{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:QZGQI36G6UDWUPQJJAM2XDIRJX","short_pith_number":"pith:QZGQI36G","canonical_record":{"source":{"id":"1509.00612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-02T09:36:00Z","cross_cats_sorted":[],"title_canon_sha256":"3d0e2019b41575b081291ab950577271e62bdd89b7606aae1c2e897dc97c2c95","abstract_canon_sha256":"65b69f2c637d784482659658e20d5d00e31a4187353fc6f9ca4cff4f19d15321"},"schema_version":"1.0"},"canonical_sha256":"864d046fc6f5076a3e094819ab8d114ddc1da907d36c128d0937007e60c92dd8","source":{"kind":"arxiv","id":"1509.00612","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00612","created_at":"2026-05-18T01:28:46Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00612v1","created_at":"2026-05-18T01:28:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00612","created_at":"2026-05-18T01:28:46Z"},{"alias_kind":"pith_short_12","alias_value":"QZGQI36G6UDW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZGQI36G6UDWUPQJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZGQI36G","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:QZGQI36G6UDWUPQJJAM2XDIRJX","target":"record","payload":{"canonical_record":{"source":{"id":"1509.00612","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-02T09:36:00Z","cross_cats_sorted":[],"title_canon_sha256":"3d0e2019b41575b081291ab950577271e62bdd89b7606aae1c2e897dc97c2c95","abstract_canon_sha256":"65b69f2c637d784482659658e20d5d00e31a4187353fc6f9ca4cff4f19d15321"},"schema_version":"1.0"},"canonical_sha256":"864d046fc6f5076a3e094819ab8d114ddc1da907d36c128d0937007e60c92dd8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:46.446202Z","signature_b64":"SLW/Cfw8i7vwf2TVYQTzSEZPaLLxqsLTkGW8h83KCD9YkcUIbScXkLKQatPDxfhvx1A62dth4Oiy1rTmKhkrCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"864d046fc6f5076a3e094819ab8d114ddc1da907d36c128d0937007e60c92dd8","last_reissued_at":"2026-05-18T01:28:46.445652Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:46.445652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.00612","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":"2026-05-18T01:28:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cyc3tNq4Pelk3p1oB9OL/1ZiJgNkfrjY2rcCzcN8o8ge6gPpitH/FCuyZavZ2/DCE4KUuWY05QwcDveVzMcqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:11:52.044477Z"},"content_sha256":"90cf555bf189ee3e383cb9b2e7f37a533ea0fc916d9f9bc685c45051e4866f53","schema_version":"1.0","event_id":"sha256:90cf555bf189ee3e383cb9b2e7f37a533ea0fc916d9f9bc685c45051e4866f53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:QZGQI36G6UDWUPQJJAM2XDIRJX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The linear-noise approximation and the chemical master equation exactly agree up to second-order moments for a class of chemical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Ramon Grima","submitted_at":"2015-09-02T09:36:00Z","abstract_excerpt":"It is well known that the linear-noise approximation (LNA) exactly agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00612","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":"2026-05-18T01:28:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ctKV7dQZGLl92Xjiwn1I7Cg6xfZYFkUTbV4Sl0Gemv4svEUhmAseKt3TiLsdzkJUYVB7MBHQc3r5wQPGFl8RCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T05:11:52.045171Z"},"content_sha256":"7b5961f22c8d3e32392e5e283c375a3a6c4d95937473651484a41ace1f30d694","schema_version":"1.0","event_id":"sha256:7b5961f22c8d3e32392e5e283c375a3a6c4d95937473651484a41ace1f30d694"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/QZGQI36G6UDWUPQJJAM2XDIRJX/bundle.json","state_url":"https://pith.science/pith/QZGQI36G6UDWUPQJJAM2XDIRJX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/QZGQI36G6UDWUPQJJAM2XDIRJX/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":"2026-06-11T05:11:52Z","links":{"resolver":"https://pith.science/pith/QZGQI36G6UDWUPQJJAM2XDIRJX","bundle":"https://pith.science/pith/QZGQI36G6UDWUPQJJAM2XDIRJX/bundle.json","state":"https://pith.science/pith/QZGQI36G6UDWUPQJJAM2XDIRJX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/QZGQI36G6UDWUPQJJAM2XDIRJX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:QZGQI36G6UDWUPQJJAM2XDIRJX","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":"65b69f2c637d784482659658e20d5d00e31a4187353fc6f9ca4cff4f19d15321","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-02T09:36:00Z","title_canon_sha256":"3d0e2019b41575b081291ab950577271e62bdd89b7606aae1c2e897dc97c2c95"},"schema_version":"1.0","source":{"id":"1509.00612","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.00612","created_at":"2026-05-18T01:28:46Z"},{"alias_kind":"arxiv_version","alias_value":"1509.00612v1","created_at":"2026-05-18T01:28:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.00612","created_at":"2026-05-18T01:28:46Z"},{"alias_kind":"pith_short_12","alias_value":"QZGQI36G6UDW","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"QZGQI36G6UDWUPQJ","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"QZGQI36G","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:7b5961f22c8d3e32392e5e283c375a3a6c4d95937473651484a41ace1f30d694","target":"graph","created_at":"2026-05-18T01:28:46Z","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":"It is well known that the linear-noise approximation (LNA) exactly agrees with the chemical master equation, up to second-order moments, for chemical systems composed of zero and first-order reactions. Here we show that this is also a property of the LNA for a subset of chemical systems with second-order reactions. This agreement is independent of the number of interacting molecules.","authors_text":"Ramon Grima","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-02T09:36:00Z","title":"The linear-noise approximation and the chemical master equation exactly agree up to second-order moments for a class of chemical systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.00612","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":"sha256:90cf555bf189ee3e383cb9b2e7f37a533ea0fc916d9f9bc685c45051e4866f53","target":"record","created_at":"2026-05-18T01:28:46Z","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":"65b69f2c637d784482659658e20d5d00e31a4187353fc6f9ca4cff4f19d15321","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-09-02T09:36:00Z","title_canon_sha256":"3d0e2019b41575b081291ab950577271e62bdd89b7606aae1c2e897dc97c2c95"},"schema_version":"1.0","source":{"id":"1509.00612","kind":"arxiv","version":1}},"canonical_sha256":"864d046fc6f5076a3e094819ab8d114ddc1da907d36c128d0937007e60c92dd8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"864d046fc6f5076a3e094819ab8d114ddc1da907d36c128d0937007e60c92dd8","first_computed_at":"2026-05-18T01:28:46.445652Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:46.445652Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SLW/Cfw8i7vwf2TVYQTzSEZPaLLxqsLTkGW8h83KCD9YkcUIbScXkLKQatPDxfhvx1A62dth4Oiy1rTmKhkrCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:46.446202Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.00612","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90cf555bf189ee3e383cb9b2e7f37a533ea0fc916d9f9bc685c45051e4866f53","sha256:7b5961f22c8d3e32392e5e283c375a3a6c4d95937473651484a41ace1f30d694"],"state_sha256":"bbc62fb2a83a903bb2bd93fb8bd47d04fb4b4fc6b928ec2508a7ee936a543ac9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"erLBFkMoHvoRqNIrCo3xEGnEQHHzNaqIMJ1JxjQTatrT5CD0xJ0PxwxWNaBG9zAy/nMO7fiaPfYEoyl3oZ36AA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T05:11:52.048987Z","bundle_sha256":"0679e9a7dc9ea6f934d3ca1c85ae59ab0cf44a13ed6f6221e0d36000a23d5aa3"}}