPPJW3CRUXGBF","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"AXHIPPJW","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:d6763e6285c313d1b1eee9f72b67eb2566bc783b15265018233d481822be6afe","target":"graph","created_at":"2026-05-18T02:57:53Z","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":"Let $\\Gamma$ be a discrete group. To every ideal in $\\ell^{\\infty}(\\G)$ we associate a C$^*$-algebra completion of the group ring that encapsulates the unitary representations with matrix coefficients belonging to the ideal. The general framework we develop unifies some classical results and leads to new insights. For example, we give the first C$^*$-algebraic characterization of a-T-menability; a new characterization of property (T); new examples of \"exotic\" quantum groups; and, after extending our construction to transformation groupoids, we improve and simplify a recent result of Douglas an","authors_text":"Erik Guentner, Nathanial P. Brown","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-21T16:23:48Z","title":"New C*-completions of discrete groups and related spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4649","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":"sha256:1bb10548f0c24b4387ddf3bedc9d62d932edf89d465ab089a237544e38f6c470","target":"record","created_at":"2026-05-18T02:57:53Z","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":"c671f2aaf230f4a5abc16f648400e4c7c71d59ca6d713ac8f30a6a1334a1dd75","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2012-05-21T16:23:48Z","title_canon_sha256":"50492a30266ddab65b034a9e9a5c60d99cd2e595ddb358f680d665d10a8d27f5"},"schema_version":"1.0","source":{"id":"1205.4649","kind":"arxiv","version":1}},"canonical_sha256":"05ce87bd36d8a34b9825245658457c928aec9b9414ba341ce7fecf71808eb4b3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"05ce87bd36d8a34b9825245658457c928aec9b9414ba341ce7fecf71808eb4b3","first_computed_at":"2026-05-18T02:57:53.545644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:57:53.545644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ucwLhtSsJGATt9IdG5Odr3etUhz+yWtUSurVJZKZz8ac571QC9ENVHI7u3f5SZnP5jF4gVkXgAEkflf5ntQuAA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:57:53.546160Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4649","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1bb10548f0c24b4387ddf3bedc9d62d932edf89d465ab089a237544e38f6c470","sha256:d6763e6285c313d1b1eee9f72b67eb2566bc783b15265018233d481822be6afe"],"state_sha256":"aaf2b2b2ba228a9a6bbd117cf524247b067414ebe71a5489f3bcacb5faa574f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nuU+1ktCa+A4IKwGUD1jxHqz2NacZZsn4e/9Z8/ZuQwrR14ntCiEsxjnwUcSoTQWe0V6ZW6Mx31Wt64zF36rBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T00:37:10.100510Z","bundle_sha256":"edd537f962190034532660f262506ebdc3e66d2efd351b55a0af575fa518658f"}}