{"paper":{"title":"Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Reentrant value fields on finite graphs form well-posed delayed reaction-diffusion systems that admit compact global attractors and delay-independent stability of principal components.","cross_cats":[],"primary_cat":"math.DS","authors_text":"Karsten Bohlen","submitted_at":"2026-05-05T16:29:44Z","abstract_excerpt":"This article develops a field theory of synthetic cognition in which a symbolic field $H_L$ and a geometric field $X_R$, each a section of a vertex bundle over a finite graph, are coupled through a bipartite Hilbert-Schmidt operator with propagation delays. The central object is a retarded functional differential equation (RFDE) on the history space: the reaction-diffusion equation is the operative equation of the theory. Nine synthetic design blueprints specify admissibility conditions for each architectural component; each condition carries a dynamical consequence. The main formal results ar"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"The main formal results are: (1) well-posedness of the full deterministic RFDE under constant input u*, (2) existence of a compact global attractor from compact viability and eventual compactness of solution segments, (3) delay-independent global stability of the principal components (H_L, X_R, P) in the closed stability regime with fixed interfield coupling operators satisfying C_K^2 < μ_L μ_R, (4) SE(d)-invariance of the scalar geometric feature dynamics, and (5) an O(1/κ_Y) fast relaxation estimate for the valuative variable.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"Joint non-emptiness of all admissible classes is assumed.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Establishes well-posedness, compact global attractors, and delay-independent global stability for retarded functional differential equations modeling reentrant value fields as coupled reaction-diffusion systems on finite graphs.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Reentrant value fields on finite graphs form well-posed delayed reaction-diffusion systems that admit compact global attractors and delay-independent stability of principal components.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b214f6b6a02fb09745d2a6ac941d7d63ed29bfba8019a49a0bbe4f3644ead624"},"source":{"id":"2605.03940","kind":"arxiv","version":3},"verdict":{"id":"f1e070d2-7196-446d-90ab-6e8c822a117d","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T00:54:31.489235Z","strongest_claim":"The main formal results are: (1) well-posedness of the full deterministic RFDE under constant input u*, (2) existence of a compact global attractor from compact viability and eventual compactness of solution segments, (3) delay-independent global stability of the principal components (H_L, X_R, P) in the closed stability regime with fixed interfield coupling operators satisfying C_K^2 < μ_L μ_R, (4) SE(d)-invariance of the scalar geometric feature dynamics, and (5) an O(1/κ_Y) fast relaxation estimate for the valuative variable.","one_line_summary":"Establishes well-posedness, compact global attractors, and delay-independent global stability for retarded functional differential equations modeling reentrant value fields as coupled reaction-diffusion systems on finite graphs.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"Joint non-emptiness of all admissible classes is assumed.","pith_extraction_headline":"Reentrant value fields on finite graphs form well-posed delayed reaction-diffusion systems that admit compact global attractors and delay-independent stability of principal components."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.03940/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T12:40:49.824335Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-20T00:01:21.481162Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T14:54:44.028199Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"f3f7f4397704ac9e8d9924700dce485b4e45c5e076fc12edb9e7d036e672dbd5"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"2eed40ff3d8136061586dfa88b7c4aac2a73b654f83b91255678450f5943f602"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}