{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:E3UW7CIHJHPRP2HDG5ZMKEOY7V","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":"df65f9e3b2fb07fae4474187fad242d86d2faf9d620782897ce9d44571d13f24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-18T13:56:27Z","title_canon_sha256":"aaec856a4589f47f813868c61ecadff6ac39d7202b040e25da638aaba4ca42e8"},"schema_version":"1.0","source":{"id":"1205.4160","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.4160","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"arxiv_version","alias_value":"1205.4160v1","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.4160","created_at":"2026-05-18T03:55:22Z"},{"alias_kind":"pith_short_12","alias_value":"E3UW7CIHJHPR","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_16","alias_value":"E3UW7CIHJHPRP2HD","created_at":"2026-05-18T12:27:04Z"},{"alias_kind":"pith_short_8","alias_value":"E3UW7CIH","created_at":"2026-05-18T12:27:04Z"}],"graph_snapshots":[{"event_id":"sha256:1af0595f6404c50c527777eed891122a1bf2f27ae64597c24154078584e319e3","target":"graph","created_at":"2026-05-18T03:55:22Z","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":"In this paper we prove a weak comparison principle for a reaction-diffusion system without uniqueness of solutions. We apply the abstract results to the Lotka-Volterra system with diffusion, a generalized logistic equation and to a model of fractional-order chemical autocatalysis with decay. Morever, in the case of the Lotka-Volterra system a weak maximum principle is given, and a suitable estimate in the space of essentially bounded functions $L^{\\infty}$ is proved for at least one solution of the problem.","authors_text":"Jos\\'e Valero","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-18T13:56:27Z","title":"A weak comparison principle for reaction-diffusion systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.4160","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:b3207d200e0a49fb2d04ca86b6bcb215c93887d63a215bc9048bb81dde6adee0","target":"record","created_at":"2026-05-18T03:55:22Z","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":"df65f9e3b2fb07fae4474187fad242d86d2faf9d620782897ce9d44571d13f24","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-05-18T13:56:27Z","title_canon_sha256":"aaec856a4589f47f813868c61ecadff6ac39d7202b040e25da638aaba4ca42e8"},"schema_version":"1.0","source":{"id":"1205.4160","kind":"arxiv","version":1}},"canonical_sha256":"26e96f890749df17e8e33772c511d8fd4e29c34ef223990496c539d9b746214c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"26e96f890749df17e8e33772c511d8fd4e29c34ef223990496c539d9b746214c","first_computed_at":"2026-05-18T03:55:22.606608Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:22.606608Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zhm2pog8VGjPujmzFYRr7WybGFZ3IVfhRs4qFK9Wl4af/UoXR9NNeybT8tyYgAq7HVI1VOz1AASSWcLOQc0ECA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:22.607141Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.4160","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b3207d200e0a49fb2d04ca86b6bcb215c93887d63a215bc9048bb81dde6adee0","sha256:1af0595f6404c50c527777eed891122a1bf2f27ae64597c24154078584e319e3"],"state_sha256":"b325bfff1f87382e0e49dd04257a0fc53aa57d6010a68e809a7bda20e763b926"}