{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:FOSBCVFOMKJ7LSXUU2GJ2KY3BN","short_pith_number":"pith:FOSBCVFO","schema_version":"1.0","canonical_sha256":"2ba41154ae6293f5caf4a68c9d2b1b0b5c18258aab8144ee269ab7e9f34ef45f","source":{"kind":"arxiv","id":"2604.06645","version":2},"attestation_state":"computed","paper":{"title":"Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control.","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Dionysis Milesis, Michael Salins","submitted_at":"2026-04-08T03:42:27Z","abstract_excerpt":"We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as reversi"},"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":true},"canonical_record":{"source":{"id":"2604.06645","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-04-08T03:42:27Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"694eac82d81639980ea36ef505569886cfee2fbed44c40efe86d7af7077554ec","abstract_canon_sha256":"d8e20e4ac3fa0813713b72e68b69a4d4b0d0120c6a6af6d466c1197c393cb519"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-27T02:05:19.276964Z","signature_b64":"uxQTbPypatq73bNoCP7/uutJJGBeBDvdPe5csLYopQH8hzfxyHA6eb1TkSTnkyrH7ABuEwNy+7+uXj4L6bOIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ba41154ae6293f5caf4a68c9d2b1b0b5c18258aab8144ee269ab7e9f34ef45f","last_reissued_at":"2026-05-27T02:05:19.276250Z","signature_status":"signed_v1","first_computed_at":"2026-05-27T02:05:19.276250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control.","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Dionysis Milesis, Michael Salins","submitted_at":"2026-04-08T03:42:27Z","abstract_excerpt":"We study systems of reaction-diffusion equations perturbed by multiplicative noise, where the reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth. Our results apply to a broad class of reaction-diffusion systems arising, most notably, in chemistry and biology. In the deterministic setting these assumptions are known to guarantee the global existence of solutions. In the stochastic setting, however, reaction-diffusion systems have typically been analyzed under different assumptions on the reactions that preclude many natural models, such as reversi"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth; the noise is suitable multiplicative noise.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Stochastic reaction-diffusion systems with triangular mass control admit global solutions under suitable multiplicative noise.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"0aa57ce445f0707b1abec4745cf5e807e127b8dd00acb451534393ab44161e04"},"source":{"id":"2604.06645","kind":"arxiv","version":2},"verdict":{"id":"bfc95e14-fd1d-4789-9d96-ed95fab75e15","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-10T18:35:40.689707Z","strongest_claim":"stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time.","one_line_summary":"Stochastic reaction-diffusion systems with triangular mass control admit global solutions under suitable multiplicative noise.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth; the noise is suitable multiplicative noise.","pith_extraction_headline":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.06645/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"51ad7780dcb341a7890b31a1e23da833417ee42f170b6a86a43870554c050b86"},"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":"2604.06645","created_at":"2026-05-27T02:05:19.276341+00:00"},{"alias_kind":"arxiv_version","alias_value":"2604.06645v2","created_at":"2026-05-27T02:05:19.276341+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.06645","created_at":"2026-05-27T02:05:19.276341+00:00"},{"alias_kind":"pith_short_12","alias_value":"FOSBCVFOMKJ7","created_at":"2026-05-27T02:05:19.276341+00:00"},{"alias_kind":"pith_short_16","alias_value":"FOSBCVFOMKJ7LSXU","created_at":"2026-05-27T02:05:19.276341+00:00"},{"alias_kind":"pith_short_8","alias_value":"FOSBCVFO","created_at":"2026-05-27T02:05:19.276341+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN","json":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN.json","graph_json":"https://pith.science/api/pith-number/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/graph.json","events_json":"https://pith.science/api/pith-number/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/events.json","paper":"https://pith.science/paper/FOSBCVFO"},"agent_actions":{"view_html":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN","download_json":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN.json","view_paper":"https://pith.science/paper/FOSBCVFO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2604.06645&json=true","fetch_graph":"https://pith.science/api/pith-number/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/graph.json","fetch_events":"https://pith.science/api/pith-number/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/action/storage_attestation","attest_author":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/action/author_attestation","sign_citation":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/action/citation_signature","submit_replication":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/action/replication_record"}},"created_at":"2026-05-27T02:05:19.276341+00:00","updated_at":"2026-05-27T02:05:19.276341+00:00"}