{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PS24DFZXHXY6COMVBILGENMPK2","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":"820c420aee4e11e7605d9ae76515bd9b39dc6d32837d93b9c3a8e9a67b26b051","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-04T09:14:54Z","title_canon_sha256":"d96a2e1da54cae8ded99eac0fb3e956af6dc35f405f69063660e97c3a1420061"},"schema_version":"1.0","source":{"id":"1708.01427","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.01427","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"arxiv_version","alias_value":"1708.01427v1","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.01427","created_at":"2026-05-18T00:16:31Z"},{"alias_kind":"pith_short_12","alias_value":"PS24DFZXHXY6","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PS24DFZXHXY6COMV","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PS24DFZX","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:ed8bcf19986d559ad7a820f3c90d213c14c88d12be7a6356add034303c44892f","target":"graph","created_at":"2026-05-18T00:16:31Z","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 convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite dimensional inequality. This inequality is proven via a contradiction argument and t","authors_text":"Bao Q. Tang, Klemens Fellner","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-04T09:14:54Z","title":"Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction-diffusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.01427","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:d2a5816d8a5b554de901efa431155d8de92dad33bd6feb951be28bf909875e9c","target":"record","created_at":"2026-05-18T00:16:31Z","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":"820c420aee4e11e7605d9ae76515bd9b39dc6d32837d93b9c3a8e9a67b26b051","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-08-04T09:14:54Z","title_canon_sha256":"d96a2e1da54cae8ded99eac0fb3e956af6dc35f405f69063660e97c3a1420061"},"schema_version":"1.0","source":{"id":"1708.01427","kind":"arxiv","version":1}},"canonical_sha256":"7cb5c197373df1e139950a1662358f56a9db0b09cbba4c724ca516e8b57450a5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7cb5c197373df1e139950a1662358f56a9db0b09cbba4c724ca516e8b57450a5","first_computed_at":"2026-05-18T00:16:31.708126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:16:31.708126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wl8I/uwyTKOyP/DZWCTZUpqgD/xtmjB9SQVwZHd3QnRCm61lkIo0mnu5k843WKStN83+ndxT6JRjak4zEdSNCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:16:31.708528Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.01427","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d2a5816d8a5b554de901efa431155d8de92dad33bd6feb951be28bf909875e9c","sha256:ed8bcf19986d559ad7a820f3c90d213c14c88d12be7a6356add034303c44892f"],"state_sha256":"38be5cfa0762f37274c337d6d075c71a1e6922cd158668b2b261f15723ee6144"}