{"paper":{"title":"Composite-Operator Scaling on Triadic Hypergraphs: Formation Transitions in Multi-Agent Architectures with Three-Body Coupling","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Multi-agent AI architectures with k-body spin correlations exhibit composite-operator criticality, yielding vanishing susceptibility for k greater than or equal to 3.","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Eduardo Salazar","submitted_at":"2026-04-29T17:06:42Z","abstract_excerpt":"We study phase transitions on dynamic triadic hypergraphs, in which a continuous formation field evolves under stochastic Ginzburg--Landau dynamics with a cubic three-body coupling $g_\\tau\\phi_i\\phi_j\\phi_k$, while a discrete opinion variable $s_i\\in\\{-1,+1\\}$ undergoes Kawasaki exchange under a Hamiltonian with pairwise alignment and an irreducible three-body energy $-\\lambda_\\tau\\prod_{a\\in\\tau}s_a$. Near the formation critical point the cubic coupling is subleading and the transition remains continuous, controlled at leading order by a pairwise Ising baseline with renormalized coupling $J_{"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Multi-agent AI architectures whose dominant collective observable is a k-body spin correlator O_k ≡ ⟨ϕ^k⟩ over a Z_2-symmetric order parameter exhibit composite-operator criticality with effective exponents β_k = k/2 and γ_k = 2-k, thereby producing a finite susceptibility for k≥2 and a vanishing susceptibility for k≥3.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the dominant collective observable in the AI architectures is the k-body spin correlator and that the formation transition reduces exactly to a triadic Ising model under controlled universality and mean-field arguments.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Multi-agent AI systems with k-body correlations exhibit composite-operator criticality with exponents β_k = k/2 and γ_k = 2-k, producing vanishing susceptibility for k ≥ 3 and reducing to an exactly solvable triadic Ising model for k=3.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Multi-agent AI architectures with k-body spin correlations exhibit composite-operator criticality, yielding vanishing susceptibility for k greater than or equal to 3.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"a0960a756b9d6d645c45ffa2968d05c6877443cea7fe68e9660a074bea08e991"},"source":{"id":"2604.27038","kind":"arxiv","version":2},"verdict":{"id":"6f440702-3b20-48d8-9878-186615ec2239","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T11:03:42.332344Z","strongest_claim":"Multi-agent AI architectures whose dominant collective observable is a k-body spin correlator O_k ≡ ⟨ϕ^k⟩ over a Z_2-symmetric order parameter exhibit composite-operator criticality with effective exponents β_k = k/2 and γ_k = 2-k, thereby producing a finite susceptibility for k≥2 and a vanishing susceptibility for k≥3.","one_line_summary":"Multi-agent AI systems with k-body correlations exhibit composite-operator criticality with exponents β_k = k/2 and γ_k = 2-k, producing vanishing susceptibility for k ≥ 3 and reducing to an exactly solvable triadic Ising model for k=3.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the dominant collective observable in the AI architectures is the k-body spin correlator and that the formation transition reduces exactly to a triadic Ising model under controlled universality and mean-field arguments.","pith_extraction_headline":"Multi-agent AI architectures with k-body spin correlations exhibit composite-operator criticality, yielding vanishing susceptibility for k greater than or equal to 3."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.27038/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:38:33.466444Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:43:30.980637Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"49745599639e4612df1eb60cb0c2442fbbd2b818debd85a510b789395b220ae4"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}