{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:5DZAJR6YXYTB6BQ5RENECRXVIP","short_pith_number":"pith:5DZAJR6Y","canonical_record":{"source":{"id":"2004.14397","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-04-29T18:00:03Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"5559eed806eb2c78c010410349edbe4ce933277b24ba32b20367e68505dec06b","abstract_canon_sha256":"ccd5efcb1f74921d41703a5eabcb18a9e14f2d4e31950c5f1c8f74c55d4e1c2c"},"schema_version":"1.0"},"canonical_sha256":"e8f204c7d8be261f061d891a4146f543ee6fd7983e5a066bb96667382dc3e2ce","source":{"kind":"arxiv","id":"2004.14397","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.14397","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"2004.14397v3","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.14397","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"5DZAJR6YXYTB","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"pith_short_16","alias_value":"5DZAJR6YXYTB6BQ5","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"pith_short_8","alias_value":"5DZAJR6Y","created_at":"2026-07-05T04:38:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:5DZAJR6YXYTB6BQ5RENECRXVIP","target":"record","payload":{"canonical_record":{"source":{"id":"2004.14397","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-04-29T18:00:03Z","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"title_canon_sha256":"5559eed806eb2c78c010410349edbe4ce933277b24ba32b20367e68505dec06b","abstract_canon_sha256":"ccd5efcb1f74921d41703a5eabcb18a9e14f2d4e31950c5f1c8f74c55d4e1c2c"},"schema_version":"1.0"},"canonical_sha256":"e8f204c7d8be261f061d891a4146f543ee6fd7983e5a066bb96667382dc3e2ce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:38:09.342014Z","signature_b64":"o5/YlVp0uKrDhnTZWkqaK4Hx3xrsdSYe8+6YLtQOOqc8OM0D1pTsF1ult/0NSGCidIqNQCei6yrLUVtay1hRBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8f204c7d8be261f061d891a4146f543ee6fd7983e5a066bb96667382dc3e2ce","last_reissued_at":"2026-07-05T04:38:09.341613Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:38:09.341613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2004.14397","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":"2026-07-05T04:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hEA4eEDhae9YU52WBFvKjvWUyEjnWh5QTs9TbGdJ+tSPRP7PF+DJ4ccZHK/VTEqNSqpBuQtSBGzQ1aHs7bJRCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T13:27:58.023012Z"},"content_sha256":"ead8130c2d0bdfdffc84e397065f4d071e331e6a4f99d07b2e5cecf3fadcda18","schema_version":"1.0","event_id":"sha256:ead8130c2d0bdfdffc84e397065f4d071e331e6a4f99d07b2e5cecf3fadcda18"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:5DZAJR6YXYTB6BQ5RENECRXVIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Theory of Ergodic Quantum Processes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Jeffrey Schenker, Ramis Movassagh","submitted_at":"2020-04-29T18:00:03Z","abstract_excerpt":"The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a replacement (rank-one) channel. Using this theorem, we derive the limiting behavior of translation-invariant channels and stochastical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.14397","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2004.14397/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T04:38:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7LUhQOGuVJzNZapaXCmu5cST6fXfBBEylKcm5ggF7Ras+hc0wP3OjwCYhkacOc8X8RwU67lkDv59RfKalwYDAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-03T13:27:58.023504Z"},"content_sha256":"8ec0a8667ffa7c30fcc7b85c991ee6eecbfbee1db5757c33edd108570ef119f8","schema_version":"1.0","event_id":"sha256:8ec0a8667ffa7c30fcc7b85c991ee6eecbfbee1db5757c33edd108570ef119f8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5DZAJR6YXYTB6BQ5RENECRXVIP/bundle.json","state_url":"https://pith.science/pith/5DZAJR6YXYTB6BQ5RENECRXVIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5DZAJR6YXYTB6BQ5RENECRXVIP/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":"2026-08-03T13:27:58Z","links":{"resolver":"https://pith.science/pith/5DZAJR6YXYTB6BQ5RENECRXVIP","bundle":"https://pith.science/pith/5DZAJR6YXYTB6BQ5RENECRXVIP/bundle.json","state":"https://pith.science/pith/5DZAJR6YXYTB6BQ5RENECRXVIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5DZAJR6YXYTB6BQ5RENECRXVIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:5DZAJR6YXYTB6BQ5RENECRXVIP","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":"ccd5efcb1f74921d41703a5eabcb18a9e14f2d4e31950c5f1c8f74c55d4e1c2c","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-04-29T18:00:03Z","title_canon_sha256":"5559eed806eb2c78c010410349edbe4ce933277b24ba32b20367e68505dec06b"},"schema_version":"1.0","source":{"id":"2004.14397","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.14397","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"arxiv_version","alias_value":"2004.14397v3","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.14397","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"pith_short_12","alias_value":"5DZAJR6YXYTB","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"pith_short_16","alias_value":"5DZAJR6YXYTB6BQ5","created_at":"2026-07-05T04:38:09Z"},{"alias_kind":"pith_short_8","alias_value":"5DZAJR6Y","created_at":"2026-07-05T04:38:09Z"}],"graph_snapshots":[{"event_id":"sha256:8ec0a8667ffa7c30fcc7b85c991ee6eecbfbee1db5757c33edd108570ef119f8","target":"graph","created_at":"2026-07-05T04:38:09Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2004.14397/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The generic behavior of quantum systems has long been of theoretical and practical interest. Any quantum process is represented by a sequence of quantum channels. We consider general ergodic sequences of stochastic channels with arbitrary correlations and non-negligible decoherence. Ergodicity includes and vastly generalizes random independence. We obtain a theorem which shows that the composition of such a sequence of channels converges exponentially fast to a replacement (rank-one) channel. Using this theorem, we derive the limiting behavior of translation-invariant channels and stochastical","authors_text":"Jeffrey Schenker, Ramis Movassagh","cross_cats":["cond-mat.str-el","math-ph","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-04-29T18:00:03Z","title":"Theory of Ergodic Quantum Processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.14397","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:ead8130c2d0bdfdffc84e397065f4d071e331e6a4f99d07b2e5cecf3fadcda18","target":"record","created_at":"2026-07-05T04:38:09Z","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":"ccd5efcb1f74921d41703a5eabcb18a9e14f2d4e31950c5f1c8f74c55d4e1c2c","cross_cats_sorted":["cond-mat.str-el","math-ph","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"quant-ph","submitted_at":"2020-04-29T18:00:03Z","title_canon_sha256":"5559eed806eb2c78c010410349edbe4ce933277b24ba32b20367e68505dec06b"},"schema_version":"1.0","source":{"id":"2004.14397","kind":"arxiv","version":3}},"canonical_sha256":"e8f204c7d8be261f061d891a4146f543ee6fd7983e5a066bb96667382dc3e2ce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e8f204c7d8be261f061d891a4146f543ee6fd7983e5a066bb96667382dc3e2ce","first_computed_at":"2026-07-05T04:38:09.341613Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:38:09.341613Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o5/YlVp0uKrDhnTZWkqaK4Hx3xrsdSYe8+6YLtQOOqc8OM0D1pTsF1ult/0NSGCidIqNQCei6yrLUVtay1hRBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T04:38:09.342014Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.14397","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ead8130c2d0bdfdffc84e397065f4d071e331e6a4f99d07b2e5cecf3fadcda18","sha256:8ec0a8667ffa7c30fcc7b85c991ee6eecbfbee1db5757c33edd108570ef119f8"],"state_sha256":"fda15d7b81a607f03bb663ea60422b7ec4d08d48a0d7d2fcbad163ff0eb93cc0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N0MulGDzy34X38a65il5W1HAfJiQb/Us2gDbBSl+jIpESWE/jRjxffiKCtZ6BbWS3Qh1DEiF144G+1RsgyPmBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-03T13:27:58.027133Z","bundle_sha256":"54ae5e9c9b98f5311dab870dfe52aad3e54ddae0d791a396e1b5193087ac7b2a"}}