{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:7YPK5WDOVJZI5AUPH7W3EGOYQ2","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":"44b12fae781cfa3eb1609709864e114dbc5aac110e4b3566d390b9b1246b44ce","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-03-29T10:39:34Z","title_canon_sha256":"4eea48ecfa50436b66679ed2a12ef067567ebe87279c70178e0861e6225493b5"},"schema_version":"1.0","source":{"id":"1603.08715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.08715","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"arxiv_version","alias_value":"1603.08715v1","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.08715","created_at":"2026-05-17T23:47:49Z"},{"alias_kind":"pith_short_12","alias_value":"7YPK5WDOVJZI","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"7YPK5WDOVJZI5AUP","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"7YPK5WDO","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:e06cb2cdfc387e564a889813907f213e8068d252fd1f92e11353ca1b3f4ac98d","target":"graph","created_at":"2026-05-17T23:47:49Z","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 consider Turing machines as actions over configurations in $\\Sigma^{\\mathbb{Z}^d}$ which only change them locally around a marked position that can move and carry a particular state. In this setting we study the monoid of Turing machines and the group of reversible Turing machines. We also study two natural subgroups, namely the group of finite-state automata, which generalizes the topological full groups studied in the theory of orbit-equivalence, and the group of oblivious Turing machines whose movement is independent of tape contents, which generalizes lamplighter groups and has connecti","authors_text":"Jarkko Kari, Sebasti\\'an Barbieri, Ville Salo","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-03-29T10:39:34Z","title":"The group of reversible Turing machines"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.08715","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:a2b0fc6960c3eb742cbde39099008ef89c7eafcf1fd3554dfad36f86775e9ca1","target":"record","created_at":"2026-05-17T23:47:49Z","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":"44b12fae781cfa3eb1609709864e114dbc5aac110e4b3566d390b9b1246b44ce","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2016-03-29T10:39:34Z","title_canon_sha256":"4eea48ecfa50436b66679ed2a12ef067567ebe87279c70178e0861e6225493b5"},"schema_version":"1.0","source":{"id":"1603.08715","kind":"arxiv","version":1}},"canonical_sha256":"fe1eaed86eaa728e828f3fedb219d88690577cbeed9c0a86a540046e75f80ca4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe1eaed86eaa728e828f3fedb219d88690577cbeed9c0a86a540046e75f80ca4","first_computed_at":"2026-05-17T23:47:49.445599Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:49.445599Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ok6ISsNxO2gs+Y8QIgUFXH9ahhXpwkiiDmpiG/1edZv29XpABHfKgDV3qGdSPJWQvp6DUix9HomlOaHnFJhOBg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:49.446134Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.08715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a2b0fc6960c3eb742cbde39099008ef89c7eafcf1fd3554dfad36f86775e9ca1","sha256:e06cb2cdfc387e564a889813907f213e8068d252fd1f92e11353ca1b3f4ac98d"],"state_sha256":"79bc7abcc17048266de905f5945626d256790f8ae8bf22f5aa159167d42f2e81"}