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","work_id":"46cb4c47-3d03-4ddc-bad5-648e30c43b6c","year":2008}],"snapshot_sha256":"09e1751064319da829d547cf2bb368be59404ef0103293826d623e1a30f351eb"},"source":{"id":"2605.16049","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-19T18:45:43.187729Z","id":"229e072c-f533-4af3-971f-0c8f57ab2741","model_set":{"reader":"grok-4.3"},"one_line_summary":"Sufficient algebraic conditions on the signs of the constant and leading coefficients of the diffusion-scaled characteristic polynomial are derived to guarantee Turing instability on suitable domains, then applied to a two-site phosphorylation network to obtain a condition involving only four rate-1","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"For reaction networks admitting a monomial steady-state parameterization, the signs of the constant and leading coefficients in the diffusion-scaled characteristic polynomial supply a sufficient condition for Turing-like spatial instability","strongest_claim":"We formulate a sufficient condition -- based on the signs of the constant and leading coefficients of the characteristic polynomial of the linearized Jacobian scaled by the diffusion coefficients -- that guarantees a Turing-like instability to spatially inhomogeneous solutions on appropriately chosen domains Ω.","weakest_assumption":"The spatially homogeneous reaction network admits a monomial steady-state parameterization (explicitly invoked in the abstract and used to obtain algebraic inequalities); if this parameterization does not exist or is not monomial, the reduction to polynomial inequalities in rate constants and diffusion coefficients fails."}},"verdict_id":"229e072c-f533-4af3-971f-0c8f57ab2741"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:47b7aac09946d061dfdc30bfa2db7c2a91187e33a85e5772214d86e13c0557b4","target":"record","created_at":"2026-05-20T00:01:50Z","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":"3dd8bba57d8ab1ee31da41e6533f149ab2f64ae30c2115b0f41aa3eff842865c","cross_cats_sorted":["math.AP","q-bio.MN"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2026-05-15T15:18:26Z","title_canon_sha256":"8681dd537cd4ba9d5623a2929024a3ae6900ebecab215c20d470dd0c01b25bda"},"schema_version":"1.0","source":{"id":"2605.16049","kind":"arxiv","version":1}},"canonical_sha256":"efb80bf418ac54e694d53c095f1c2b35076974829f11358f81fe4d8627b31177","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"efb80bf418ac54e694d53c095f1c2b35076974829f11358f81fe4d8627b31177","first_computed_at":"2026-05-20T00:01:50.649253Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-20T00:01:50.649253Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MeMcZ93XJkIjtQv4E6FW40Z+BuJvlLRZ3pEVAO+foAJRNiOE7bQdZFUqjvQ0J2yP86zOtsuZyJ7xT/EBL32KCg==","signature_status":"signed_v1","signed_at":"2026-05-20T00:01:50.649913Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.16049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:47b7aac09946d061dfdc30bfa2db7c2a91187e33a85e5772214d86e13c0557b4","sha256:e9d8ec566e743c52276cba64258f356269a21b3de5e601b6e30c85ca819ed43d"],"state_sha256":"027b64cd67348bd2ca59b244e0948083bcc603fedd32beda3add45e977bef7ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aJcY8CxgQ+osQhSZ54kSbCSTc2EbCGwJbxjijZf7mtl+mDeYW9qlVFGabhmRFcfksGfu+X8kFDeunxPcVjoxBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-23T15:34:45.602539Z","bundle_sha256":"af55ae5e9243b701fc9acd6ed84646a5f45f20566c6cf2ef995aae6ebfcd28f2"}}