{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:BAI6JIKUZRSPF3CXAZNLSACHWM","short_pith_number":"pith:BAI6JIKU","canonical_record":{"source":{"id":"2405.04343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-05-07T14:16:33Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cfcac2a045a0bd9454d3caeb94263ab2052b0c9212ef3b8b292f427a43328cb0","abstract_canon_sha256":"e94de1dfd67a21b8c445652fbc8c90c749c8876fdfe69b7e726813334deed7e3"},"schema_version":"1.0"},"canonical_sha256":"0811e4a154cc64f2ec57065ab90047b32cfc6a994b4a8602f59e5c8068ca734e","source":{"kind":"arxiv","id":"2405.04343","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.04343","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"2405.04343v1","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04343","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"BAI6JIKUZRSP","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"pith_short_16","alias_value":"BAI6JIKUZRSPF3CX","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"pith_short_8","alias_value":"BAI6JIKU","created_at":"2026-07-05T08:16:35Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:BAI6JIKUZRSPF3CXAZNLSACHWM","target":"record","payload":{"canonical_record":{"source":{"id":"2405.04343","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-05-07T14:16:33Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"cfcac2a045a0bd9454d3caeb94263ab2052b0c9212ef3b8b292f427a43328cb0","abstract_canon_sha256":"e94de1dfd67a21b8c445652fbc8c90c749c8876fdfe69b7e726813334deed7e3"},"schema_version":"1.0"},"canonical_sha256":"0811e4a154cc64f2ec57065ab90047b32cfc6a994b4a8602f59e5c8068ca734e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:16:35.772074Z","signature_b64":"+vUS5+QmQOCUgGgVq6ascJL0WVN2SB5wOJlcOite5LdqYud7pl2zd46Y6YjENPdKTqx/VWhmLVsPvuc2yRl0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0811e4a154cc64f2ec57065ab90047b32cfc6a994b4a8602f59e5c8068ca734e","last_reissued_at":"2026-07-05T08:16:35.771629Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:16:35.771629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2405.04343","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":"2026-07-05T08:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gX+6bNTsb7PZfA4yarwL+/KTZHmdusTtHIhaftmVqcKjKDbv6zh4D3aSdMKvDJ1CyjDPy2M3Gw6mNsxqlYZ0DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T05:52:52.729959Z"},"content_sha256":"8f753c8be9ea256ffcc7ab12263613352cb02cbda96b7a65f8cd317a61dd60d4","schema_version":"1.0","event_id":"sha256:8f753c8be9ea256ffcc7ab12263613352cb02cbda96b7a65f8cd317a61dd60d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:BAI6JIKUZRSPF3CXAZNLSACHWM","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Essential freeness, allostery and $\\mathcal{Z}$-stability of crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"Eusebio Gardella, Grigoris Kopsacheilis, Petr Naryshkin, Rafaela Gesing, Shirly Geffen","submitted_at":"2024-05-07T14:16:33Z","abstract_excerpt":"We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are simple, separable, unital, nuclear and satisfy the UCT: these properties are equivalent to the combination of minimality and topological freeness, and the challenge in this context is establishing $\\mathcal{Z}$-stability. While most of the existing results in this direction assume freeness of the action, there exist numerous natural examples of minimal, topologically free (but not free) actions whose crossed products ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04343","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/2405.04343/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":"2026-07-05T08:16:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8oMGNn5ZncCN314/D6SGI0LU6gkSlHAHutPUu5JalQnT3IU9DQLvvn3Zy0ul2GfRFULhOKsAzI9J7/z+Jp53DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T05:52:52.730754Z"},"content_sha256":"19f4abe3f495ebc6b74b9ccef083fb591381a4c91b4fd2a2f45166dcc1325ca9","schema_version":"1.0","event_id":"sha256:19f4abe3f495ebc6b74b9ccef083fb591381a4c91b4fd2a2f45166dcc1325ca9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BAI6JIKUZRSPF3CXAZNLSACHWM/bundle.json","state_url":"https://pith.science/pith/BAI6JIKUZRSPF3CXAZNLSACHWM/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BAI6JIKUZRSPF3CXAZNLSACHWM/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":"2026-08-10T05:52:52Z","links":{"resolver":"https://pith.science/pith/BAI6JIKUZRSPF3CXAZNLSACHWM","bundle":"https://pith.science/pith/BAI6JIKUZRSPF3CXAZNLSACHWM/bundle.json","state":"https://pith.science/pith/BAI6JIKUZRSPF3CXAZNLSACHWM/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BAI6JIKUZRSPF3CXAZNLSACHWM/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:BAI6JIKUZRSPF3CXAZNLSACHWM","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":"e94de1dfd67a21b8c445652fbc8c90c749c8876fdfe69b7e726813334deed7e3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-05-07T14:16:33Z","title_canon_sha256":"cfcac2a045a0bd9454d3caeb94263ab2052b0c9212ef3b8b292f427a43328cb0"},"schema_version":"1.0","source":{"id":"2405.04343","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.04343","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"arxiv_version","alias_value":"2405.04343v1","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.04343","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"pith_short_12","alias_value":"BAI6JIKUZRSP","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"pith_short_16","alias_value":"BAI6JIKUZRSPF3CX","created_at":"2026-07-05T08:16:35Z"},{"alias_kind":"pith_short_8","alias_value":"BAI6JIKU","created_at":"2026-07-05T08:16:35Z"}],"graph_snapshots":[{"event_id":"sha256:19f4abe3f495ebc6b74b9ccef083fb591381a4c91b4fd2a2f45166dcc1325ca9","target":"graph","created_at":"2026-07-05T08:16:35Z","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/2405.04343/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We explore classifiability of crossed products of actions of countable amenable groups on compact, metrizable spaces. It is completely understood when such crossed products are simple, separable, unital, nuclear and satisfy the UCT: these properties are equivalent to the combination of minimality and topological freeness, and the challenge in this context is establishing $\\mathcal{Z}$-stability. While most of the existing results in this direction assume freeness of the action, there exist numerous natural examples of minimal, topologically free (but not free) actions whose crossed products ar","authors_text":"Eusebio Gardella, Grigoris Kopsacheilis, Petr Naryshkin, Rafaela Gesing, Shirly Geffen","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-05-07T14:16:33Z","title":"Essential freeness, allostery and $\\mathcal{Z}$-stability of crossed products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.04343","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":"sha256:8f753c8be9ea256ffcc7ab12263613352cb02cbda96b7a65f8cd317a61dd60d4","target":"record","created_at":"2026-07-05T08:16:35Z","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":"e94de1dfd67a21b8c445652fbc8c90c749c8876fdfe69b7e726813334deed7e3","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2024-05-07T14:16:33Z","title_canon_sha256":"cfcac2a045a0bd9454d3caeb94263ab2052b0c9212ef3b8b292f427a43328cb0"},"schema_version":"1.0","source":{"id":"2405.04343","kind":"arxiv","version":1}},"canonical_sha256":"0811e4a154cc64f2ec57065ab90047b32cfc6a994b4a8602f59e5c8068ca734e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0811e4a154cc64f2ec57065ab90047b32cfc6a994b4a8602f59e5c8068ca734e","first_computed_at":"2026-07-05T08:16:35.771629Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:16:35.771629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+vUS5+QmQOCUgGgVq6ascJL0WVN2SB5wOJlcOite5LdqYud7pl2zd46Y6YjENPdKTqx/VWhmLVsPvuc2yRl0CA==","signature_status":"signed_v1","signed_at":"2026-07-05T08:16:35.772074Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.04343","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8f753c8be9ea256ffcc7ab12263613352cb02cbda96b7a65f8cd317a61dd60d4","sha256:19f4abe3f495ebc6b74b9ccef083fb591381a4c91b4fd2a2f45166dcc1325ca9"],"state_sha256":"4504f9756519865861d247b7b44b21c6e80596b08b93c43c4ae67be1fe85f702"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"unAH0wqPg3JneUNb0hlk11DrpQv1Rmp9c3M0oaHjsS4n+38Z1RjY3YhJIxtKMoyn8ULyuTg/xuXTNk7tpOCiBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T05:52:52.780461Z","bundle_sha256":"c8ca2dd69799be8465ef8d53cd1306da0cf7ff4cf02055a9544d02b5f5cd12cb"}}