Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915449420120064 |
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| author | Alpay, Faruk Alpay, Taylan |
| author_facet | Alpay, Faruk Alpay, Taylan |
| contents | We formalize three design axioms for sustained adoption of agent-centric AI systems executing multi-step tasks: (A1) Reliability > Novelty; (A2) Embed > Destination; (A3) Agency > 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 & 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12896 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption Alpay, Faruk Alpay, Taylan Artificial Intelligence Human-Computer Interaction Methodology 62M10, 62J02, 62F12, 62P20, 91B16 We formalize three design axioms for sustained adoption of agent-centric AI systems executing multi-step tasks: (A1) Reliability > Novelty; (A2) Embed > Destination; (A3) Agency > 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 & 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. |
| title | Reliability, Embeddedness, and Agency: A Utility-Driven Mathematical Framework for Agent-Centric AI Adoption |
| topic | Artificial Intelligence Human-Computer Interaction Methodology 62M10, 62J02, 62F12, 62P20, 91B16 |
| url | https://arxiv.org/abs/2508.12896 |