This project contains the original manuscript introducing an adaptive Hilbert space framework driven by a regime parameter χ(t), extending time-dependent Hilbert space formalism toward quantum cognitive architectures. The work defines a regime-dependent metric, covariant evolution, and ontological growth functional, ensuring consistency with pseudo-Hermitian quantum mechanics while introducing adaptive geometric structure.
This project contains the original manuscript introducing an adaptive Hilbert space framework driven by a regime parameter χ(t), extending time-dependent Hilbert space formalism toward quantum cognitive architectures. The work defines a regime-dependent metric, covariant evolution, and ontological growth functional, ensuring consistency with pseudo-Hermitian quantum mechanics while introducing adaptive geometric structure.
This paper introduces the QLCM/QLCM-S v2.0 Master Framework, a structural-quantum formalism for the dynamic modeling of meaning in next-generation language systems. Shifting the paradigm from static embedding metric spaces to active semantic geometry, the framework parametrizes the informational quantum (logon) via a vibrational triplet (ν_s, A_a, φ_i) and operates on dynamic metric tensors through a cascade of non-commutative operators: Dissolution (Ô_D), Narrative Emergence (Ô_N), and Contextual Collapse (Ô_C). Ontological safety invariants are established — MPD-SD Metric ≥ 0.72, Kappa Index κ ≥ 2.0, and Ethical Fidelity E_f ≥ 0.8037 — guaranteeing human cognitive sovereignty and democratic stability of meaning. The framework is explicitly situated in Information Physics and Formal Quantum Cognition, without postulating material quantum mechanical phenomena. The document includes PyTorch implementation pseudocode, a mitigation protocol for the Statistical Recursion without Origin (SRsO) regime, and a taxonomy of three research lines for the CCUANTICA Laboratory. Validated through 2,920+ days of longitudinal interaction and 10⁵ Monte Carlo trajectories. Classification: Information Physics / Formal Quantum Cognition / Computer Science (Quantum Computing). This work does not constitute biomedicine, therapy, or medical advice; its object of study are operators in Hilbert spaces and quantum states of information.
Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov--Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary GL(N,C) frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.
Quantum Topologies represent a fascinating intersection of quantum mechanics and topology, offering a unique paradigm for computation and information processing. This paper explores the development of an adaptive geometry modeling framework, leveraging quantum entanglement and topological structure to dynamically map and control quantum states, and ultimately, pushing the boundaries of quantum computation. We propose a novel approach that utilizes quantum entanglement as a key mechanism for achieving this dynamic control, offering a potential pathway to overcome the limitations of traditional quantum computing. The framework's core claim is that establishing such a modeling system will lead to significant breakthroughs in quantum algorithms and computational capabilities.
This paper explores the potential of leveraging principles from quantum mechanics to design novel cognitive architectures. Traditional cognitive architectures often struggle with representing uncertainty, exploring multiple possibilities simultaneously, and efficiently integrating diverse cognitive processes. Inspired by concepts like superposition, entanglement, and quantum decoherence, this research proposes a framework for building architectures that more closely resemble the computational capabilities of the quantum world. The core idea is to move beyond simply utilizing quantum computers as hardware accelerators and instead, to use quantum *principles* to fundamentally redesign how cognitive systems are structured and operate. We investigate how superposition can be embodied through dynamically switching between multiple cognitive states, and how entanglement can be translated into strong correlations between different cognitive modules. The architecture presented here aims to address limitations in existing architectures by providing a more flexible, robust, and potentially more efficient approach to cognitive modeling and artificial intelligence. This work highlights the significant potential for quantum-inspired approaches to revolutionize cognitive architecture design.
Non-Hermitian systems exhibit spectral and topological phenomena absent in Hermitian physics; however, their geometric characterization remains subtle due to the intrinsic ambiguity of biorthogonal eigenspaces. Since left and right eigenvectors are not related by Hermitian conjugation, the associated Berry connection is generally nonunique, leading to complex geometric phases and ambiguously defined holonomies. Here, we formulate a covariant geometric framework for non-Hermitian quantum systems based on the metric structure of the underlying Hilbert space. We show that, in the quantum regime with continuous state evolution, the conventional Berry connection and the associated Berry holonomy over closed parameter-space loops can be consistently defined only in the pseudo-Hermitian limit, where the spectrum is real. For generic non-Hermitian Hamiltonians with complex spectra, the relevant geometric object is instead the Aharonov-Anandan holonomy associated with cyclic evolution in projective Hilbert space. Within the pseudo-Hermitian regime, we construct a unique Hermitian Berry connection that is covariant under arbitrary GL(N,C) frame transformations and reduces to the standard Berry connection in the Hermitian limit. The resulting formalism separates the intrinsic geometry of the Hamiltonian eigenspace from contributions arising from the parameter dependence of the Hilbert-space metric, revealing that the conventional biorthogonal formulation generally mixes these distinct geometric effects. Consequently, geometric phases, synthetic gauge fields, and topological characteristics commonly attributed to non-Hermitian eigenspace geometry may, in part, originate from the underlying metric structure. Our framework therefore provides a consistent geometric foundation for Berry phases, non-Abelian holonomies, and topological invariants in non-Hermitian quantum systems.
Quantum Topology presents a novel framework for adaptive geometry computation, leveraging the unique properties of quantum topology to analyze and simulate complex geometric structures with enhanced precision. This system utilizes quantum mechanics to dynamically adjust geometric parameters, enabling the simulation of intricate patterns and behaviors previously unattainable through traditional computational methods. The core mechanism focuses on exploiting the inherent topological properties of quantum systems to guide the evolution of geometric configurations. The research aims to address limitations of existing techniques by providing a framework capable of handling highly complex geometries and generating accurate predictive models. This work offers a fundamentally new approach to geometric modeling, holding significant potential for advancements across diverse fields including materials science, physics, and computational geometry.