{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:FI3MEJQEO37FFE36XA6EFZTGRK","short_pith_number":"pith:FI3MEJQE","canonical_record":{"source":{"id":"1401.0126","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T10:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"1f85c1830af51a1fafb9e0c9b652addc0969f14418c1c3bc78c8b810ba0c6a28","abstract_canon_sha256":"615fa084bb9ada1b07606a9653c4944c7418a56ddc30a9f157c42e96413e9e84"},"schema_version":"1.0"},"canonical_sha256":"2a36c2260476fe52937eb83c42e6668a8504f3ffaf0373de92437d1829442ca5","source":{"kind":"arxiv","id":"1401.0126","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0126","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0126v4","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0126","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"FI3MEJQEO37F","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FI3MEJQEO37FFE36","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FI3MEJQE","created_at":"2026-05-18T12:27:45Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:FI3MEJQEO37FFE36XA6EFZTGRK","target":"record","payload":{"canonical_record":{"source":{"id":"1401.0126","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T10:38:10Z","cross_cats_sorted":[],"title_canon_sha256":"1f85c1830af51a1fafb9e0c9b652addc0969f14418c1c3bc78c8b810ba0c6a28","abstract_canon_sha256":"615fa084bb9ada1b07606a9653c4944c7418a56ddc30a9f157c42e96413e9e84"},"schema_version":"1.0"},"canonical_sha256":"2a36c2260476fe52937eb83c42e6668a8504f3ffaf0373de92437d1829442ca5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:45.624376Z","signature_b64":"IA4PrKL+623WUjsiG7zEgFP+I619CYpYOrGS5moRjtj9Rjucjbv7dHhCLhEz4tiS1GwfxHjQ5hw7aUGTtVjGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2a36c2260476fe52937eb83c42e6668a8504f3ffaf0373de92437d1829442ca5","last_reissued_at":"2026-05-18T00:43:45.623723Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:45.623723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.0126","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/OpOA0usjhuvb8JpSUl1PVEjTSmjN5e9jLgk5xKl90Cf2Lwo8Ue1oFsS7GgKRy9XHhPtF0KLSLwDrTlhuIieDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:17:12.901249Z"},"content_sha256":"b5b3adaa39461d26cef16c7f5614ec9a9740af2a90879d8193d7fdcc915cc541","schema_version":"1.0","event_id":"sha256:b5b3adaa39461d26cef16c7f5614ec9a9740af2a90879d8193d7fdcc915cc541"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:FI3MEJQEO37FFE36XA6EFZTGRK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological conjugacy of constant length substitution dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Ethan M. Coven, F. Michel Dekking, Michael S. Keane","submitted_at":"2013-12-31T10:38:10Z","abstract_excerpt":"Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems.\n  We show that each conjugacy class contains infinitely substitutions which are not injective. As examples, the Toeplitz conjugacy class contains three injective substitutions (two on two symbols and one on three symbols), and the length two Thue-Morse conjugacy class contains twelve substitutions, among which are two on six symbols. Together, they cons"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0126","kind":"arxiv","version":4},"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":"2026-05-18T00:43:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"joct0Y4nX9EEFHcZn//lDfypOIUAjfAJSbfBUx/nG3HZJI7+YDbyRkMVhmibf7s9YDDJZuaDqzXrWaXSYzIKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T15:17:12.901621Z"},"content_sha256":"fafdaf897122a57dbfd924721951b436f8f6d0a3c008c6bf5de4e1c5847d2f77","schema_version":"1.0","event_id":"sha256:fafdaf897122a57dbfd924721951b436f8f6d0a3c008c6bf5de4e1c5847d2f77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FI3MEJQEO37FFE36XA6EFZTGRK/bundle.json","state_url":"https://pith.science/pith/FI3MEJQEO37FFE36XA6EFZTGRK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FI3MEJQEO37FFE36XA6EFZTGRK/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":"2026-06-26T15:17:12Z","links":{"resolver":"https://pith.science/pith/FI3MEJQEO37FFE36XA6EFZTGRK","bundle":"https://pith.science/pith/FI3MEJQEO37FFE36XA6EFZTGRK/bundle.json","state":"https://pith.science/pith/FI3MEJQEO37FFE36XA6EFZTGRK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FI3MEJQEO37FFE36XA6EFZTGRK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FI3MEJQEO37FFE36XA6EFZTGRK","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":"615fa084bb9ada1b07606a9653c4944c7418a56ddc30a9f157c42e96413e9e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T10:38:10Z","title_canon_sha256":"1f85c1830af51a1fafb9e0c9b652addc0969f14418c1c3bc78c8b810ba0c6a28"},"schema_version":"1.0","source":{"id":"1401.0126","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.0126","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"arxiv_version","alias_value":"1401.0126v4","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.0126","created_at":"2026-05-18T00:43:45Z"},{"alias_kind":"pith_short_12","alias_value":"FI3MEJQEO37F","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FI3MEJQEO37FFE36","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FI3MEJQE","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:fafdaf897122a57dbfd924721951b436f8f6d0a3c008c6bf5de4e1c5847d2f77","target":"graph","created_at":"2026-05-18T00:43:45Z","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":"Primitive constant length substitutions generate minimal symbolic dynamical systems. In this article we present an algorithm which can produce the list of injective substitutions of the same length that generate topologically conjugate systems.\n  We show that each conjugacy class contains infinitely substitutions which are not injective. As examples, the Toeplitz conjugacy class contains three injective substitutions (two on two symbols and one on three symbols), and the length two Thue-Morse conjugacy class contains twelve substitutions, among which are two on six symbols. Together, they cons","authors_text":"Ethan M. Coven, F. Michel Dekking, Michael S. Keane","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T10:38:10Z","title":"Topological conjugacy of constant length substitution dynamical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.0126","kind":"arxiv","version":4},"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:b5b3adaa39461d26cef16c7f5614ec9a9740af2a90879d8193d7fdcc915cc541","target":"record","created_at":"2026-05-18T00:43:45Z","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":"615fa084bb9ada1b07606a9653c4944c7418a56ddc30a9f157c42e96413e9e84","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-12-31T10:38:10Z","title_canon_sha256":"1f85c1830af51a1fafb9e0c9b652addc0969f14418c1c3bc78c8b810ba0c6a28"},"schema_version":"1.0","source":{"id":"1401.0126","kind":"arxiv","version":4}},"canonical_sha256":"2a36c2260476fe52937eb83c42e6668a8504f3ffaf0373de92437d1829442ca5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2a36c2260476fe52937eb83c42e6668a8504f3ffaf0373de92437d1829442ca5","first_computed_at":"2026-05-18T00:43:45.623723Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:45.623723Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IA4PrKL+623WUjsiG7zEgFP+I619CYpYOrGS5moRjtj9Rjucjbv7dHhCLhEz4tiS1GwfxHjQ5hw7aUGTtVjGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:45.624376Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.0126","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b5b3adaa39461d26cef16c7f5614ec9a9740af2a90879d8193d7fdcc915cc541","sha256:fafdaf897122a57dbfd924721951b436f8f6d0a3c008c6bf5de4e1c5847d2f77"],"state_sha256":"480ef6719f478c35c29ee4067ede3f619848a43ea26eb06e78801607c1ad5460"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v6vQTRifMjRFW2SF3LrdI+LY7Dhg6euS7hKZJBo5dO7C8dK32GpjayJCa9y5XKwin4r/LXLkei9HfYuRa3WFDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T15:17:12.903576Z","bundle_sha256":"94c2eaadb9b6e4872ea0aa427cf21ab3a4ad78b283bdcaadf05d7cbc7f737f8a"}}