{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:OUHX63TFAXFTDBHX57ZAIRR3A5","short_pith_number":"pith:OUHX63TF","canonical_record":{"source":{"id":"1104.1216","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-04-06T23:51:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"416cc2a20a843075d90e76ad601635f6b327ea1092f44a8f9e4cfbd592a80de5","abstract_canon_sha256":"3e12fbc867936eef989984745badb732799463a6c3585424f1d86607a1987074"},"schema_version":"1.0"},"canonical_sha256":"750f7f6e6505cb3184f7eff204463b074986d4de17e27d687c48c25a7148a680","source":{"kind":"arxiv","id":"1104.1216","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1216","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1216v2","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1216","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"OUHX63TFAXFT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OUHX63TFAXFTDBHX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OUHX63TF","created_at":"2026-05-18T12:26:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:OUHX63TFAXFTDBHX57ZAIRR3A5","target":"record","payload":{"canonical_record":{"source":{"id":"1104.1216","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-04-06T23:51:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"416cc2a20a843075d90e76ad601635f6b327ea1092f44a8f9e4cfbd592a80de5","abstract_canon_sha256":"3e12fbc867936eef989984745badb732799463a6c3585424f1d86607a1987074"},"schema_version":"1.0"},"canonical_sha256":"750f7f6e6505cb3184f7eff204463b074986d4de17e27d687c48c25a7148a680","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:10.433595Z","signature_b64":"J0yPMFldmYNrzAidWrMb4MIeIMyfO9UVcE2Ag+lv14wY1SygQCkH/Pr7xoRO18Q7fZ7LW+4i4ayR6aiZiOMQCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"750f7f6e6505cb3184f7eff204463b074986d4de17e27d687c48c25a7148a680","last_reissued_at":"2026-05-18T04:21:10.432938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:10.432938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1104.1216","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":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ekuy1iBAMA2Y48cMZ8dIW+uTaeoRKOAlWZr8zvLnXEdrMODxvoCp1SEPv26E8wT65WzNMvgg/GQp4ORlRwiJDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:44:24.987817Z"},"content_sha256":"a582cc419f6c5308a089c16e8518d35925f25f333d5e9357cae16d916c99478c","schema_version":"1.0","event_id":"sha256:a582cc419f6c5308a089c16e8518d35925f25f333d5e9357cae16d916c99478c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:OUHX63TFAXFTDBHX57ZAIRR3A5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Residually finite actions and crossed products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.OA","authors_text":"David Kerr, Piotr W. Nowak","submitted_at":"2011-04-06T23:51:16Z","abstract_excerpt":"We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., is an MF algebra."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1216","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":"2026-05-18T04:21:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mx4FE/no7Cgq8GB+cHngh2pxnTWjlrizRrXiquoKKU8yVdiKSM1XmxtrBdlQQm0s1tKa6+Yz6x+LSTY4BRZDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:44:24.988575Z"},"content_sha256":"cdc447bc786b858fc12809328f74cccd365c128402dc34f22b7fcf0fd3efd50f","schema_version":"1.0","event_id":"sha256:cdc447bc786b858fc12809328f74cccd365c128402dc34f22b7fcf0fd3efd50f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/OUHX63TFAXFTDBHX57ZAIRR3A5/bundle.json","state_url":"https://pith.science/pith/OUHX63TFAXFTDBHX57ZAIRR3A5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/OUHX63TFAXFTDBHX57ZAIRR3A5/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":"2026-05-30T02:44:24Z","links":{"resolver":"https://pith.science/pith/OUHX63TFAXFTDBHX57ZAIRR3A5","bundle":"https://pith.science/pith/OUHX63TFAXFTDBHX57ZAIRR3A5/bundle.json","state":"https://pith.science/pith/OUHX63TFAXFTDBHX57ZAIRR3A5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/OUHX63TFAXFTDBHX57ZAIRR3A5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:OUHX63TFAXFTDBHX57ZAIRR3A5","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":"3e12fbc867936eef989984745badb732799463a6c3585424f1d86607a1987074","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-04-06T23:51:16Z","title_canon_sha256":"416cc2a20a843075d90e76ad601635f6b327ea1092f44a8f9e4cfbd592a80de5"},"schema_version":"1.0","source":{"id":"1104.1216","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.1216","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"arxiv_version","alias_value":"1104.1216v2","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.1216","created_at":"2026-05-18T04:21:10Z"},{"alias_kind":"pith_short_12","alias_value":"OUHX63TFAXFT","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"OUHX63TFAXFTDBHX","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"OUHX63TF","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:cdc447bc786b858fc12809328f74cccd365c128402dc34f22b7fcf0fd3efd50f","target":"graph","created_at":"2026-05-18T04:21:10Z","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":"We study a notion of residual finiteness for continuous actions of discrete groups on compact Hausdorff spaces and how it relates to the existence of norm microstates for the reduced crossed product. Our main result asserts that an action of a free group on a zero-dimensional compact metrizable space is residually finite if and only if its reduced crossed product admits norm microstates, i.e., is an MF algebra.","authors_text":"David Kerr, Piotr W. Nowak","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-04-06T23:51:16Z","title":"Residually finite actions and crossed products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1216","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:a582cc419f6c5308a089c16e8518d35925f25f333d5e9357cae16d916c99478c","target":"record","created_at":"2026-05-18T04:21:10Z","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":"3e12fbc867936eef989984745badb732799463a6c3585424f1d86607a1987074","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2011-04-06T23:51:16Z","title_canon_sha256":"416cc2a20a843075d90e76ad601635f6b327ea1092f44a8f9e4cfbd592a80de5"},"schema_version":"1.0","source":{"id":"1104.1216","kind":"arxiv","version":2}},"canonical_sha256":"750f7f6e6505cb3184f7eff204463b074986d4de17e27d687c48c25a7148a680","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"750f7f6e6505cb3184f7eff204463b074986d4de17e27d687c48c25a7148a680","first_computed_at":"2026-05-18T04:21:10.432938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:21:10.432938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J0yPMFldmYNrzAidWrMb4MIeIMyfO9UVcE2Ag+lv14wY1SygQCkH/Pr7xoRO18Q7fZ7LW+4i4ayR6aiZiOMQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:21:10.433595Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.1216","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a582cc419f6c5308a089c16e8518d35925f25f333d5e9357cae16d916c99478c","sha256:cdc447bc786b858fc12809328f74cccd365c128402dc34f22b7fcf0fd3efd50f"],"state_sha256":"862217bdfa52e22049b25fbf8516a099752b9e58790166bb39b3f7cc2fda2e30"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iEYBcVYXOsguH4FpnYum1maOuIvnkDfy4xoxMnfPOam2bqe2TuV+h8ihUpcDVPqCyfFaKiFoOMz2//DukTA/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:44:24.991920Z","bundle_sha256":"feff0c847b1544daef003dd30f6446a5c61cd6825982387bdab2ff89179b0c65"}}