{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:E6LLVN2OWFGAQHEALPSKCMVYBN","short_pith_number":"pith:E6LLVN2O","canonical_record":{"source":{"id":"2111.07497","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-11-15T02:22:57Z","cross_cats_sorted":[],"title_canon_sha256":"bb273842e3be6eb156647b0447c11d19e2fc1e97c3748dd757f29a655aecd5cd","abstract_canon_sha256":"2bc9102cf711c3d2ee5fefa12774837b9fe900cd1be768e45a8777e3486792b3"},"schema_version":"1.0"},"canonical_sha256":"2796bab74eb14c081c805be4a132b80b4801b6e859eae57cffc1589efda675d6","source":{"kind":"arxiv","id":"2111.07497","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.07497","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"arxiv_version","alias_value":"2111.07497v1","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07497","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"pith_short_12","alias_value":"E6LLVN2OWFGA","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"pith_short_16","alias_value":"E6LLVN2OWFGAQHEA","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"pith_short_8","alias_value":"E6LLVN2O","created_at":"2026-07-05T03:31:40Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:E6LLVN2OWFGAQHEALPSKCMVYBN","target":"record","payload":{"canonical_record":{"source":{"id":"2111.07497","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-11-15T02:22:57Z","cross_cats_sorted":[],"title_canon_sha256":"bb273842e3be6eb156647b0447c11d19e2fc1e97c3748dd757f29a655aecd5cd","abstract_canon_sha256":"2bc9102cf711c3d2ee5fefa12774837b9fe900cd1be768e45a8777e3486792b3"},"schema_version":"1.0"},"canonical_sha256":"2796bab74eb14c081c805be4a132b80b4801b6e859eae57cffc1589efda675d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:31:40.466187Z","signature_b64":"kgVsajsI53iMkaoXBggAiHqFoRXavGnQeaISOtXuYTq20qop+4NikHPS6a5JMWcBp5IrPVgk+4D7gwN9DmKBDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2796bab74eb14c081c805be4a132b80b4801b6e859eae57cffc1589efda675d6","last_reissued_at":"2026-07-05T03:31:40.465813Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:31:40.465813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.07497","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":"2026-07-05T03:31:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gZUf3TX7ir9d8Iz+mBAwLO0FJ0TSxmMRcOhoqsKim4xFOfJD+mC5OdowOPcnZQuTGD0agDrlTAkzYMDVD00rCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:24:23.042585Z"},"content_sha256":"30bf571f211bd956b442f29ee6210ee82f0724af0048048ad8b512f4b72c2a06","schema_version":"1.0","event_id":"sha256:30bf571f211bd956b442f29ee6210ee82f0724af0048048ad8b512f4b72c2a06"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:E6LLVN2OWFGAQHEALPSKCMVYBN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The limit of mesoscopic one-way fluxes in a nonequilibrium chemical reaction with complex mechanism","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lu-Yao Qiao, Wu-Jun Gao, Ying Sheng, Yong Chen","submitted_at":"2021-11-15T02:22:57Z","abstract_excerpt":"Peng et al.(2020) formulated one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. Species are classified into internal Y's and external X's. They defined the limit of mesoscopic one-way fluxes when the volume of the tank reactor tends to infinity as macroscopic one-way fluxes, but a rigorous proof of the existence of this limit is still awaiting. In this article, we fill this gap under a mild hypothesis: the Markov chain associated with the chemical master equation has finite states and any "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07497","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.07497/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":"2026-07-05T03:31:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eYWxK6B1sADNc/MWoRXKIO/T0aP9f5XS11fWQJGf9RKLTwYER6BU77vHmoYDpLVH/7CNFEABc6hV/NvHmrwmDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T19:24:23.043224Z"},"content_sha256":"099257639665a42a74f28ad4a795bbb347884ce7fea6a61eca3f500298c6d77d","schema_version":"1.0","event_id":"sha256:099257639665a42a74f28ad4a795bbb347884ce7fea6a61eca3f500298c6d77d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/E6LLVN2OWFGAQHEALPSKCMVYBN/bundle.json","state_url":"https://pith.science/pith/E6LLVN2OWFGAQHEALPSKCMVYBN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/E6LLVN2OWFGAQHEALPSKCMVYBN/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":"2026-08-04T19:24:23Z","links":{"resolver":"https://pith.science/pith/E6LLVN2OWFGAQHEALPSKCMVYBN","bundle":"https://pith.science/pith/E6LLVN2OWFGAQHEALPSKCMVYBN/bundle.json","state":"https://pith.science/pith/E6LLVN2OWFGAQHEALPSKCMVYBN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/E6LLVN2OWFGAQHEALPSKCMVYBN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:E6LLVN2OWFGAQHEALPSKCMVYBN","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":"2bc9102cf711c3d2ee5fefa12774837b9fe900cd1be768e45a8777e3486792b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-11-15T02:22:57Z","title_canon_sha256":"bb273842e3be6eb156647b0447c11d19e2fc1e97c3748dd757f29a655aecd5cd"},"schema_version":"1.0","source":{"id":"2111.07497","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.07497","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"arxiv_version","alias_value":"2111.07497v1","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.07497","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"pith_short_12","alias_value":"E6LLVN2OWFGA","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"pith_short_16","alias_value":"E6LLVN2OWFGAQHEA","created_at":"2026-07-05T03:31:40Z"},{"alias_kind":"pith_short_8","alias_value":"E6LLVN2O","created_at":"2026-07-05T03:31:40Z"}],"graph_snapshots":[{"event_id":"sha256:099257639665a42a74f28ad4a795bbb347884ce7fea6a61eca3f500298c6d77d","target":"graph","created_at":"2026-07-05T03:31:40Z","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/2111.07497/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Peng et al.(2020) formulated one-way fluxes for a general chemical reaction far from equilibrium, with arbitrary complex mechanisms, multiple intermediates, and internal kinetic cycles. Species are classified into internal Y's and external X's. They defined the limit of mesoscopic one-way fluxes when the volume of the tank reactor tends to infinity as macroscopic one-way fluxes, but a rigorous proof of the existence of this limit is still awaiting. In this article, we fill this gap under a mild hypothesis: the Markov chain associated with the chemical master equation has finite states and any ","authors_text":"Lu-Yao Qiao, Wu-Jun Gao, Ying Sheng, Yong Chen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-11-15T02:22:57Z","title":"The limit of mesoscopic one-way fluxes in a nonequilibrium chemical reaction with complex mechanism"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.07497","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":"sha256:30bf571f211bd956b442f29ee6210ee82f0724af0048048ad8b512f4b72c2a06","target":"record","created_at":"2026-07-05T03:31:40Z","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":"2bc9102cf711c3d2ee5fefa12774837b9fe900cd1be768e45a8777e3486792b3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2021-11-15T02:22:57Z","title_canon_sha256":"bb273842e3be6eb156647b0447c11d19e2fc1e97c3748dd757f29a655aecd5cd"},"schema_version":"1.0","source":{"id":"2111.07497","kind":"arxiv","version":1}},"canonical_sha256":"2796bab74eb14c081c805be4a132b80b4801b6e859eae57cffc1589efda675d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2796bab74eb14c081c805be4a132b80b4801b6e859eae57cffc1589efda675d6","first_computed_at":"2026-07-05T03:31:40.465813Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:31:40.465813Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kgVsajsI53iMkaoXBggAiHqFoRXavGnQeaISOtXuYTq20qop+4NikHPS6a5JMWcBp5IrPVgk+4D7gwN9DmKBDg==","signature_status":"signed_v1","signed_at":"2026-07-05T03:31:40.466187Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.07497","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:30bf571f211bd956b442f29ee6210ee82f0724af0048048ad8b512f4b72c2a06","sha256:099257639665a42a74f28ad4a795bbb347884ce7fea6a61eca3f500298c6d77d"],"state_sha256":"64702d6edb42a7b3d34dfd801ec180327d15e1cc7dd68c56b0f684a5b5f04fba"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fiq/fqJxwZCEQ4V+/OUvIPE2dDwmFU3Pa94dGl0+r1/UNkImFIBJEAif8Tgpx301wqsLqM8VytivZY+yKaVXAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T19:24:23.051349Z","bundle_sha256":"556487c0319530c5fe738ff461e13428a3f496617e969c1b621acd7f869b4b5b"}}