Contemporary artificial intelligence excels at pattern recognition but lacks genuine understanding, temporal awareness, and ethical reasoning. Critics argue that AI systems manipulate statistical correlations without grasping concepts, time, or moral implications. This article presents Phase 2, a component of the emerging infrastructure called Sophimatics, a computational framework that translates philosophical categories into working algorithms through the integration of complex time. Our approach operationalizes Aristotelian substance theory, Augustinian temporal consciousness, Husserlian intentionality, and Hegelian dialectics within a unified temporal–semantic architecture. The system represents time as both chronological and experiential, allowing navigation between memory and imagination while maintaining conceptual coherence. Validation through a Data Protection Policy use case demonstrates significant improvements: confidence in decisions increased from 6.50 to 9.40 on a decimal scale, temporal awareness from 2.00 to 9.50, and regulatory compliance from 6.00 to 9.00 compared to traditional approaches. The framework successfully links philosophical authenticity with computational practicality, offering greater ethical consistency and contextual adaptability for AI systems that require temporal reasoning and ethical foundations.

This work represents the natural continuation of the development of the cognitive architecture developed and named Sophimatics, organically integrating the spatio-temporal processing mechanisms of the Super Time Cognitive Neural Network (STCNN) with the advanced principles of Sophimatics. Sophimatics’ goal is as challenging as it is fraught with obstacles, but its ultimate aim is to achieve a more humanized post-generative artificial intelligence, capable of understanding and analyzing context and evaluating the user’s purpose and intent, viewing time not only as a chronological sequence but also as an experiential continuum. The path to achieving this extremely ambitious goal has been made possible thanks to some previous work in which the philosophical thinking of interest in AI was first inherited as the inspiration for the aforementioned capabilities of the Sophimatic framework, then the issue of mapping concepts and philosophical thinking in Sophimatics’ AI infrastructure was addressed, and finally a cognitive-inspired network such as STCNN was created. This work, on the other hand, addresses the challenge of how to endow the infrastructure with both chronological and experiential time and its powerful implications, such as the innate ability to resolve paradoxes, which generative AI does not have among its prerogatives precisely because of structural limitations. To reach these results, the model operates in the two-dimensional complex time domain ℂ², extending cognitive processing capabilities through the implementation of dual temporal operators that simultaneously manage the real temporal dimension, where past, present, and future are managed and the imaginary one, that considers memory, creativity, and imagination. The resulting architecture demonstrates superior capabilities in resolving informational paradoxes and integrating apparently contradictory cognitive states, maintaining computational coherence through adaptive Sophimatic mechanisms. In conclusion, this work introduces Phase 4 of the Sophimatic framework, enabling management of two-dimensional time within a novel cognitively inspired neural architecture grounded in philosophical concepts. It connects with existing research on temporal cognition, hybrid symbolic–connectionist models, and ethical AI. The methodology translates philosophical insights into formal computational systems, culminating in a mathematical formalization that supports two-dimensional temporal reasoning and paradox resolution. Experimental results demonstrate efficiency, predictive accuracy, and computational feasibility, highlighting potential real-world applications, future research directions, and present limitations.

Contemporary artificial intelligence is dominated by generative systems that excel at extracting patterns but fail to grasp meaning, sense, context, and experiential temporality. This limitation highlights the need for new computational wisdom that combines philosophical insights with advanced models to produce AI systems capable of authentic understanding. Sophimatics, as elaborated upon in this article, is introduced as a science of computational wisdom that rejects the purely syntactic manipulation of symbols characteristic of classical physical symbolic systems and addresses the shortcomings of generative statistical approaches. Building on philosophical foundations of dynamic ontology, intentionality and dialectical reasoning, Sophimatics integrates complex temporality, multidimensional semantic modeling, hybrid symbolic–connectionist logic, and layered memory structures to that the AI can perceive, remember, reason, and act in ethically grounded ways. This article, which is part of a set of papers, summarizes the theoretical framework underlying Sophimatics and outlines the conceptual results of the materials and methods, illustrating the potential of this approach to improve interpretability, contextual adaptation, and ethical deliberation compared to basic generative models. This is followed by a methodology and a complete formal model for translating philosophical categories into an operational model and specific architecture. This article represents Phase 1 of a six-phase research program, providing mathematical foundations for the architectural implementation and empirical validation presented in companion publications. Following this, several use cases are outlined, and then the Discussion Section anticipates the main results and perspectives for post-generative AI solutions within the Sophimatic paradigm.

Current generative AI systems, despite extraordinary progress, face fundamental limitations in temporal reasoning, contextual understanding, and ethical decision-making. These systems process information statistically without authentic comprehension of experiential time or intentional context, limiting their applicability in security-critical domains where reasoning about past experiences, present situations, and future implications is essential. We present Phase 3 of the Sophimatics framework: Super Time-Cognitive Neural Networks (STCNNs), which address these limitations through complex-time representation T ∈ ℂ where chronological time (Re(T)) integrates with experiential dimensions of memory (Im(T) < 0), present awareness (Im(T) ≈ 0), and imagination (Im(T) > 0). The STCNN architecture implements philosophical constraints through geometric parameters α and β that bound memory accessibility and creative projection, enabling neural systems to perform temporal-philosophical reasoning while maintaining computational tractability. We demonstrate STCNN’s effectiveness across five security-critical applications: threat intelligence (AUC 0.94, 1.8 s anticipation), privacy-preserving AI (84% utility at ε = 1.0), intrusion detection (96.3% detection, 2.1% false positives), secure multi-party computation (ethical compliance 0.93), and blockchain anomaly detection (94% detection, 3.2% false positives). Empirical evaluation shows 23–45% improvement over baseline systems while maintaining temporal coherence > 0.9, demonstrating that integration of temporal-philosophical reasoning with neural architectures enables AI systems to reason about security threats through simultaneous processing of historical patterns, current contexts, and projected risks.

While large language models (LLMs) such as ChatGPT, Claude, and DeepSeek are evaluated based on their accuracy and truthfulness, “hallucinations” betray underlying structural limitations. These results are not simply incorrect answers, but statistical resonances; they are instances where models stabilize into statistically significant (though semantically unfounded) response patterns. Current frameworks fail to accommodate contextual semantics, experiential time, and intentionality as key dimensions for effective experience-based decision-making in complex digital spaces. This article presents an integration paradigm offered by the theory of uncertainty and incompleteness of information, extended by the Sophimatics approach with 2D complex time (t = t + i·t₀) and Super Time Cognitive Neural Network (STCNN) that provides both memory management, imagination enhancement, and creativity generation as computational primitives. By integrating probability with plausibility, credibility, and possibility, our model reconsiders the issue of evaluating the reliability of LLM results as a problem that goes beyond traditional probabilistic approaches. Accepting that hallucinations are an emerging phenomenon of resonance between statistical distributions, we suggest an extended probability method in which these resonances can be mitigated and directed towards a coherent cognitive understanding. The paper places this approach in the broader perspective of digital transformation at the information systems level and its implications for AI reliability, explainability, and adaptive decision-making in post-generative AI. Intuitive scenarios are described, based on the inclusion of complex time and Sophimatics in theoretical modelling, illustrating how prediction, historical-contextual adoption, and resistance to paradoxical or contradictory information are strengthened. The results point to this paradigm as a springboard for reliable, human-aligned AI capable of enabling digital transformation in sectors such as healthcare, finance, and governance.

Phase 6 of the Sophimatics framework represents the culmination of a comprehensive research program integrating philosophical wisdom with computational sophistication to address fundamental challenges in artificial intelligence systems. Building upon the Complex-Time Recursive Model established in Phase 5, this phase introduces a human-in-the-loop iterative refinement methodology specifically designed for security-critical applications. Through systematic validation across real-world cybersecurity datasets, including NSL-KDD and CICIDS2017, alongside healthcare privacy scenarios using MIMIC-III derived data, we demonstrate that collaborative human–AI co-creation significantly enhances system performance across multiple dimensions, including interpretive accuracy, contextual fidelity, and ethical consistency. The proposed architecture implements three complementary feedback mechanisms: symbolic knowledge base refinement through expert-provided ontological corrections, neural parameter optimization guided by human evaluation of ethical alignment, and dynamic weight adjustment for value-system integration. Experimental results show substantial improvements over baseline approaches, with intrusion detection accuracy reaching 98.7% on NSL-KDD while maintaining 94.3% privacy preservation scores as measured by differential privacy guarantees. The healthcare privacy experiments demonstrate 97.2% sensitive attribute protection with only 2.1% utility loss compared to non-private baselines. Critical analysis reveals that human oversight mechanisms reduce false positive rates in ethical constraint violations by 67% compared to purely automated systems, while convergence analysis indicates stable performance after approximately 12–15 iterations across diverse application domains. These findings establish Phase 6 as an essential bridge between theoretical Sophimatics foundations and practical deployment in privacy-sensitive contexts, demonstrating that philosophically grounded AI architectures can achieve superior performance when augmented with structured human feedback loops. The work contributes both methodological innovations in human–AI collaboration and empirical validation, demonstrating the viability of Sophimatics principles for addressing contemporary challenges in data protection and cybersecurity.