{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:ZI5MILXESGXQVRODF43GJ5SO24","short_pith_number":"pith:ZI5MILXE","canonical_record":{"source":{"id":"1509.09104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2015-09-30T09:53:38Z","cross_cats_sorted":["cond-mat.stat-mech","math.NA","q-bio.MN","q-bio.SC"],"title_canon_sha256":"74a29debf1084e4485e7e6f721b618cf74903b3b373d1c9aa8d01968209e48b5","abstract_canon_sha256":"4099838ffc390773823e69102db0a0a70923d3213b8240bc7e945684019c366f"},"schema_version":"1.0"},"canonical_sha256":"ca3ac42ee491af0ac5c32f3664f64ed716c9fdb50075ff9d4b917aeee1e66159","source":{"kind":"arxiv","id":"1509.09104","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.09104","created_at":"2026-05-18T01:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"1509.09104v1","created_at":"2026-05-18T01:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09104","created_at":"2026-05-18T01:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"ZI5MILXESGXQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZI5MILXESGXQVROD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZI5MILXE","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:ZI5MILXESGXQVRODF43GJ5SO24","target":"record","payload":{"canonical_record":{"source":{"id":"1509.09104","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2015-09-30T09:53:38Z","cross_cats_sorted":["cond-mat.stat-mech","math.NA","q-bio.MN","q-bio.SC"],"title_canon_sha256":"74a29debf1084e4485e7e6f721b618cf74903b3b373d1c9aa8d01968209e48b5","abstract_canon_sha256":"4099838ffc390773823e69102db0a0a70923d3213b8240bc7e945684019c366f"},"schema_version":"1.0"},"canonical_sha256":"ca3ac42ee491af0ac5c32f3664f64ed716c9fdb50075ff9d4b917aeee1e66159","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:27.149651Z","signature_b64":"dKCTDjotZ5YYROW+yYio2xU9R3RtOEUHk/uGKRl1oHEK5aSa8xV0hhRtomcInZ4tokNwvZW44/FsjJRPs0X2AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca3ac42ee491af0ac5c32f3664f64ed716c9fdb50075ff9d4b917aeee1e66159","last_reissued_at":"2026-05-18T01:31:27.149134Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:27.149134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.09104","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":"2026-05-18T01:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GmpqVCY7wCsO05985G3r82gsjaUg/VkzAgNTIUh75tJyQZ8vywtPQHhLRHZ1dQ2TpvQ/YKqZx2QhHTCyJIMOAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:00:26.561368Z"},"content_sha256":"1b6221a03f1f75073671c581f747e598fdd9a640ec819f92f5fb13dbdae64500","schema_version":"1.0","event_id":"sha256:1b6221a03f1f75073671c581f747e598fdd9a640ec819f92f5fb13dbdae64500"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:ZI5MILXESGXQVRODF43GJ5SO24","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distribution approximations for the chemical master equation: comparison of the method of moments and the system size expansion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.NA","q-bio.MN","q-bio.SC"],"primary_cat":"q-bio.QM","authors_text":"Alexander Andreychenko, Luca Bortolussi, Philipp Thomas, Ramon Grima, Verena Wolf","submitted_at":"2015-09-30T09:53:38Z","abstract_excerpt":"The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying probability distributions of the CME. The first approach is based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle. The second approach"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09104","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":""},"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":"2026-05-18T01:31:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gyniquaw6rS+aI5IB2Y9r1VO2a+1bBilSyIEHj02nfHU0znVGjnSqdpGJaFkldkItZ7QvbGntO/U7SPv46v9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T23:00:26.561746Z"},"content_sha256":"721052d7b0fd772fb5aa0c2ab1c58f13e9a4ca5fbb89b776f993a4ed5836aa6d","schema_version":"1.0","event_id":"sha256:721052d7b0fd772fb5aa0c2ab1c58f13e9a4ca5fbb89b776f993a4ed5836aa6d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZI5MILXESGXQVRODF43GJ5SO24/bundle.json","state_url":"https://pith.science/pith/ZI5MILXESGXQVRODF43GJ5SO24/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZI5MILXESGXQVRODF43GJ5SO24/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":"2026-05-28T23:00:26Z","links":{"resolver":"https://pith.science/pith/ZI5MILXESGXQVRODF43GJ5SO24","bundle":"https://pith.science/pith/ZI5MILXESGXQVRODF43GJ5SO24/bundle.json","state":"https://pith.science/pith/ZI5MILXESGXQVRODF43GJ5SO24/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZI5MILXESGXQVRODF43GJ5SO24/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZI5MILXESGXQVRODF43GJ5SO24","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":"4099838ffc390773823e69102db0a0a70923d3213b8240bc7e945684019c366f","cross_cats_sorted":["cond-mat.stat-mech","math.NA","q-bio.MN","q-bio.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2015-09-30T09:53:38Z","title_canon_sha256":"74a29debf1084e4485e7e6f721b618cf74903b3b373d1c9aa8d01968209e48b5"},"schema_version":"1.0","source":{"id":"1509.09104","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.09104","created_at":"2026-05-18T01:31:27Z"},{"alias_kind":"arxiv_version","alias_value":"1509.09104v1","created_at":"2026-05-18T01:31:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.09104","created_at":"2026-05-18T01:31:27Z"},{"alias_kind":"pith_short_12","alias_value":"ZI5MILXESGXQ","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZI5MILXESGXQVROD","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZI5MILXE","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:721052d7b0fd772fb5aa0c2ab1c58f13e9a4ca5fbb89b776f993a4ed5836aa6d","target":"graph","created_at":"2026-05-18T01:31:27Z","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":"The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying probability distributions of the CME. The first approach is based on an integration of the statistical moments and the reconstruction of the distribution based on the maximum entropy principle. The second approach","authors_text":"Alexander Andreychenko, Luca Bortolussi, Philipp Thomas, Ramon Grima, Verena Wolf","cross_cats":["cond-mat.stat-mech","math.NA","q-bio.MN","q-bio.SC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2015-09-30T09:53:38Z","title":"Distribution approximations for the chemical master equation: comparison of the method of moments and the system size expansion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.09104","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":"sha256:1b6221a03f1f75073671c581f747e598fdd9a640ec819f92f5fb13dbdae64500","target":"record","created_at":"2026-05-18T01:31:27Z","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":"4099838ffc390773823e69102db0a0a70923d3213b8240bc7e945684019c366f","cross_cats_sorted":["cond-mat.stat-mech","math.NA","q-bio.MN","q-bio.SC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.QM","submitted_at":"2015-09-30T09:53:38Z","title_canon_sha256":"74a29debf1084e4485e7e6f721b618cf74903b3b373d1c9aa8d01968209e48b5"},"schema_version":"1.0","source":{"id":"1509.09104","kind":"arxiv","version":1}},"canonical_sha256":"ca3ac42ee491af0ac5c32f3664f64ed716c9fdb50075ff9d4b917aeee1e66159","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca3ac42ee491af0ac5c32f3664f64ed716c9fdb50075ff9d4b917aeee1e66159","first_computed_at":"2026-05-18T01:31:27.149134Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:27.149134Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"dKCTDjotZ5YYROW+yYio2xU9R3RtOEUHk/uGKRl1oHEK5aSa8xV0hhRtomcInZ4tokNwvZW44/FsjJRPs0X2AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:27.149651Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.09104","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1b6221a03f1f75073671c581f747e598fdd9a640ec819f92f5fb13dbdae64500","sha256:721052d7b0fd772fb5aa0c2ab1c58f13e9a4ca5fbb89b776f993a4ed5836aa6d"],"state_sha256":"01f715ef814f5417203f02fc843760779aacee930f182b6ecbd0cf2866688f4e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jcqhBRuRyJpI8XgH57DarC4TUASNMd1rL/cSbnAzrJdi4HdhjD07h8Li2HRbI+5Uh2dceAOPJgK0G+Qgzv3NBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T23:00:26.563910Z","bundle_sha256":"414ee07562ff620c5ac24d7e569a0fce3dfa39ca5b8ad263de8242ae58ecaf0d"}}