{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:H4TUJEGBGLJYKTNOTNI52B4X3U","short_pith_number":"pith:H4TUJEGB","canonical_record":{"source":{"id":"1006.1145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-06-06T22:30:20Z","cross_cats_sorted":[],"title_canon_sha256":"b031cf53f1e394243c9cfcba184f02dc4e613a50630bda66957a3d34b6650008","abstract_canon_sha256":"0f8145f82dbd4304123728767a20b9ea9527a51ed346be15406b92b279c41473"},"schema_version":"1.0"},"canonical_sha256":"3f274490c132d3854dae9b51dd0797dd23bce797a53d0930eb1589e71f1fee92","source":{"kind":"arxiv","id":"1006.1145","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1145","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1145v2","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1145","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"H4TUJEGBGLJY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H4TUJEGBGLJYKTNO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H4TUJEGB","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:H4TUJEGBGLJYKTNOTNI52B4X3U","target":"record","payload":{"canonical_record":{"source":{"id":"1006.1145","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-06-06T22:30:20Z","cross_cats_sorted":[],"title_canon_sha256":"b031cf53f1e394243c9cfcba184f02dc4e613a50630bda66957a3d34b6650008","abstract_canon_sha256":"0f8145f82dbd4304123728767a20b9ea9527a51ed346be15406b92b279c41473"},"schema_version":"1.0"},"canonical_sha256":"3f274490c132d3854dae9b51dd0797dd23bce797a53d0930eb1589e71f1fee92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:58:02.118431Z","signature_b64":"x48lkbBEesVCz/NVhyFeSnmwwCopc7mAxqbeqxjW0F7Adi2JiGPi28pI30F5wxgIa44PB6zt6bIbcPuuutKwCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3f274490c132d3854dae9b51dd0797dd23bce797a53d0930eb1589e71f1fee92","last_reissued_at":"2026-05-18T02:58:02.117911Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:58:02.117911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1006.1145","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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1X+hR3qDHniFTsYQxOzsrV86OYGu0a5g0wBEySAQDdkUC7+bUmhmZYU4cdtcCYInQ0Xc7VyCSY93Ka1T7h5BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:45:01.151095Z"},"content_sha256":"09ea8b27f79f894a5954448a900d2b5e8693c71c252d1d19ca6ac59a95137ba5","schema_version":"1.0","event_id":"sha256:09ea8b27f79f894a5954448a900d2b5e8693c71c252d1d19ca6ac59a95137ba5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:H4TUJEGBGLJYKTNOTNI52B4X3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Full Groups and Orbit Equivalence in Cantor Dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Konstantin Medynets","submitted_at":"2010-06-06T22:30:20Z","abstract_excerpt":"In this note we consider dynamical systems $(X,G)$ on a Cantor set $X$ satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems $(X_1,G_1)$ and $(X_2,G_2)$ are orbit equivalent if and only if their full groups are isomorphic as abstract groups. This result is a topological version of the well-known Dye's theorem established originally for ergodic measure-preserving actions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1145","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":"2026-05-18T02:58:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OUC8kBOKVjEBUVjP0ixD0lYfpl8zdzYM7cXWTNYV+zi9brE3LqPLpxG1KDnPrPsmRpLwga5FEQMJJ0E/nsHWCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T21:45:01.151453Z"},"content_sha256":"02247e99cddb469c601cd1543e0c44f13d525c8bf57441ad33f1b14d573adc51","schema_version":"1.0","event_id":"sha256:02247e99cddb469c601cd1543e0c44f13d525c8bf57441ad33f1b14d573adc51"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H4TUJEGBGLJYKTNOTNI52B4X3U/bundle.json","state_url":"https://pith.science/pith/H4TUJEGBGLJYKTNOTNI52B4X3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H4TUJEGBGLJYKTNOTNI52B4X3U/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":"2026-06-24T21:45:01Z","links":{"resolver":"https://pith.science/pith/H4TUJEGBGLJYKTNOTNI52B4X3U","bundle":"https://pith.science/pith/H4TUJEGBGLJYKTNOTNI52B4X3U/bundle.json","state":"https://pith.science/pith/H4TUJEGBGLJYKTNOTNI52B4X3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H4TUJEGBGLJYKTNOTNI52B4X3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:H4TUJEGBGLJYKTNOTNI52B4X3U","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":"0f8145f82dbd4304123728767a20b9ea9527a51ed346be15406b92b279c41473","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-06-06T22:30:20Z","title_canon_sha256":"b031cf53f1e394243c9cfcba184f02dc4e613a50630bda66957a3d34b6650008"},"schema_version":"1.0","source":{"id":"1006.1145","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1006.1145","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1006.1145v2","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1006.1145","created_at":"2026-05-18T02:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"H4TUJEGBGLJY","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"H4TUJEGBGLJYKTNO","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"H4TUJEGB","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:02247e99cddb469c601cd1543e0c44f13d525c8bf57441ad33f1b14d573adc51","target":"graph","created_at":"2026-05-18T02:58:02Z","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 note we consider dynamical systems $(X,G)$ on a Cantor set $X$ satisfying some mild technical conditions. The considered class includes, in particular, minimal and transitive aperiodic systems. We prove that two such systems $(X_1,G_1)$ and $(X_2,G_2)$ are orbit equivalent if and only if their full groups are isomorphic as abstract groups. This result is a topological version of the well-known Dye's theorem established originally for ergodic measure-preserving actions.","authors_text":"Konstantin Medynets","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-06-06T22:30:20Z","title":"Full Groups and Orbit Equivalence in Cantor Dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1006.1145","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":"sha256:09ea8b27f79f894a5954448a900d2b5e8693c71c252d1d19ca6ac59a95137ba5","target":"record","created_at":"2026-05-18T02:58:02Z","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":"0f8145f82dbd4304123728767a20b9ea9527a51ed346be15406b92b279c41473","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2010-06-06T22:30:20Z","title_canon_sha256":"b031cf53f1e394243c9cfcba184f02dc4e613a50630bda66957a3d34b6650008"},"schema_version":"1.0","source":{"id":"1006.1145","kind":"arxiv","version":2}},"canonical_sha256":"3f274490c132d3854dae9b51dd0797dd23bce797a53d0930eb1589e71f1fee92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3f274490c132d3854dae9b51dd0797dd23bce797a53d0930eb1589e71f1fee92","first_computed_at":"2026-05-18T02:58:02.117911Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:02.117911Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"x48lkbBEesVCz/NVhyFeSnmwwCopc7mAxqbeqxjW0F7Adi2JiGPi28pI30F5wxgIa44PB6zt6bIbcPuuutKwCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:02.118431Z","signed_message":"canonical_sha256_bytes"},"source_id":"1006.1145","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:09ea8b27f79f894a5954448a900d2b5e8693c71c252d1d19ca6ac59a95137ba5","sha256:02247e99cddb469c601cd1543e0c44f13d525c8bf57441ad33f1b14d573adc51"],"state_sha256":"6b42b25f10c0ac0892f64be2e84ff8526ed408bb68d916447f65842fc6acd2dd"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ItLWSb52wWv6QPr19Wo+IyFFekYhPnVkLz6knAS1N6wYyhXH52hJfnrpQssVJAo8cSjhrJBZ5uZUAOLLhzZ0BQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T21:45:01.153343Z","bundle_sha256":"88206c11fdbd761bbee5fb1f32e972dddec57994135b0247b388674c5e846b08"}}