{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:FCVA5CI4BHA72WRVYLBKDTY7NR","short_pith_number":"pith:FCVA5CI4","canonical_record":{"source":{"id":"1411.4861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T15:15:09Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"9032fc137c7cda906ba0f79cdb72885389ab0b86e7f0c9443b53a03cf38554e4","abstract_canon_sha256":"a0cc254fb5e3d164038eff7ffefac89587b457d285581a666f5d5043ab3b57ef"},"schema_version":"1.0"},"canonical_sha256":"28aa0e891c09c1fd5a35c2c2a1cf1f6c76dae76164f04516c808597b928e69f4","source":{"kind":"arxiv","id":"1411.4861","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4861","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4861v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4861","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"FCVA5CI4BHA7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FCVA5CI4BHA72WRV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FCVA5CI4","created_at":"2026-05-18T12:28:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:FCVA5CI4BHA72WRVYLBKDTY7NR","target":"record","payload":{"canonical_record":{"source":{"id":"1411.4861","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T15:15:09Z","cross_cats_sorted":["math.QA"],"title_canon_sha256":"9032fc137c7cda906ba0f79cdb72885389ab0b86e7f0c9443b53a03cf38554e4","abstract_canon_sha256":"a0cc254fb5e3d164038eff7ffefac89587b457d285581a666f5d5043ab3b57ef"},"schema_version":"1.0"},"canonical_sha256":"28aa0e891c09c1fd5a35c2c2a1cf1f6c76dae76164f04516c808597b928e69f4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:34:51.103832Z","signature_b64":"OKJRtlEtYEmwHmEgA77H7BANu5WWUuLEtzrkBJNYIUne95LR1zxPVvQa3OaBAIG4XLICnjpfKN8YHNn0Q6VoBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"28aa0e891c09c1fd5a35c2c2a1cf1f6c76dae76164f04516c808597b928e69f4","last_reissued_at":"2026-05-18T02:34:51.103358Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:34:51.103358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1411.4861","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":"2026-05-18T02:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AWT/1Rltd+rtk5J676jmBiNLeMSoEQFJIPKZaidRywS5np8LT1f/a4rOR0ogpX19Awx8yF1ISmtycpUem4lqAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:50:29.117041Z"},"content_sha256":"ddee19e5bfcf958b9b745f6e7779893aaf2980114706ea4990d929581d0fa0dc","schema_version":"1.0","event_id":"sha256:ddee19e5bfcf958b9b745f6e7779893aaf2980114706ea4990d929581d0fa0dc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:FCVA5CI4BHA72WRVYLBKDTY7NR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on reduced and von Neumann algebraic free wreath products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.OA","authors_text":"Jonas Wahl","submitted_at":"2014-11-18T15:15:09Z","abstract_excerpt":"In this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\\mathbb G \\wr_* S_N^+$, where $\\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation theory by Lemeux and Tarrago, we prove that $\\mathbb G \\wr_* S_N^+$ is of Kac type whenever $\\mathbb G$ is, and that the reduced version of $\\mathbb G \\wr_* S_N^+$ is simple with unique trace state whenever $N \\geq 8$. Moreover, we prove that the reduced von Neumann algebra of $\\mathbb G \\wr_* S_N^+$ does not have property $\\Gamma$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4861","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":"2026-05-18T02:34:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hv8cKHF/vSGcAt57gDHdoPGkyzbAWAMGGRs3Q73VRK5wetmP5cS+g/RFO9qJJJZJfkUnCc64da88RuEglpgRAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T00:50:29.117399Z"},"content_sha256":"f1548bcdeec4c9b3ea3fb25aa68701c2f2b920184967cbf23b9e3842c34d1079","schema_version":"1.0","event_id":"sha256:f1548bcdeec4c9b3ea3fb25aa68701c2f2b920184967cbf23b9e3842c34d1079"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FCVA5CI4BHA72WRVYLBKDTY7NR/bundle.json","state_url":"https://pith.science/pith/FCVA5CI4BHA72WRVYLBKDTY7NR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FCVA5CI4BHA72WRVYLBKDTY7NR/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":"2026-05-27T00:50:29Z","links":{"resolver":"https://pith.science/pith/FCVA5CI4BHA72WRVYLBKDTY7NR","bundle":"https://pith.science/pith/FCVA5CI4BHA72WRVYLBKDTY7NR/bundle.json","state":"https://pith.science/pith/FCVA5CI4BHA72WRVYLBKDTY7NR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FCVA5CI4BHA72WRVYLBKDTY7NR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:FCVA5CI4BHA72WRVYLBKDTY7NR","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":"a0cc254fb5e3d164038eff7ffefac89587b457d285581a666f5d5043ab3b57ef","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T15:15:09Z","title_canon_sha256":"9032fc137c7cda906ba0f79cdb72885389ab0b86e7f0c9443b53a03cf38554e4"},"schema_version":"1.0","source":{"id":"1411.4861","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1411.4861","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"arxiv_version","alias_value":"1411.4861v1","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1411.4861","created_at":"2026-05-18T02:34:51Z"},{"alias_kind":"pith_short_12","alias_value":"FCVA5CI4BHA7","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_16","alias_value":"FCVA5CI4BHA72WRV","created_at":"2026-05-18T12:28:28Z"},{"alias_kind":"pith_short_8","alias_value":"FCVA5CI4","created_at":"2026-05-18T12:28:28Z"}],"graph_snapshots":[{"event_id":"sha256:f1548bcdeec4c9b3ea3fb25aa68701c2f2b920184967cbf23b9e3842c34d1079","target":"graph","created_at":"2026-05-18T02:34:51Z","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 this paper, we study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\\mathbb G \\wr_* S_N^+$, where $\\mathbb G$ is a compact matrix quantum group. Based on recent result on their corepresentation theory by Lemeux and Tarrago, we prove that $\\mathbb G \\wr_* S_N^+$ is of Kac type whenever $\\mathbb G$ is, and that the reduced version of $\\mathbb G \\wr_* S_N^+$ is simple with unique trace state whenever $N \\geq 8$. Moreover, we prove that the reduced von Neumann algebra of $\\mathbb G \\wr_* S_N^+$ does not have property $\\Gamma$.","authors_text":"Jonas Wahl","cross_cats":["math.QA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T15:15:09Z","title":"A note on reduced and von Neumann algebraic free wreath products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4861","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:ddee19e5bfcf958b9b745f6e7779893aaf2980114706ea4990d929581d0fa0dc","target":"record","created_at":"2026-05-18T02:34:51Z","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":"a0cc254fb5e3d164038eff7ffefac89587b457d285581a666f5d5043ab3b57ef","cross_cats_sorted":["math.QA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-11-18T15:15:09Z","title_canon_sha256":"9032fc137c7cda906ba0f79cdb72885389ab0b86e7f0c9443b53a03cf38554e4"},"schema_version":"1.0","source":{"id":"1411.4861","kind":"arxiv","version":1}},"canonical_sha256":"28aa0e891c09c1fd5a35c2c2a1cf1f6c76dae76164f04516c808597b928e69f4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"28aa0e891c09c1fd5a35c2c2a1cf1f6c76dae76164f04516c808597b928e69f4","first_computed_at":"2026-05-18T02:34:51.103358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:34:51.103358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OKJRtlEtYEmwHmEgA77H7BANu5WWUuLEtzrkBJNYIUne95LR1zxPVvQa3OaBAIG4XLICnjpfKN8YHNn0Q6VoBw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:34:51.103832Z","signed_message":"canonical_sha256_bytes"},"source_id":"1411.4861","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddee19e5bfcf958b9b745f6e7779893aaf2980114706ea4990d929581d0fa0dc","sha256:f1548bcdeec4c9b3ea3fb25aa68701c2f2b920184967cbf23b9e3842c34d1079"],"state_sha256":"7b44f43969d02756929577257067c33ea42f2dde0b05c529453f0428ea3bdaa0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SDUFPRYMXMrgHnjFRe3YSleYMu2F98Xv5HA2773mapxpo+jux5uPPlcW9ckI/6EsuBbdo74nNEMFiu12Hhw1AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T00:50:29.119681Z","bundle_sha256":"00da62697158abf4f55c816fe2b46ead8c76345b1be754942a5685a6fa421288"}}