{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2APTE2AYASDTILU3K75FVIPE45","short_pith_number":"pith:2APTE2AY","schema_version":"1.0","canonical_sha256":"d01f3268180487342e9b57fa5aa1e4e740db43380d9576dd002fadb45809fb7d","source":{"kind":"arxiv","id":"1508.05990","version":2},"attestation_state":"computed","paper":{"title":"A Multi-Time-Scale Analysis of Chemical Reaction Networks : II. Stochastic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chang Hyeong Lee, Hans G. Othmer, Xingye Kan","submitted_at":"2015-08-24T22:49:51Z","abstract_excerpt":"We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the full chemical master equation for arbitrary systems, and show how to obtain a reduced equation that governs the evolution on the slow time scale. This is done by applying a state space decomposition to the full equation that leads to the reduced dynamics in terms of certain projections and the invariant distributions of the fast system. The rates or propensit"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1508.05990","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-08-24T22:49:51Z","cross_cats_sorted":[],"title_canon_sha256":"1d41e32984028f95ee849e36833589d963d79827f4b8e89420ae4b6ee1e8c3cb","abstract_canon_sha256":"bd73b6d003606ea23cb5d6eeaa22cfe71628c38d8fcfb693ac12e6b6783d09aa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:38.223754Z","signature_b64":"Q5Ct3XF0k1Bzf9541gW5EYDm8gsivYCblNP8blvuS1FpjH/+k+z2JcA2Ottf7oSZy8y5gABF1ofrx7sQUcJxBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d01f3268180487342e9b57fa5aa1e4e740db43380d9576dd002fadb45809fb7d","last_reissued_at":"2026-05-18T01:24:38.223338Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:38.223338Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Multi-Time-Scale Analysis of Chemical Reaction Networks : II. Stochastic Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chang Hyeong Lee, Hans G. Othmer, Xingye Kan","submitted_at":"2015-08-24T22:49:51Z","abstract_excerpt":"We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the full chemical master equation for arbitrary systems, and show how to obtain a reduced equation that governs the evolution on the slow time scale. This is done by applying a state space decomposition to the full equation that leads to the reduced dynamics in terms of certain projections and the invariant distributions of the fast system. The rates or propensit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05990","kind":"arxiv","version":2},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1508.05990","created_at":"2026-05-18T01:24:38.223405+00:00"},{"alias_kind":"arxiv_version","alias_value":"1508.05990v2","created_at":"2026-05-18T01:24:38.223405+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.05990","created_at":"2026-05-18T01:24:38.223405+00:00"},{"alias_kind":"pith_short_12","alias_value":"2APTE2AYASDT","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2APTE2AYASDTILU3","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2APTE2AY","created_at":"2026-05-18T12:28:59.999130+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45","json":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45.json","graph_json":"https://pith.science/api/pith-number/2APTE2AYASDTILU3K75FVIPE45/graph.json","events_json":"https://pith.science/api/pith-number/2APTE2AYASDTILU3K75FVIPE45/events.json","paper":"https://pith.science/paper/2APTE2AY"},"agent_actions":{"view_html":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45","download_json":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45.json","view_paper":"https://pith.science/paper/2APTE2AY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1508.05990&json=true","fetch_graph":"https://pith.science/api/pith-number/2APTE2AYASDTILU3K75FVIPE45/graph.json","fetch_events":"https://pith.science/api/pith-number/2APTE2AYASDTILU3K75FVIPE45/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45/action/storage_attestation","attest_author":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45/action/author_attestation","sign_citation":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45/action/citation_signature","submit_replication":"https://pith.science/pith/2APTE2AYASDTILU3K75FVIPE45/action/replication_record"}},"created_at":"2026-05-18T01:24:38.223405+00:00","updated_at":"2026-05-18T01:24:38.223405+00:00"}