{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:FOSBCVFOMKJ7LSXUU2GJ2KY3BN","short_pith_number":"pith:FOSBCVFO","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"},"canonical_sha256":"2ba41154ae6293f5caf4a68c9d2b1b0b5c18258aab8144ee269ab7e9f34ef45f","source":{"kind":"arxiv","id":"2604.06645","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.06645","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.06645v2","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.06645","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"FOSBCVFOMKJ7","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"pith_short_16","alias_value":"FOSBCVFOMKJ7LSXU","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"pith_short_8","alias_value":"FOSBCVFO","created_at":"2026-05-27T02:05:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:FOSBCVFOMKJ7LSXUU2GJ2KY3BN","target":"record","payload":{"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"},"canonical_sha256":"2ba41154ae6293f5caf4a68c9d2b1b0b5c18258aab8144ee269ab7e9f34ef45f","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"},"source_kind":"arxiv","source_id":"2604.06645","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":"2026-05-27T02:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GBV+KOdXEhtvGKxXLea8nu7TeTRx0T6JVKFTH5B0Qh/HIb1GFT/vfFMzlQnF8ZR/wqUErw7g22feSnJpLkmsCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:31:40.502080Z"},"content_sha256":"afbb34767a9539ddfc785d1d3c07d1ade8c860a6cf583f9d835abc408237a1fe","schema_version":"1.0","event_id":"sha256:afbb34767a9539ddfc785d1d3c07d1ade8c860a6cf583f9d835abc408237a1fe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:FOSBCVFOMKJ7LSXUU2GJ2KY3BN","target":"graph","payload":{"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"},"verdict_id":"bfc95e14-fd1d-4789-9d96-ed95fab75e15"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-27T02:05:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4e9TAUYToaNmJuDZv2xIuaTxBbFRO0Q2ynv7aIvAoCN51rL+ETjeMT2sxx8s4c8KI+iC3Tz8xmYlHojdSEgMCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T02:31:40.503019Z"},"content_sha256":"d7db7ede0fe4ad17ce543e8c1c5cf0465b4d4f22552f81771dece84ef1078a44","schema_version":"1.0","event_id":"sha256:d7db7ede0fe4ad17ce543e8c1c5cf0465b4d4f22552f81771dece84ef1078a44"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/bundle.json","state_url":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/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":"2026-06-09T02:31:40Z","links":{"resolver":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN","bundle":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/bundle.json","state":"https://pith.science/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/FOSBCVFOMKJ7LSXUU2GJ2KY3BN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:FOSBCVFOMKJ7LSXUU2GJ2KY3BN","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":"d8e20e4ac3fa0813713b72e68b69a4d4b0d0120c6a6af6d466c1197c393cb519","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-04-08T03:42:27Z","title_canon_sha256":"694eac82d81639980ea36ef505569886cfee2fbed44c40efe86d7af7077554ec"},"schema_version":"1.0","source":{"id":"2604.06645","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2604.06645","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"arxiv_version","alias_value":"2604.06645v2","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2604.06645","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"pith_short_12","alias_value":"FOSBCVFOMKJ7","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"pith_short_16","alias_value":"FOSBCVFOMKJ7LSXU","created_at":"2026-05-27T02:05:19Z"},{"alias_kind":"pith_short_8","alias_value":"FOSBCVFO","created_at":"2026-05-27T02:05:19Z"}],"graph_snapshots":[{"event_id":"sha256:d7db7ede0fe4ad17ce543e8c1c5cf0465b4d4f22552f81771dece84ef1078a44","target":"graph","created_at":"2026-05-27T02:05:19Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth; the noise is suitable multiplicative noise."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Stochastic reaction-diffusion systems with triangular mass control admit global solutions under suitable multiplicative noise."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control."}],"snapshot_sha256":"0aa57ce445f0707b1abec4745cf5e807e127b8dd00acb451534393ab44161e04"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"51ad7780dcb341a7890b31a1e23da833417ee42f170b6a86a43870554c050b86"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2604.06645/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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","authors_text":"Dionysis Milesis, Michael Salins","cross_cats":["math.AP"],"headline":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-04-08T03:42:27Z","title":"Global in time solutions to stochastic reaction-diffusion systems with superlinear reactions satisfying a triangular control of mass"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2604.06645","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-10T18:35:40.689707Z","id":"bfc95e14-fd1d-4789-9d96-ed95fab75e15","model_set":{"reader":"grok-4.3"},"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","pith_extraction_headline":"Suitable multiplicative noise ensures global-in-time solutions for stochastic reaction-diffusion systems obeying triangular mass control.","strongest_claim":"stochastically perturbing reaction-diffusion systems with triangular mass control by suitable multiplicative noise leads to solutions that exist for all time.","weakest_assumption":"The reaction terms satisfy quasipositivity, a triangular mass-control structure, and polynomial growth; the noise is suitable multiplicative noise."}},"verdict_id":"bfc95e14-fd1d-4789-9d96-ed95fab75e15"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:afbb34767a9539ddfc785d1d3c07d1ade8c860a6cf583f9d835abc408237a1fe","target":"record","created_at":"2026-05-27T02:05:19Z","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":"d8e20e4ac3fa0813713b72e68b69a4d4b0d0120c6a6af6d466c1197c393cb519","cross_cats_sorted":["math.AP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-04-08T03:42:27Z","title_canon_sha256":"694eac82d81639980ea36ef505569886cfee2fbed44c40efe86d7af7077554ec"},"schema_version":"1.0","source":{"id":"2604.06645","kind":"arxiv","version":2}},"canonical_sha256":"2ba41154ae6293f5caf4a68c9d2b1b0b5c18258aab8144ee269ab7e9f34ef45f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ba41154ae6293f5caf4a68c9d2b1b0b5c18258aab8144ee269ab7e9f34ef45f","first_computed_at":"2026-05-27T02:05:19.276250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-27T02:05:19.276250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"uxQTbPypatq73bNoCP7/uutJJGBeBDvdPe5csLYopQH8hzfxyHA6eb1TkSTnkyrH7ABuEwNy+7+uXj4L6bOIDA==","signature_status":"signed_v1","signed_at":"2026-05-27T02:05:19.276964Z","signed_message":"canonical_sha256_bytes"},"source_id":"2604.06645","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afbb34767a9539ddfc785d1d3c07d1ade8c860a6cf583f9d835abc408237a1fe","sha256:d7db7ede0fe4ad17ce543e8c1c5cf0465b4d4f22552f81771dece84ef1078a44"],"state_sha256":"deba8bcd118c4da13d1758eab8f250076a6d6309ffa6ac61d466c7c438434a6e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IYQXUGCyeiNwMq4nz7yCivp6AwRHaTUBj+DuFfvcocvZiaA5gHMERbm1TXG6MfdVS7quFzFuw5UEpyx8sYgyAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T02:31:40.507728Z","bundle_sha256":"0fb2ac0b808a68acd92a5f9ec4d89336d9e0d79a84c7ba8fc161eee53ecce1c0"}}