{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:7NY66TCU5CLSCQX37YAA63BURE","short_pith_number":"pith:7NY66TCU","canonical_record":{"source":{"id":"1201.1622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-08T10:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"b8bb0cc9eab2b88bc7a29ef740929caa184f7e34a6a6870d1d35c37b9c7ff80f","abstract_canon_sha256":"f71a74683384e24c1f304b4d671f6651d3086eca27dde12f14042aa8f52c9125"},"schema_version":"1.0"},"canonical_sha256":"fb71ef4c54e8972142fbfe000f6c3489024fa19069e53a6fc26484d5503b90b1","source":{"kind":"arxiv","id":"1201.1622","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1622","created_at":"2026-05-18T04:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1622v1","created_at":"2026-05-18T04:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1622","created_at":"2026-05-18T04:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"7NY66TCU5CLS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7NY66TCU5CLSCQX3","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7NY66TCU","created_at":"2026-05-18T12:26:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:7NY66TCU5CLSCQX37YAA63BURE","target":"record","payload":{"canonical_record":{"source":{"id":"1201.1622","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-08T10:50:43Z","cross_cats_sorted":[],"title_canon_sha256":"b8bb0cc9eab2b88bc7a29ef740929caa184f7e34a6a6870d1d35c37b9c7ff80f","abstract_canon_sha256":"f71a74683384e24c1f304b4d671f6651d3086eca27dde12f14042aa8f52c9125"},"schema_version":"1.0"},"canonical_sha256":"fb71ef4c54e8972142fbfe000f6c3489024fa19069e53a6fc26484d5503b90b1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:02.937401Z","signature_b64":"q9U/33CMfQA82nUBPp0YDqBiMu57HfqVePDvOumwlIN1o2Pbx0Sog3RdjS5rR51fNmCmCugdB3rWjMpBT0GAAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fb71ef4c54e8972142fbfe000f6c3489024fa19069e53a6fc26484d5503b90b1","last_reissued_at":"2026-05-18T04:05:02.936789Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:02.936789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.1622","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":"2026-05-18T04:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Y4y1XPGM7d4dKZQQkSPIS6lnfDBxkDVP06hD7dnbtgu2ekTP3skHBXAD3bXLIGB2LNPqc27VjZGBWhqSPMvDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:02:40.178607Z"},"content_sha256":"97f588f19f69457b77f7a3828b688ad6c2a65ecaa212a4715625abff772dbf1a","schema_version":"1.0","event_id":"sha256:97f588f19f69457b77f7a3828b688ad6c2a65ecaa212a4715625abff772dbf1a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:7NY66TCU5CLSCQX37YAA63BURE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Orbit equivalent substitution dynamical systems and complexity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"O. Karpel, S. Bezuglyi","submitted_at":"2012-01-08T10:50:43Z","abstract_excerpt":"For any primitive proper substitution \\sigma, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems {(X_{\\zeta_n}, T_{\\zeta_n})}_{n=1}^{\\infty} such that they all are (strong) orbit equivalent to (X_{\\sigma}, T_{\\sigma}). We show that the complexity of the substitution dynamical systems {(X_{\\zeta_n}, T_{\\zeta_n})} is essentially different that prevents them from being isomorphic. Given a primitive (not necessarily proper) substitution \\tau, we find a stationary simple properly ordered Bratteli diagram with the least possible number of vertices"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1622","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":""},"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":"2026-05-18T04:05:02Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Lz/xYwy74erC/Htzx9d4DNG6VBrTHX3yiUfQbG0XXxxX32EIkpqFXgUiTa7VBe48TqCWONM4qjcOsjmjv7P1Ag==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T01:02:40.178958Z"},"content_sha256":"ef414abae05e8127308070afe73db990d29007ffd330d85311181ec834c10ed5","schema_version":"1.0","event_id":"sha256:ef414abae05e8127308070afe73db990d29007ffd330d85311181ec834c10ed5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7NY66TCU5CLSCQX37YAA63BURE/bundle.json","state_url":"https://pith.science/pith/7NY66TCU5CLSCQX37YAA63BURE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7NY66TCU5CLSCQX37YAA63BURE/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":"2026-06-23T01:02:40Z","links":{"resolver":"https://pith.science/pith/7NY66TCU5CLSCQX37YAA63BURE","bundle":"https://pith.science/pith/7NY66TCU5CLSCQX37YAA63BURE/bundle.json","state":"https://pith.science/pith/7NY66TCU5CLSCQX37YAA63BURE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7NY66TCU5CLSCQX37YAA63BURE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:7NY66TCU5CLSCQX37YAA63BURE","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":"f71a74683384e24c1f304b4d671f6651d3086eca27dde12f14042aa8f52c9125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-08T10:50:43Z","title_canon_sha256":"b8bb0cc9eab2b88bc7a29ef740929caa184f7e34a6a6870d1d35c37b9c7ff80f"},"schema_version":"1.0","source":{"id":"1201.1622","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.1622","created_at":"2026-05-18T04:05:02Z"},{"alias_kind":"arxiv_version","alias_value":"1201.1622v1","created_at":"2026-05-18T04:05:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.1622","created_at":"2026-05-18T04:05:02Z"},{"alias_kind":"pith_short_12","alias_value":"7NY66TCU5CLS","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_16","alias_value":"7NY66TCU5CLSCQX3","created_at":"2026-05-18T12:26:58Z"},{"alias_kind":"pith_short_8","alias_value":"7NY66TCU","created_at":"2026-05-18T12:26:58Z"}],"graph_snapshots":[{"event_id":"sha256:ef414abae05e8127308070afe73db990d29007ffd330d85311181ec834c10ed5","target":"graph","created_at":"2026-05-18T04:05:02Z","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":"For any primitive proper substitution \\sigma, we give explicit constructions of countably many pairwise non-isomorphic substitution dynamical systems {(X_{\\zeta_n}, T_{\\zeta_n})}_{n=1}^{\\infty} such that they all are (strong) orbit equivalent to (X_{\\sigma}, T_{\\sigma}). We show that the complexity of the substitution dynamical systems {(X_{\\zeta_n}, T_{\\zeta_n})} is essentially different that prevents them from being isomorphic. Given a primitive (not necessarily proper) substitution \\tau, we find a stationary simple properly ordered Bratteli diagram with the least possible number of vertices","authors_text":"O. Karpel, S. Bezuglyi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-08T10:50:43Z","title":"Orbit equivalent substitution dynamical systems and complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.1622","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":"sha256:97f588f19f69457b77f7a3828b688ad6c2a65ecaa212a4715625abff772dbf1a","target":"record","created_at":"2026-05-18T04:05:02Z","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":"f71a74683384e24c1f304b4d671f6651d3086eca27dde12f14042aa8f52c9125","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-01-08T10:50:43Z","title_canon_sha256":"b8bb0cc9eab2b88bc7a29ef740929caa184f7e34a6a6870d1d35c37b9c7ff80f"},"schema_version":"1.0","source":{"id":"1201.1622","kind":"arxiv","version":1}},"canonical_sha256":"fb71ef4c54e8972142fbfe000f6c3489024fa19069e53a6fc26484d5503b90b1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fb71ef4c54e8972142fbfe000f6c3489024fa19069e53a6fc26484d5503b90b1","first_computed_at":"2026-05-18T04:05:02.936789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:05:02.936789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"q9U/33CMfQA82nUBPp0YDqBiMu57HfqVePDvOumwlIN1o2Pbx0Sog3RdjS5rR51fNmCmCugdB3rWjMpBT0GAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:05:02.937401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.1622","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:97f588f19f69457b77f7a3828b688ad6c2a65ecaa212a4715625abff772dbf1a","sha256:ef414abae05e8127308070afe73db990d29007ffd330d85311181ec834c10ed5"],"state_sha256":"e460b9432151b9a69e5369812f41d89583e38c9baea00f2a5eb8c0368eab1f4b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ik+t7BiVWiTXMv9L3kL2RA2rniEC2Gx+jAFHBMilcijVyjb5cCtB5UmKbtNoZVpHTmjArfcsuWCx8dN9iWGtBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T01:02:40.180896Z","bundle_sha256":"82650bd842f8f78646aa0efa7dda01d472b2528f06b48d15631ca8f85c027fe9"}}