{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,12]],"date-time":"2026-06-12T02:56:08Z","timestamp":1781232968547,"version":"3.54.1"},"reference-count":67,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T00:00:00Z","timestamp":1780617600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>The proliferation of AI-generated content and personalized AI systems has sharpened two fundamental and related computational problems: the progressive erosion of authentic identity in AI-mediated representations, and the growing difficulty of distinguishing human-originated from AI-generated behavioral and textual streams. This paper proposes a rigorous computational framework in which digital identity is formalized as a holomorphic function of complex time T = (a + ib) \u2208 \u2102, where the real component Re(T) encodes chronological progression and the imaginary component Im(T) spans a continuum from episodic memory (Im(T)\u00a0&lt;\u00a00) through the present moment (Im(T)\u00a0=\u00a00) to prospective imagination (Im(T)\u00a0&gt;\u00a00). We argue that holomorphicity\u2014enforced via Cauchy\u2013Riemann regularization during CTNN learning (Proposition 1)\u2014provides a theoretically grounded encoding of identity coherence, and discuss its advantages over alternative mathematical choices, including Lipschitz continuity, C\u221e smoothness, piecewise analytic functions, and stochastic models. Under four explicit Assumptions 1\u20134 covering the Markovian structure and fixed context window of current LLM architectures, we establish via Lemmas 1 and 2 and Theorem 1 that AI-generated behavioral trajectories exhibit structural limitations in satisfying the Cauchy\u2013Riemann conditions at temporal depths characteristic of human biographical memory\u2014limitations that do not arise for human trajectories learned under CTNN regularization. Building on this result, we introduce the Human\u2013AI Authenticity Discriminant (HAAD), a theoretically grounded classifier with a fully specified calibration algorithm and sensitivity analysis (\u03ba \u0394AUROC \u2264 0.04 over \u00b130% perturbation). Five metrics\u2014TCS, ISI, PAS, GAS, and HAAD\u2014are derived analytically from the holomorphic structure. The algorithmic framework is instantiated on four real-world datasets: MovieLens 25M, the Pushshift Reddit corpus, the Stack Overflow Data Dump, and the LIAR dataset. On the LIAR benchmark, TDT-HAAD achieves AUROC = 0.82 (95% CI: [0.79, 0.85]), exceeding a RoBERTa-based LLM detector baseline (AUROC = 0.75, DeLong p &lt; 0.01); an ablation study supports the structural contribution of each component. A credibility harvesting signature is detectable 45.3 \u00b1 12.1 days before standard temporal models reach statistical significance.<\/jats:p>","DOI":"10.3390\/a19060458","type":"journal-article","created":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T17:18:16Z","timestamp":1780679896000},"page":"458","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Complex-Time Framework for Authenticity and Identity in Personalized AI"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3119-4608","authenticated-orcid":false,"given":"Gerardo","family":"Iovane","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Salerno, 84084 Fisciano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Giovanni","family":"Iovane","sequence":"additional","affiliation":[{"name":"Liceo Scientifico Statale Francesco Severi, 84100 Salerno, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Antonio","family":"De Rosa","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Salerno, 84084 Fisciano, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-8126-8755","authenticated-orcid":false,"given":"Francesco","family":"Barbato","sequence":"additional","affiliation":[{"name":"Department of Physics, Sapienza University of Rome, 00185 Rome, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,6,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/MC.2009.263","article-title":"Matrix factorization techniques for recommender systems","volume":"42","author":"Koren","year":"2009","journal-title":"Computer"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"He, X., Liao, L., Zhang, H., Nie, L., Hu, X., and Chua, T.-S. 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