{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:OL3WPGDJLRJFNSF4GQ3V2VHQDY","short_pith_number":"pith:OL3WPGDJ","canonical_record":{"source":{"id":"2605.22430","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-05-21T12:54:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"6c798cf5a654114a3e4e51bb2172cd9f36f872391bf99f135e95732a74e7119c","abstract_canon_sha256":"0a9c5e5f3eb8ee53a79abf19294cf116b075f0856976438f5f8ef8315f2e718e"},"schema_version":"1.0"},"canonical_sha256":"72f76798695c5256c8bc34375d54f01e2c659c6191a24da4540717df5346cc11","source":{"kind":"arxiv","id":"2605.22430","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22430","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22430v1","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22430","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"OL3WPGDJLRJF","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"OL3WPGDJLRJFNSF4","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"OL3WPGDJ","created_at":"2026-05-22T01:04:42Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:OL3WPGDJLRJFNSF4GQ3V2VHQDY","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22430","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-05-21T12:54:41Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"6c798cf5a654114a3e4e51bb2172cd9f36f872391bf99f135e95732a74e7119c","abstract_canon_sha256":"0a9c5e5f3eb8ee53a79abf19294cf116b075f0856976438f5f8ef8315f2e718e"},"schema_version":"1.0"},"canonical_sha256":"72f76798695c5256c8bc34375d54f01e2c659c6191a24da4540717df5346cc11","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:42.779782Z","signature_b64":"t8X1NsOZU1OlTzCxEd7RwAFhp54uTgw26WxK2AaMpTpOtMWhcAnbeHOQKcD70hvc13E7gnDjIGnd3jwaTtqLDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72f76798695c5256c8bc34375d54f01e2c659c6191a24da4540717df5346cc11","last_reissued_at":"2026-05-22T01:04:42.778980Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:42.778980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22430","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":"2026-05-22T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vAJEUZLW63G05+Lj6JQj4KYLzWmk4G2bOvbFhfbK2qSI/b83/9rHFKueVWw1XT2PINTWjae0sSKTvW04cJNhAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:12:49.492629Z"},"content_sha256":"ba66af3bee404b11db35bf65374a5612cc0a891e64cc9d5948215ae5d67051ca","schema_version":"1.0","event_id":"sha256:ba66af3bee404b11db35bf65374a5612cc0a891e64cc9d5948215ae5d67051ca"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:OL3WPGDJLRJFNSF4GQ3V2VHQDY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stabilizer Subgroups and the Simplicity of Reduced Crossed Products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.OA","authors_text":"Mehrdad Kalantar, Yair Hartman","submitted_at":"2026-05-21T12:54:41Z","abstract_excerpt":"Given a minimal action $G\\curvearrowright X$ of a countable group $G$ on a compact space $X$, we prove that if the reduced crossed product $G\\ltimes_rC(X)$ is simple, then there exists a point whose stabilizer subgroup has trivial amenable radical. As a consequence, we give a complete characterization of the simplicity of the reduced crossed product of minimal actions of countable linear groups, hyperbolic groups, and, more generally, for groups with countably many amenable subgroups. This answers a question of Ozawa (2014) for these classes of groups. Furthermore, in the case of an infinite u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22430","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22430/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":"2026-05-22T01:04:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9LqqfF/KDrwL6vcbds+DrsPScVDPoB2KhYMsIa3tZ08uoeX2S8tOZrFJ8mebie7gCnLcxTdKbHb7JI00gPNXAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T12:12:49.493463Z"},"content_sha256":"a75446a9c548df5136d706f0ed7fe07b6c1be1881d6a33e02d84a603ea2ac6e1","schema_version":"1.0","event_id":"sha256:a75446a9c548df5136d706f0ed7fe07b6c1be1881d6a33e02d84a603ea2ac6e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY/bundle.json","state_url":"https://pith.science/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY/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":"2026-06-10T12:12:49Z","links":{"resolver":"https://pith.science/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY","bundle":"https://pith.science/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY/bundle.json","state":"https://pith.science/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OL3WPGDJLRJFNSF4GQ3V2VHQDY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:OL3WPGDJLRJFNSF4GQ3V2VHQDY","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":"0a9c5e5f3eb8ee53a79abf19294cf116b075f0856976438f5f8ef8315f2e718e","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-05-21T12:54:41Z","title_canon_sha256":"6c798cf5a654114a3e4e51bb2172cd9f36f872391bf99f135e95732a74e7119c"},"schema_version":"1.0","source":{"id":"2605.22430","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22430","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22430v1","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22430","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"pith_short_12","alias_value":"OL3WPGDJLRJF","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"pith_short_16","alias_value":"OL3WPGDJLRJFNSF4","created_at":"2026-05-22T01:04:42Z"},{"alias_kind":"pith_short_8","alias_value":"OL3WPGDJ","created_at":"2026-05-22T01:04:42Z"}],"graph_snapshots":[{"event_id":"sha256:a75446a9c548df5136d706f0ed7fe07b6c1be1881d6a33e02d84a603ea2ac6e1","target":"graph","created_at":"2026-05-22T01:04:42Z","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/2605.22430/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Given a minimal action $G\\curvearrowright X$ of a countable group $G$ on a compact space $X$, we prove that if the reduced crossed product $G\\ltimes_rC(X)$ is simple, then there exists a point whose stabilizer subgroup has trivial amenable radical. As a consequence, we give a complete characterization of the simplicity of the reduced crossed product of minimal actions of countable linear groups, hyperbolic groups, and, more generally, for groups with countably many amenable subgroups. This answers a question of Ozawa (2014) for these classes of groups. Furthermore, in the case of an infinite u","authors_text":"Mehrdad Kalantar, Yair Hartman","cross_cats":["math.GR"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-05-21T12:54:41Z","title":"Stabilizer Subgroups and the Simplicity of Reduced Crossed Products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22430","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:ba66af3bee404b11db35bf65374a5612cc0a891e64cc9d5948215ae5d67051ca","target":"record","created_at":"2026-05-22T01:04:42Z","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":"0a9c5e5f3eb8ee53a79abf19294cf116b075f0856976438f5f8ef8315f2e718e","cross_cats_sorted":["math.GR"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.OA","submitted_at":"2026-05-21T12:54:41Z","title_canon_sha256":"6c798cf5a654114a3e4e51bb2172cd9f36f872391bf99f135e95732a74e7119c"},"schema_version":"1.0","source":{"id":"2605.22430","kind":"arxiv","version":1}},"canonical_sha256":"72f76798695c5256c8bc34375d54f01e2c659c6191a24da4540717df5346cc11","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"72f76798695c5256c8bc34375d54f01e2c659c6191a24da4540717df5346cc11","first_computed_at":"2026-05-22T01:04:42.778980Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:42.778980Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t8X1NsOZU1OlTzCxEd7RwAFhp54uTgw26WxK2AaMpTpOtMWhcAnbeHOQKcD70hvc13E7gnDjIGnd3jwaTtqLDw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:42.779782Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22430","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba66af3bee404b11db35bf65374a5612cc0a891e64cc9d5948215ae5d67051ca","sha256:a75446a9c548df5136d706f0ed7fe07b6c1be1881d6a33e02d84a603ea2ac6e1"],"state_sha256":"5851d3886c626f9211a2b7f4701321b5bb00bd34f3ab2d222cf61e56bdd9c10e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cFaqfq2gOVY1f8AckkrMH9NNjzQCGnpFNkR4wMBDNKqA+B1VAJkcVnEjd9EkECSXEoMIY9UYlFkn2srAMRoaDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T12:12:49.498021Z","bundle_sha256":"c0e96d292774781b8337558810066263a60c52695e86adb62391e46b06c507ad"}}