{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4K4WBYAIXLD5AGLSRN3XV3G7HI","short_pith_number":"pith:4K4WBYAI","schema_version":"1.0","canonical_sha256":"e2b960e008bac7d019728b777aecdf3a1c084656c7fe45f6aad00076f7efe35d","source":{"kind":"arxiv","id":"1810.00225","version":3},"attestation_state":"computed","paper":{"title":"Revisiting Persistence of Chemical Reaction Networks through Lyapunov Function Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chuanhou Gao, Xiaoyu Zhang, Zhou Fang","submitted_at":"2018-09-29T15:50:50Z","abstract_excerpt":"In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a Lyapuonv function PDE and a boundary condition whose solutions are expected to be Lyapunov functions for the network. By means of solution of the PDEs, either in the forms of itself or its time derivative, some checkable criteria are proposed for persistence of network systems. These criteria show high validity in proving that neither non-semilocking boundary po"},"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":"1810.00225","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-09-29T15:50:50Z","cross_cats_sorted":[],"title_canon_sha256":"9150eaac9edb656f786e0b1650b01dedcd07552f950eb3635741d908d9723056","abstract_canon_sha256":"2b6e49f692f87d7bf19ffa02af2ae64b3a95a817a96614c77b54d81e4a6e86a2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:03.252921Z","signature_b64":"bEr5L0bBQAqmPSEWDEoBhJcDwPt3Ur/0hjvbSXNKnTCzTJQ2QORzRa1LehLKnZn/j6361Dk2GaYdnAblALSKCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e2b960e008bac7d019728b777aecdf3a1c084656c7fe45f6aad00076f7efe35d","last_reissued_at":"2026-05-17T23:55:03.252549Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:03.252549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Revisiting Persistence of Chemical Reaction Networks through Lyapunov Function Partial Differential Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Chuanhou Gao, Xiaoyu Zhang, Zhou Fang","submitted_at":"2018-09-29T15:50:50Z","abstract_excerpt":"In this paper, we propose a novel technique, referred to as the Lyapunov Function PDEs technique, to diagnose persistence of chemical reaction networks with mass-action kinetics. The technique allows that every network is attached to a Lyapuonv function PDE and a boundary condition whose solutions are expected to be Lyapunov functions for the network. By means of solution of the PDEs, either in the forms of itself or its time derivative, some checkable criteria are proposed for persistence of network systems. These criteria show high validity in proving that neither non-semilocking boundary po"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00225","kind":"arxiv","version":3},"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":"1810.00225","created_at":"2026-05-17T23:55:03.252616+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00225v3","created_at":"2026-05-17T23:55:03.252616+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00225","created_at":"2026-05-17T23:55:03.252616+00:00"},{"alias_kind":"pith_short_12","alias_value":"4K4WBYAIXLD5","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_16","alias_value":"4K4WBYAIXLD5AGLS","created_at":"2026-05-18T12:32:05.422762+00:00"},{"alias_kind":"pith_short_8","alias_value":"4K4WBYAI","created_at":"2026-05-18T12:32:05.422762+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2605.24629","citing_title":"A Perron-Frobenius strong threshold theorem for (A, B, P, {\\phi}) balanced bilinear models, and the role of left and right Perron eigenvectors in mathematical epidemiology","ref_index":48,"is_internal_anchor":true},{"citing_arxiv_id":"2605.01755","citing_title":"Perron-Volterra Lyapunov functions and competitive exclusion partitions in n-strain models with diagonal Metzler transversal Jacobian and rank-one blocks","ref_index":158,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI","json":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI.json","graph_json":"https://pith.science/api/pith-number/4K4WBYAIXLD5AGLSRN3XV3G7HI/graph.json","events_json":"https://pith.science/api/pith-number/4K4WBYAIXLD5AGLSRN3XV3G7HI/events.json","paper":"https://pith.science/paper/4K4WBYAI"},"agent_actions":{"view_html":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI","download_json":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI.json","view_paper":"https://pith.science/paper/4K4WBYAI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00225&json=true","fetch_graph":"https://pith.science/api/pith-number/4K4WBYAIXLD5AGLSRN3XV3G7HI/graph.json","fetch_events":"https://pith.science/api/pith-number/4K4WBYAIXLD5AGLSRN3XV3G7HI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI/action/storage_attestation","attest_author":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI/action/author_attestation","sign_citation":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI/action/citation_signature","submit_replication":"https://pith.science/pith/4K4WBYAIXLD5AGLSRN3XV3G7HI/action/replication_record"}},"created_at":"2026-05-17T23:55:03.252616+00:00","updated_at":"2026-05-17T23:55:03.252616+00:00"}