{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:7OCE2NPHIEIXWOZIQAIVEMH7O6","short_pith_number":"pith:7OCE2NPH","canonical_record":{"source":{"id":"1508.01766","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-07T17:37:59Z","cross_cats_sorted":[],"title_canon_sha256":"8f5b4ab0862de55a7e4f15cec5299d353e329316af59c703922c0bf1d98bab2f","abstract_canon_sha256":"c5e0c1c628934bfa46af0444ef84ba4293630eeea942510e9b0bd4cece68a712"},"schema_version":"1.0"},"canonical_sha256":"fb844d35e741117b3b2880115230ff779c282959ed0cb960cf3bf5fdcb0b8ae5","source":{"kind":"arxiv","id":"1508.01766","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01766","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01766v3","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01766","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"7OCE2NPHIEIX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OCE2NPHIEIXWOZI","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OCE2NPH","created_at":"2026-05-18T12:29:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:7OCE2NPHIEIXWOZIQAIVEMH7O6","target":"record","payload":{"canonical_record":{"source":{"id":"1508.01766","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-07T17:37:59Z","cross_cats_sorted":[],"title_canon_sha256":"8f5b4ab0862de55a7e4f15cec5299d353e329316af59c703922c0bf1d98bab2f","abstract_canon_sha256":"c5e0c1c628934bfa46af0444ef84ba4293630eeea942510e9b0bd4cece68a712"},"schema_version":"1.0"},"canonical_sha256":"fb844d35e741117b3b2880115230ff779c282959ed0cb960cf3bf5fdcb0b8ae5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:44:28.246476Z","signature_b64":"pW/acpgbJoIInuljLYl92dd001qKkUzSVRwEYZ6mCliOqli7MoPKC56+t/3rfsK6QhnIi7g3GvCK/lmr/JWaAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb844d35e741117b3b2880115230ff779c282959ed0cb960cf3bf5fdcb0b8ae5","last_reissued_at":"2026-05-18T00:44:28.245901Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:44:28.245901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.01766","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ffNuZWAQMwRBatiiE5cI+pJpl5+n2IaNn6I3lZ/x62nygA6QWjIvxAfJncGv4YmxRjwqRjg29hmHw/aiO0H8DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:07:37.554405Z"},"content_sha256":"08a094b662f52c892029e59df9ed91708baceaf21ae0a13e9a414770d108fc9a","schema_version":"1.0","event_id":"sha256:08a094b662f52c892029e59df9ed91708baceaf21ae0a13e9a414770d108fc9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:7OCE2NPHIEIXWOZIQAIVEMH7O6","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Virtual Conjugacy of Generalized Odometers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Konstantin Medynets, Mar\\'ia Isabel Cortez","submitted_at":"2015-08-07T17:37:59Z","abstract_excerpt":"The paper is focused on the study of continuous orbit equivalence for generalized odometers (profinite actions). We show that two generalized odometers are continuously orbit equivalent if and only if the acting groups have finite index subgroups (having the same index) whose actions are piecewise conjugate. This result extends M.~Boyle's flip-conjugacy theorem originally established for $\\mathbb Z$-actions. As a corollary we obtain a dynamical classification of the restricted isomorphism between generalized Bunce-Deddens $C^*$-algebras. We also show that the full group associated with a gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01766","kind":"arxiv","version":3},"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":"2026-05-18T00:44:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sFi2nYccVemuQ/cgSqvmXp3DuLsTwCZLxY5FPqBCBfoYqa43edOF64nCLsg9DkxEaRHWXyinKtICKETLj448Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T18:07:37.554758Z"},"content_sha256":"98a58c6b7a79d3b4a4b1690d2a3b34ca20661e7886f1ef006a95dde6f01b1e9a","schema_version":"1.0","event_id":"sha256:98a58c6b7a79d3b4a4b1690d2a3b34ca20661e7886f1ef006a95dde6f01b1e9a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6/bundle.json","state_url":"https://pith.science/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6/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":"2026-06-24T18:07:37Z","links":{"resolver":"https://pith.science/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6","bundle":"https://pith.science/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6/bundle.json","state":"https://pith.science/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7OCE2NPHIEIXWOZIQAIVEMH7O6/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:7OCE2NPHIEIXWOZIQAIVEMH7O6","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":"c5e0c1c628934bfa46af0444ef84ba4293630eeea942510e9b0bd4cece68a712","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-07T17:37:59Z","title_canon_sha256":"8f5b4ab0862de55a7e4f15cec5299d353e329316af59c703922c0bf1d98bab2f"},"schema_version":"1.0","source":{"id":"1508.01766","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01766","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01766v3","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01766","created_at":"2026-05-18T00:44:28Z"},{"alias_kind":"pith_short_12","alias_value":"7OCE2NPHIEIX","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_16","alias_value":"7OCE2NPHIEIXWOZI","created_at":"2026-05-18T12:29:10Z"},{"alias_kind":"pith_short_8","alias_value":"7OCE2NPH","created_at":"2026-05-18T12:29:10Z"}],"graph_snapshots":[{"event_id":"sha256:98a58c6b7a79d3b4a4b1690d2a3b34ca20661e7886f1ef006a95dde6f01b1e9a","target":"graph","created_at":"2026-05-18T00:44:28Z","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":"The paper is focused on the study of continuous orbit equivalence for generalized odometers (profinite actions). We show that two generalized odometers are continuously orbit equivalent if and only if the acting groups have finite index subgroups (having the same index) whose actions are piecewise conjugate. This result extends M.~Boyle's flip-conjugacy theorem originally established for $\\mathbb Z$-actions. As a corollary we obtain a dynamical classification of the restricted isomorphism between generalized Bunce-Deddens $C^*$-algebras. We also show that the full group associated with a gener","authors_text":"Konstantin Medynets, Mar\\'ia Isabel Cortez","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-07T17:37:59Z","title":"On Virtual Conjugacy of Generalized Odometers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01766","kind":"arxiv","version":3},"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":"sha256:08a094b662f52c892029e59df9ed91708baceaf21ae0a13e9a414770d108fc9a","target":"record","created_at":"2026-05-18T00:44:28Z","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":"c5e0c1c628934bfa46af0444ef84ba4293630eeea942510e9b0bd4cece68a712","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-07T17:37:59Z","title_canon_sha256":"8f5b4ab0862de55a7e4f15cec5299d353e329316af59c703922c0bf1d98bab2f"},"schema_version":"1.0","source":{"id":"1508.01766","kind":"arxiv","version":3}},"canonical_sha256":"fb844d35e741117b3b2880115230ff779c282959ed0cb960cf3bf5fdcb0b8ae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb844d35e741117b3b2880115230ff779c282959ed0cb960cf3bf5fdcb0b8ae5","first_computed_at":"2026-05-18T00:44:28.245901Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:44:28.245901Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pW/acpgbJoIInuljLYl92dd001qKkUzSVRwEYZ6mCliOqli7MoPKC56+t/3rfsK6QhnIi7g3GvCK/lmr/JWaAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:44:28.246476Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01766","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a094b662f52c892029e59df9ed91708baceaf21ae0a13e9a414770d108fc9a","sha256:98a58c6b7a79d3b4a4b1690d2a3b34ca20661e7886f1ef006a95dde6f01b1e9a"],"state_sha256":"4c80209ea0993c68f5b9fd7e02cb746b87847814ab38e877571a78be6f8ed666"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GEgydpYpd2Wh+4xurhXQc0qCHQjSm9ZbZroFHFiUBAxuBimEUPaQ3zD17Fg0ltFUDFpGTzHIbVGjhFDNO4rmCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T18:07:37.556797Z","bundle_sha256":"df5a069de248646bc46ce1348bef4b29fe1298dd68c4b50bb5830eb85455da24"}}