{"ID":2881112,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.12896","arxiv_id":"2508.12896","title":"Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption","abstract":"We formalize three design axioms for sustained adoption of agent-centric AI systems executing multi-step tasks: (A1) Reliability \u003e Novelty; (A2) Embed \u003e Destination; (A3) Agency \u003e Chat. We model adoption as a sum of a decaying novelty term and a growing utility term and derive the phase conditions for troughs/overshoots with full proofs. We introduce: (i) an identifiability/confounding analysis for $(α,β,N_0,U_{\\max})$ with delta-method gradients; (ii) a non-monotone comparator (logistic-with-transient-bump) evaluated on the same series to provide additional model comparison; (iii) ablations over hazard families $h(\\cdot)$ mapping $ΔV \\to β$; (iv) a multi-series benchmark (varying trough depth, noise, AR structure) reporting coverage (type-I error, power); (v) calibration of friction proxies against time-motion/survey ground truth with standard errors; (vi) residual analyses (autocorrelation and heteroskedasticity) for each fitted curve; (vii) preregistered windowing choices for pre/post estimation; (viii) Fisher information \u0026 CRLB for $(α,β)$ under common error models; (ix) microfoundations linking $\\mathcal{T}$ to $(N_0,U_{\\max})$; (x) explicit comparison to bi-logistic, double-exponential, and mixture models; and (xi) threshold sensitivity to $C_f$ heterogeneity. Figures and tables are reflowed for readability, and the bibliography restores and extends non-logistic/Bass adoption references (Gompertz, Richards, Fisher-Pry, Mansfield, Griliches, Geroski, Peres). All code and logs necessary to reproduce the synthetic analyses are embedded as LaTeX listings.","short_abstract":"We formalize three design axioms for sustained adoption of agent-centric AI systems executing multi-step tasks: (A1) Reliability \u003e Novelty; (A2) Embed \u003e Destination; (A3) Agency \u003e Chat. We model adoption as a sum of a decaying novelty term and a growing utility term and derive the phase conditions for troughs/overshoot...","url_abs":"https://arxiv.org/abs/2508.12896","url_pdf":"https://arxiv.org/pdf/2508.12896v1","authors":"[\"Faruk Alpay\",\"Taylan Alpay\"]","published":"2025-08-18T12:53:38Z","proceeding":"cs.AI","tasks":"[\"cs.AI\",\"cs.HC\",\"stat.ME\"]","methods":"[]","has_code":false}