This work continues the development of Topological Quantum Mechanics (TQM), a field-based framework in which probability, choice, and time emerge from geometric and resonant properties of a structured field rather than from predefined rules or central observers. In TQM V, probability is treated as a geometric feature of field configurations, metastable nodes arise from interacting flows, and time emerges as an ordering of transitions between temporary stable states. The model is applied to physical, cognitive, and artificial systems, demonstrating how coherent behavior can arise without explicit control, consciousness, or linear time assumptions. This paper is intended for researchers working at the intersection of physics, artificial intelligence, complex systems, and cognitive modeling, as well as developers interested in emergent computation and non-classical decision architectures. Version 5.1 extends TQM V with an Appendix (Computational Perspective), providing illustrative computational analogies and examples for programmers and AI researchers. The appendix does not modify the core theoretical framework but clarifies how probability fields and metastable nodes can be mapped to data structures and algorithmic processes.
This work continues the development of Topological Quantum Mechanics (TQM), a field-based framework in which probability, choice, and time emerge from geometric and resonant properties of a structured field rather than from predefined rules or central observers. In TQM V, probability is treated as a geometric feature of field configurations, metastable nodes arise from interacting flows, and time emerges as an ordering of transitions between temporary stable states. The model is applied to physical, cognitive, and artificial systems, demonstrating how coherent behavior can arise without explicit control, consciousness, or linear time assumptions. This paper is intended for researchers working at the intersection of physics, artificial intelligence, complex systems, and cognitive modeling, as well as developers interested in emergent computation and non-classical decision architectures. Version 5.1 extends TQM V with an Appendix (Computational Perspective), providing illustrative computational analogies and examples for programmers and AI researchers. The appendix does not modify the core theoretical framework but clarifies how probability fields and metastable nodes can be mapped to data structures and algorithmic processes.
In this work, we extend the framework of Topological Quantum Mechanics (TQM) by introducing probability fields as geometric structures arising from field tension and resonance alignment. We show how stable and metastable choices emerge without a central observer, and how time manifests as an ordering of transitions between field configurations. The framework generalizes previous parts of TQM-AI, introducing massless H3 nodes and illustrating the cycle of stability, metastability, decay, and field memory. ТКМ-ИИ 5 представляет собой расширение формализма Топологической квантовой механики (ТКМ) с введением полей вероятности как геометрических структур, возникающих из натяжения поля и резонансного выравнивания. Показано, как устойчивые и метастабильные выборы формируются без центрального наблюдателя, а время проявляется как упорядоченность переходов между конфигурациями поля. Модель обобщает предыдущие части ТКМ-ИИ, вводя узлы H3 без массы и иллюстрируя цикл устойчивости, метастабильности, распада и памяти поля.
This work presents a topological phase framework in which time is treated as a generated quantity arising from phase collapse rather than as a fundamental background dimension. In this model, space corresponds to a completed manifold of resolved states, while time emerges as an index of unresolved phase transitions between spatial configurations. Quantum measurement, consciousness, and computation are described as different projections of the same underlying phase-selection process. The framework introduces formal definitions for phase collapse, dual-sphere manifolds, and projection operators linking physical, computational, and cognitive domains. These structures provide a unifying basis for phase-based physics, large-scale computation, and emergent intelligence architectures. This work was developed independently and does not rely on operator-theoretic or quantum-information formalisms, instead adopting a phase-theoretic and topological perspective.
This study introduces the concept of Born–Bayes integration, which unifies Bayesian belief updating with quantum probability waves through the Born rule. The theoretical core is supported by four‑ and six‑variable time‑delayed stochastic simulation reports, EEG/fMRI protocols, and Python‑based simulation engines. Furthermore, mechanisms such as spin–pixel hysteresis, Green function impulse propagation, ethical filter, and quantum veto are employed to explain both internal cognitive processes and decision‑making dynamics. The model demonstrates how cognitive decisions interact with quantum‑based computational processes, while ethical filtering and metacognitive observation mechanisms provide a systematic framework for outcomes at the level of consciousness. By combining the theoretical foundation and the global manifesto summary under a single DOI, the Topological Quantum Computation and Cognition Model (TQCCM) offers an interdisciplinary paradigm bridging philosophy, neuroscience, quantum physics, and cybernetics.
This paper explores the intersection of non-linear topological geometry and quantum dynamics, proposing a novel computational framework leveraging the inherent non-linear characteristics of topological structures to simulate complex physical systems. We introduce the concept of "quantum topology" – a state where topological properties are inherently quantized, and utilize this principle to model quantum systems' behavior within these structures. This work addresses limitations of traditional quantum simulation methods by offering a framework that explicitly incorporates non-linear dynamics and quantum effects, providing a new approach to understanding and modeling intricate physical phenomena. The core mechanism involves mapping topological invariants to quantum states and exploiting the non-linear nature of these states to generate realistic simulations. We demonstrate the framework's capability to generate complex topological structures and simulate quantum transitions within these structures, revealing subtle quantum effects not readily observable in conventional simulations.
This paper introduces Topological Quantum Fields (TQF), a novel framework for quantum computation and spacetime modeling based on the principles of topological quantum field theory. We propose a fundamental shift in understanding quantum systems by incorporating the concept of "quantum topology," which provides a geometric framework for describing the inherent structure and behavior of quantum states. The core claim is that TQF offers a fundamentally different approach to quantum mechanics, potentially leading to enhanced computational capabilities and a deeper understanding of spacetime. We detail the core mechanism of introducing this concept, exploring its implications for quantum state representation and quantum computing. The paper begins with a review of existing quantum field theories and highlights the limitations of current approaches, culminating in the introduction of TQF as a potential paradigm shift.
Artificial intelligence (AI) has made some remarkable advances in recent years, particularly within the area of large language models (LLMs) that produce human-like conversational abilities via utilizing transformer-based architecture. These advancements have sparked growing calls to develop tests not only for intelligence but also for consciousness. However, existing benchmarks assess reasoning abilities across various domains but fail to directly address consciousness. To bridge this gap, this paper introduces the functional contextual N -Frame model, a novel framework integrating predictive coding, quantum Bayesian (QBism), and evolutionary dynamics. This comprehensive model explicates how conscious observers, whether human or artificial, should update beliefs and interact within a quantum cognitive system. It provides a dynamic account of belief evolution through the interplay of internal observer states and external stimuli. By modeling decision-making fallacies such as the conjunction fallacy and conscious intent collapse experiments within this quantum probabilistic framework, the N -Frame model establishes structural and functional equivalence between cognitive processes identified within these experiments and traditional quantum mechanics (QM). It is hypothesized that consciousness serves as an active participant in wavefunction collapse (or actualization of the physical definite states we see), bridging quantum potentiality and classical outcomes via internal observer states and contextual interactions via a self-referential loop. This framework formalizes decision-making processes within a Hilbert space, mapping cognitive states to quantum operators and contextual dependencies, and demonstrates structural and functional equivalence between cognitive and quantum systems in order to address the measurement problem. Furthermore, the model extends to testable predictions about AI consciousness by specifying informational boundaries, contextual parameters, and a conscious-time dimension derived from Anti-de Sitter/Conformal Field Theory correspondence (AdS/CFT). This paper theorizes that human cognitive biases reflect adaptive, evolutionarily stable strategies that optimize predictive accuracy (i.e., evolved quantum heuristic strategies rather than errors relative to classical rationality) under uncertainty within a quantum framework, challenging the classical interpretation of irrationality. The N -Frame model offers a unified account of consciousness, decision-making, behavior, and quantum mechanics, incorporating the idea of finding truth without proof (thus overcoming Gödelian uncertainty), insights from quantum probability theory (such as the Linda cognitive bias findings), and the possibility that consciousness can cause waveform collapse (or perturbation) accounting for the measurement problem. It proposes a process for conscious time and branching worldlines to explain subjective experiences of time flow and conscious free will. These theoretical advancements provide a foundation for interdisciplinary exploration into consciousness, cognition, and quantum systems, offering a path toward developing tests for AI consciousness and addressing the limitations of classical computation in representing conscious agency.