{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:UATYCBLD347BQPUMNWMWGQGVIW","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":"9a22175d5fb3b515f73654c83ea6014559ade4d4c0b31a2ce037b7a50a3522f6","cross_cats_sorted":["cs.IT","math.DS","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-08T18:35:03Z","title_canon_sha256":"e090a2c95f927a18cc9291b5f2905948aa69880cbc4beec25d75dc29d3ce3cd9"},"schema_version":"1.0","source":{"id":"1412.2690","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.2690","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"arxiv_version","alias_value":"1412.2690v3","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2690","created_at":"2026-05-18T01:22:03Z"},{"alias_kind":"pith_short_12","alias_value":"UATYCBLD347B","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_16","alias_value":"UATYCBLD347BQPUM","created_at":"2026-05-18T12:28:52Z"},{"alias_kind":"pith_short_8","alias_value":"UATYCBLD","created_at":"2026-05-18T12:28:52Z"}],"graph_snapshots":[{"event_id":"sha256:61a51fd3ff0ad14148ba3b426ad6895c634e2125722f93aa516e63739da308c1","target":"graph","created_at":"2026-05-18T01:22:03Z","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":"Computational mechanics quantifies structure in a stochastic process via its causal states, leading to the process's minimal, optimal predictor---the $\\epsilon$-machine. We extend computational mechanics to communication channels between two processes, obtaining an analogous optimal model---the $\\epsilon$-transducer---of the stochastic mapping between them. Here, we lay the foundation of a structural analysis of communication channels, treating joint processes and processes with input. The result is a principled structural analysis of mechanisms that support information flow between processes.","authors_text":"James P. Crutchfield, Nix Barnett","cross_cats":["cs.IT","math.DS","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-08T18:35:03Z","title":"Computational Mechanics of Input-Output Processes: Structured transformations and the $\\epsilon$-transducer"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2690","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":"sha256:4f5317eab4072898cd18151bc330632d0e3cb6e2bf3d2361619ce1459f51353c","target":"record","created_at":"2026-05-18T01:22:03Z","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":"9a22175d5fb3b515f73654c83ea6014559ade4d4c0b31a2ce037b7a50a3522f6","cross_cats_sorted":["cs.IT","math.DS","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2014-12-08T18:35:03Z","title_canon_sha256":"e090a2c95f927a18cc9291b5f2905948aa69880cbc4beec25d75dc29d3ce3cd9"},"schema_version":"1.0","source":{"id":"1412.2690","kind":"arxiv","version":3}},"canonical_sha256":"a027810563df3e183e8c6d996340d545a342fc094943df28b5e5eded4b45cf8d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a027810563df3e183e8c6d996340d545a342fc094943df28b5e5eded4b45cf8d","first_computed_at":"2026-05-18T01:22:03.257179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:03.257179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jcP2HLyR730hSMzrNgCkSyk3g4Pm4FA5b2w7SUaJVlFZ3SQZN2rdgy8N1tg1uwk2dve8RuvqtFFlgux52zUXDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:03.257642Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.2690","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4f5317eab4072898cd18151bc330632d0e3cb6e2bf3d2361619ce1459f51353c","sha256:61a51fd3ff0ad14148ba3b426ad6895c634e2125722f93aa516e63739da308c1"],"state_sha256":"47fbce3f98fc5e5b1b4f3a3198d11fab41f2dccffa7ee743763683f675e750ef"}