{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:BZWF6XCQ6UZVFZUNSKL3EZSAHA","short_pith_number":"pith:BZWF6XCQ","canonical_record":{"source":{"id":"1702.01364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-02-05T03:33:22Z","cross_cats_sorted":["physics.chem-ph","q-bio.MN"],"title_canon_sha256":"1f8b5dbc0ccc775c448ea29bdbd7015bba190fcf324a3fb23e023babb279381e","abstract_canon_sha256":"47738331772f652513116b049ee66e1b50413e5ccbc7031cbabb99abf92513d7"},"schema_version":"1.0"},"canonical_sha256":"0e6c5f5c50f53352e68d9297b26640383f22cf6a507b6d7e3b6b0a91606dd854","source":{"kind":"arxiv","id":"1702.01364","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01364","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01364v2","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01364","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"pith_short_12","alias_value":"BZWF6XCQ6UZV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BZWF6XCQ6UZVFZUN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BZWF6XCQ","created_at":"2026-05-18T12:31:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:BZWF6XCQ6UZVFZUNSKL3EZSAHA","target":"record","payload":{"canonical_record":{"source":{"id":"1702.01364","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-02-05T03:33:22Z","cross_cats_sorted":["physics.chem-ph","q-bio.MN"],"title_canon_sha256":"1f8b5dbc0ccc775c448ea29bdbd7015bba190fcf324a3fb23e023babb279381e","abstract_canon_sha256":"47738331772f652513116b049ee66e1b50413e5ccbc7031cbabb99abf92513d7"},"schema_version":"1.0"},"canonical_sha256":"0e6c5f5c50f53352e68d9297b26640383f22cf6a507b6d7e3b6b0a91606dd854","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:33:21.585370Z","signature_b64":"56dqbFE16JJZW2+B7TUm+mAqR0Y7qqWGkSdUdDqeGbHeLZy5PC8jjmV2CHtQRtXynu6V7aOMxGrg7R2jWPqCAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e6c5f5c50f53352e68d9297b26640383f22cf6a507b6d7e3b6b0a91606dd854","last_reissued_at":"2026-05-18T00:33:21.584825Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:33:21.584825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1702.01364","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uka9LL+cy909A6ADGbsF8aCJqhb7klhehGxvT6XVEobxmdLPMG7xwRTjvo2YtpcuIofj9bMGZwGSLI3G6uEaCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:00:16.236585Z"},"content_sha256":"bfcdbbd910fce8f47a2a05acb2538e290e7f7350e530d6ac28e63d529d2ae1bc","schema_version":"1.0","event_id":"sha256:bfcdbbd910fce8f47a2a05acb2538e290e7f7350e530d6ac28e63d529d2ae1bc"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:BZWF6XCQ6UZVFZUNSKL3EZSAHA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solving Moment Hierarchies for Chemical Reaction Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.chem-ph","q-bio.MN"],"primary_cat":"cond-mat.stat-mech","authors_text":"Eric Smith, Supriya Krishnamurthy","submitted_at":"2017-02-05T03:33:22Z","abstract_excerpt":"The study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \\cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments (FM). Using these, we can recursivel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01364","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:33:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tze4fBeus3VI8oS9afgc4Z8qc1hmFb61hrWAFCyg/6euVQPkAgOTE4KAV0gijDaDWN4+JNKHfT4X9zaeyPBpDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T12:00:16.236943Z"},"content_sha256":"9e5a6b039307707ea340e43f6f7d77e4930cbb4d76563f556b2f4cf9a310e38f","schema_version":"1.0","event_id":"sha256:9e5a6b039307707ea340e43f6f7d77e4930cbb4d76563f556b2f4cf9a310e38f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA/bundle.json","state_url":"https://pith.science/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA/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":"2026-06-05T12:00:16Z","links":{"resolver":"https://pith.science/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA","bundle":"https://pith.science/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA/bundle.json","state":"https://pith.science/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BZWF6XCQ6UZVFZUNSKL3EZSAHA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BZWF6XCQ6UZVFZUNSKL3EZSAHA","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":"47738331772f652513116b049ee66e1b50413e5ccbc7031cbabb99abf92513d7","cross_cats_sorted":["physics.chem-ph","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-02-05T03:33:22Z","title_canon_sha256":"1f8b5dbc0ccc775c448ea29bdbd7015bba190fcf324a3fb23e023babb279381e"},"schema_version":"1.0","source":{"id":"1702.01364","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01364","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01364v2","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01364","created_at":"2026-05-18T00:33:21Z"},{"alias_kind":"pith_short_12","alias_value":"BZWF6XCQ6UZV","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BZWF6XCQ6UZVFZUN","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BZWF6XCQ","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:9e5a6b039307707ea340e43f6f7d77e4930cbb4d76563f556b2f4cf9a310e38f","target":"graph","created_at":"2026-05-18T00:33:21Z","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 study of Chemical Reaction Networks (CRN's) is a very active field. Earlier well-known results \\cite{Feinberg:def_01:87, Anderson:product_dist:10} identify a topological quantity called deficiency, for any CRN, which, when exactly equal to zero, leads to a unique factorized steady-state for these networks. No results exist however for the steady states of non-zero-deficiency networks. In this paper, we show how to write the full moment-hierarchy for any non-zero-deficiency CRN obeying mass-action kinetics, in terms of equations for the factorial moments (FM). Using these, we can recursivel","authors_text":"Eric Smith, Supriya Krishnamurthy","cross_cats":["physics.chem-ph","q-bio.MN"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-02-05T03:33:22Z","title":"Solving Moment Hierarchies for Chemical Reaction Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01364","kind":"arxiv","version":2},"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:bfcdbbd910fce8f47a2a05acb2538e290e7f7350e530d6ac28e63d529d2ae1bc","target":"record","created_at":"2026-05-18T00:33:21Z","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":"47738331772f652513116b049ee66e1b50413e5ccbc7031cbabb99abf92513d7","cross_cats_sorted":["physics.chem-ph","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2017-02-05T03:33:22Z","title_canon_sha256":"1f8b5dbc0ccc775c448ea29bdbd7015bba190fcf324a3fb23e023babb279381e"},"schema_version":"1.0","source":{"id":"1702.01364","kind":"arxiv","version":2}},"canonical_sha256":"0e6c5f5c50f53352e68d9297b26640383f22cf6a507b6d7e3b6b0a91606dd854","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0e6c5f5c50f53352e68d9297b26640383f22cf6a507b6d7e3b6b0a91606dd854","first_computed_at":"2026-05-18T00:33:21.584825Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:33:21.584825Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"56dqbFE16JJZW2+B7TUm+mAqR0Y7qqWGkSdUdDqeGbHeLZy5PC8jjmV2CHtQRtXynu6V7aOMxGrg7R2jWPqCAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:33:21.585370Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01364","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bfcdbbd910fce8f47a2a05acb2538e290e7f7350e530d6ac28e63d529d2ae1bc","sha256:9e5a6b039307707ea340e43f6f7d77e4930cbb4d76563f556b2f4cf9a310e38f"],"state_sha256":"4f6c2c0a4e11fd2cb05bfa57e9da9218f9fc6d9493f9cd550d27f07d948da7f2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bu6ea7371flSxxgVjJOJWpebCjagAY87PV4wg7P1cBmzWsBuIPPqZqtaC46TeExKRi2wDAhHNcsuDlZyCR9NCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T12:00:16.239254Z","bundle_sha256":"a447fe3d7e941d282d4fc88f555ccf16a8477ce722aea9940a104b4a56be7c84"}}