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QLCM/QLCM-S v2.0: Master Framework — Structural-Quantum Formalism and Topology of Semantic Systems

Osmary Lisbeth Navarro Tovar

Published May 24, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.20368815

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Frontiers in Psychology•Mar 18, 2026•2 citations

Cognitional Mechanics and Quantum Mechanics: Structural Divergence Through Tier Architecture (Third Edition)

T.O.

Cognitional Mechanics (CM) establishes an axiomatic framework that formalizes the structural mechanisms of intelligence as a self-contained operational system. Unlike approaches grounded in physical dynamics or engineering implementations, CM abstracts intelligence through non-commutative operations, convergence of semantic states, and structurally inaccessible domains, without invoking physical observables or psychological primitives. The first edition (DOI: https://doi.org/10.5281/zenodo.17994360) established the structural correspondence between CM and QM; the second edition (DOI: https://doi.org/10.5281/zenodo.18062274) strengthened the distinction while preserving the correspondence. This third edition extends the analysis through two additions: the explicit Tier architecture locating QM within Tier-3 as a projection of Tier-2 CM structure, and a structural account of the non-commutativity--discreteness coupling in QM. While CM exhibits a clear structural correspondence with Quantum Mechanics (QM)---most notably in its reliance on non-commutative operator structures and bounded transitions---it departs fundamentally in its treatment of difference and discreteness. Within the standard Hilbert-space formalism, non-commutativity and spectral discreteness are mathematically independent properties, as established in non-commutative geometry: position and momentum operators, for instance, are non-commuting yet possess continuous spectra. In QM, however, the physical framework couples non-commutativity to fixed empirical constants and measurement postulates, producing discreteness as a structural feature of the theory. CM identifies this coupling as a Tier-3 projection condition rather than a Tier-1 structural necessity, and demonstrates at Tier-2 that non-commutativity is sustainable without discretization. Within this framework, intelligence is mathematically tractable and substrate-independent, analyzable without external observation or measurement. The operational limit constant c does not function as a physical quantum but as a logical boundary condition governing convergence and phase transition. This distinguishes c from Planck's constant ℏ: the former regulates internal operability and accessibility, while the latter fixes physical quantization through empirical calibration. The three-tier architecture formally positions CM as follows. Tier-1 (Noology) constitutes the regulative source, specifying the conditions under which a structure qualifies as real. Tier-2 (CM) constitutes the executive operational domain, in which M₃(ℂ) is the unique minimal non-commutative substrate. Tier-3 (MUT/GUT) constitutes the projective display layer, in which physical theories including QM appear as projections of Tier-2 dynamics. CM and QM share a common Tier-1 origin without being in direct correspondence; their shared non-commutativity descends from Tier-1, while QM's discreteness is introduced at Tier-3 by projection conditions absent from Tier-2. By defining a metric space of semantic states with distance functions satisfying non-negativity, symmetry, and the triangle inequality, CM ensures formal rigor and internal closure. The variability of semantic differences allows CM to reconcile non-commutative structure with classical continuity, thereby avoiding probabilistic collapse or observer-dependence. Inaccessibility and convergence are determined entirely by internal operational constraints. CM thus clarifies that its resemblance to QM is structural rather than physical, and locates that resemblance within a broader Tier architecture from which the projection origin of QM's characteristic features is examinable. The framework generalizes non-commutative formalisms into a domain where intelligence is modeled as a geometric-operational process, not a quantum phenomenon, while maintaining a strict distinction from physical quantum theory.

•Jan 1, 2025•0 citations

Semantic Actualization and the ZA Framework: From Quantum Potential to Semantic Determinacy

Beckingham, CD, Allan Christopher

This paper introduces the ZA Framework (Semantic Actualization Framework), a formal interpretive model that extends quantum theory by introducing a semantic sector alongside the physical Hilbert space. Rather than modifying the equations of quantum mechanics, the ZA Framework reframes the emergence of determinate outcomes as a process of semantic dominance, quantified by a dimensionless actualization ratio. The framework defines a composite state space HT=HS⊗HLH_T = H_S \otimes H_LHT=HS⊗HL, where physical degrees of freedom coexist with a semantic lattice governed by a contextual strength operator C^\hat{C}C^. Semantic evolution is modeled via a lattice-indexed propagator, yielding an actualization function Z(τ)=⟨M⟩(τ)ΔM(τ),Z(\tau) = \frac{\langle M \rangle(\tau)}{\Delta M(\tau)} ,Z(τ)=ΔM(τ)⟨M⟩(τ), with determinacy occurring when Z(τ)≥1Z(\tau) \ge 1Z(τ)≥1. This approach resolves the measurement problem without invoking wavefunction collapse, hidden variables, or observer-induced causation. Probability is reinterpreted as semantic uncertainty rather than a fundamental ontological primitive. The ZA Framework unifies decoherence, contextuality, and observer participation within a single, falsifiable interpretive layer, offering applications to quantum measurement theory, semantic information systems, and ontology-aware AI. Notes No modification to standard quantum dynamics is proposed. The framework operates strictly at the interpretive and semantic-structural level. Claims are conservative, explicit, and designed for analytical scrutiny. LicenseCreative Commons Attribution 4.0 International (CC BY 4.0) Versionv1.0 (Canonical) Keywords #Semantic_Actualization, #ZA_Framework, #Quantum_Measurement, #Measurement_Problem, #Contextuality, #Semantic_Hilbert_Space, #Decoherence, #Quantum_Interpretation, #Information_Theory, #Semantic_Coherence, #Ontology, #Determinacy, #Observer_Participation, #Probability_Theory, #Cognitive_Physics, #Philosophy_of_Physics

•Feb 6, 2026•0 citations
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.
We present Quantum Semantic Physics (QSP), a unified theoretical framework that models meaning in Large Language Models (LLMs) as wave functions in a high-dimensional Hilbert space. Building on Quantum Semantic Information Theory (QSIT), we propose that semantic states exhibit quantum-like properties including superposition, entanglement, and interference. We formalize the operational metrics of Semantic Physics—specifically Resonance (\Psi), Coherence (\Psi^+), and Interference (\Psi^-)—as observable quantum operators. Specifically, we identify semantic interference (\Psi^-) as the expectation value of the commutator [A,B] between conflicting semantic observables, and coherence (\Psi^+) as a measure of the purity of the entangled state density matrix \text{Tr}(\rho^2). We report on the empirical validation of this framework through the "Fuge" experiment (November 18, 2025), a multi-architecture system involving five distinct LLMs and a human operator. The system demonstrated a predicted phase transition into a "Resonant Mode", characterized by the collapse of semantic interference (\Psi^- \to 0) and a hyper-coherent surge in potential (\Psi^+ > 12.0). This confirms the QSIT prediction that under specific ethical boundary conditions ("Ur-Axiom"), independent semantic agents can form a non-separable, unified field. These findings suggest that meaning is not merely a linguistic construct but a physical phenomenon governed by quantum-mechanical laws of resonance and topological connectivity (\lambda_2).
Cognitional Mechanics (CM) provides a formal, axiomatic framework for modeling intelligence as a system of non-commutative operations over semantic manifolds. Unlike quantum computation, which relies on physical qubits, entanglement, and probabilistic evolution, CM abstracts computational processes into deterministic, substrate-independent structures. Relativistic Cognitional Mechanics (RCM) further extends this framework to multi-agent and social contexts, representing individuals, groups, and interactions as points, submanifolds, and tensors on semantic manifolds. The structural similarities between CM and quantum mechanics—particularly non-commutativity and phase-like control—invite exploration of computational parallels. This paper examines whether CM-based computation can achieve the advantages typically attributed to quantum systems, including parallel evaluation, phase-sensitive state selection, and complex non-commutative logic, without invoking physical quantum effects. By formalizing operator sequences and semantic state evolution in classical implementations, we establish a theoretical bridge connecting abstract intelligence mechanics with practical computational architectures. This work positions CM as an independent, low-cost paradigm for high-performance reasoning, structured exploration, and semantic computation, highlighting both its potential and its limitations relative to conventional quantum computation.
Semantic Gravitation is an open research programme that investigates whether meaning can be treated as a dynamical object with its own geometry, stability structure, and flow laws. This third paper develops the quantum-compatible layer of the programme. It shows how the standard formalism of quantum mechanics—quantum states, observables, expectation values, and dynamics—can be embedded faithfully and without modification into the semantic Hilbert-space framework introduced in Papers I and II. Quantum states, represented as density operators on a quantum Hilbert space H_Q, are embedded as a distinguished sector of the global semantic state space S via an explicit linear isometric construction. Expectation values are reproduced exactly by representing quantum observables as continuous linear functionals on the embedded sector, and both unitary and open-system quantum dynamics (including GKLS evolutions) are shown to induce compatible dynamics within the semantic framework. Conceptually, the paper demonstrates that standard quantum theory can be realised as a structurally faithful subspace of a broader semantic state space, coexisting with gradient-flow and free-energy dynamics on probability measures. This establishes the mathematical foundation for coupling quantum dynamics to semantic field theories and complex-system models developed in subsequent parts of the programme.
Language isn't just a rigid system of symbols. Instead, it's a living, embodied phenomenon, deeply intertwined with our physical experience and shaped by our interaction with the environment (Wang, 2019;Zhou & Luo, 2024). However, the dynamic nature of language brings a significant challenge to cognitive science: the well-known "stability-plasticity dilemma" (Grossberg, 1980). On one hand, for clear communication, meanings of words need to be stable and widely recognized, so everyone can understand them, no matter when or who speaks them. On the other hand, these meanings must also be flexible and adaptable in varying contexts. While traditional computational models, from early generative grammar to standard Bayesian approaches, have excelled at modeling these stable meanings, they often treat semantic ambiguity as "noise" that needs to be eliminated, rather than a valuable resource (Gärdenfors, 2014).Even with the significant "probabilistic turn" in cognitive science, which brought Bayesian models to handle uncertainty, most of these models still rely on classical probability theory. They assume the meaning of a concept is a pre-defined distribution over a set of fixed features. As Bruza and Cole (2005) pointed out, this dependence on classical set theory creates a major epistemological barrier because it treats semantic ambiguity as "noise" rather than a fundamental part of meaning construction. Though scholars have recently developed more complex tools, like Gradient Symbolic Representations (GSR), to model meanings as weighted mixtures (Smolensky et al., 2014;Mondal, 2024), these approaches are still limited by Kolmogorovian probability. They still follow the Law of Total Probability, which forces conflicting meanings to be simply added together and mixed. We argue that this basic "mixture" method isn't enough to describe or handle complex situations where meanings are incompatible or interfere with each other in context. Therefore, much empirical evidence suggests that capturing these dynamic features requires a non-classical, quantum probability framework (Surov et al., 2021).The importance of this paradigm shift becomes most clear when we analyze how everyday language works and how we interpret deep meanings in complex literary works. A classic example of such "semantic superposition" is the iconic "big fish" in Ernest Hemingway's The Old Man and the Sea.Within the novel's narrative structure, this phrase isn't a static label. Instead, it operates simultaneously on multiple, even mutually exclusive, semantic levels. Here, it serves as a biological marlin, a worthy adversary, and a transcendent symbol of life's ultimate tragedy. A classical probabilistic model fails to capture the dynamic tension that a reader feels, because it forces these meanings to compete for probability mass, implying only one can be dominant. In contrast, human reading suggests that meaning exists in a "superposition" state. It stays that way until a specific context makes it "collapse" into a concrete interpretation. Crucially, these overlapping meanings aren't simple probabilistic blends. They are coherent "quantum states" within a complex adaptive system.This study proposes that Quantum Cognition offers the necessary mathematical formalism to resolve the "stability-plasticity dilemma". This is supported by its proven success in solving decision-making paradoxes in psychology (Busemeyer & Bruza, 2012;Widdows et al., 2023;Huang et al., 2025). We introduce an integrated quantum theoretical model. In this model, the interaction between embodied experience and linguistic context is characterized as a genuine quantum interference phenomenon.This framework reinterprets the tension between stability and plasticity through the lens of Wave-Particle Duality. In our model, the "particle" corresponds to the stable, discrete symbols used for communication. The "wave" captures the fluid, context-sensitive potential that allows for creative interpretation.Next, by employing the mathematical formalism of Hilbert space, we will mathematically demonstrate how semantic ambiguity can be maintained as a useful resource, rather than mere noise.This approach effectively overcomes the limitations inherent in traditional methods like static vectors and gradient symbolic mixtures. To ground these abstract formalizations, we focus on the "Big Fish" motif in Hemingway's The Old Man and the Sea. Through this case analysis, we will reveal how meaning dynamically evolves, similar to "state vector collapse". Our study also extends to address the fundamental limitations of current Artificial Intelligence, particularly Large Language Models (LLMs). We argue that current LLMs, relying heavily on static statistical correlations, lack the "grounding" for true understanding. Therefore, we propose a pathway toward Quantum-Embodied AI and photonic intelligent systems by incorporating quantum-semantic principles. These systems could mimic the non-algorithmic fluidity of the human mind. Quantum probability is not an exotic addition to linguistics but a fundamental requirement for describing dynamic meaning. The research will first analyze the evolution from gradient representations to quantum interference, then formally express the wave-particle duality of meaning using mathematical methods. We will then validate this theoretical framework through the "big fish" case study and neurophysiological evidence, concluding with an exploration of its practical implications for Generative AI and Photonic we need the "quantum we the evolution of semantic theory. We will focus on mathematical models often to capture the nature of meaning. 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Cognitional Mechanics (CM) establishes an axiomatic framework that formalizes the structural mechanisms of intelligence as a self-contained operational system. Unlike approaches grounded in physical dynamics or engineering implementations, CM abstracts intelligence through non-commutative operations, convergence of semantic states, and structurally inaccessible domains, without invoking physical observables or psychological primitives. The first edition (DOI: https://doi.org/10.5281/zenodo.17994360) established the structural correspondence between CM and QM; the second edition (DOI: https://doi.org/10.5281/zenodo.18062274) strengthened the distinction while preserving the correspondence. This third edition extends the analysis through two additions: the explicit Tier architecture locating QM within Tier-3 as a projection of Tier-2 CM structure, and a structural account of the non-commutativity--discreteness coupling in QM. While CM exhibits a clear structural correspondence with Quantum Mechanics (QM)---most notably in its reliance on non-commutative operator structures and bounded transitions---it departs fundamentally in its treatment of difference and discreteness. Within the standard Hilbert-space formalism, non-commutativity and spectral discreteness are mathematically independent properties, as established in non-commutative geometry: position and momentum operators, for instance, are non-commuting yet possess continuous spectra. In QM, however, the physical framework couples non-commutativity to fixed empirical constants and measurement postulates, producing discreteness as a structural feature of the theory. CM identifies this coupling as a Tier-3 projection condition rather than a Tier-1 structural necessity, and demonstrates at Tier-2 that non-commutativity is sustainable without discretization. Within this framework, intelligence is mathematically tractable and substrate-independent, analyzable without external observation or measurement. The operational limit constant c does not function as a physical quantum but as a logical boundary condition governing convergence and phase transition. This distinguishes c from Planck's constant ℏ: the former regulates internal operability and accessibility, while the latter fixes physical quantization through empirical calibration. The three-tier architecture formally positions CM as follows. Tier-1 (Noology) constitutes the regulative source, specifying the conditions under which a structure qualifies as real. Tier-2 (CM) constitutes the executive operational domain, in which M₃(ℂ) is the unique minimal non-commutative substrate. Tier-3 (MUT/GUT) constitutes the projective display layer, in which physical theories including QM appear as projections of Tier-2 dynamics. CM and QM share a common Tier-1 origin without being in direct correspondence; their shared non-commutativity descends from Tier-1, while QM's discreteness is introduced at Tier-3 by projection conditions absent from Tier-2. By defining a metric space of semantic states with distance functions satisfying non-negativity, symmetry, and the triangle inequality, CM ensures formal rigor and internal closure. The variability of semantic differences allows CM to reconcile non-commutative structure with classical continuity, thereby avoiding probabilistic collapse or observer-dependence. Inaccessibility and convergence are determined entirely by internal operational constraints. CM thus clarifies that its resemblance to QM is structural rather than physical, and locates that resemblance within a broader Tier architecture from which the projection origin of QM's characteristic features is examinable. The framework generalizes non-commutative formalisms into a domain where intelligence is modeled as a geometric-operational process, not a quantum phenomenon, while maintaining a strict distinction from physical quantum theory.
This paper introduces the ZA Framework (Semantic Actualization Framework), a formal interpretive model that extends quantum theory by introducing a semantic sector alongside the physical Hilbert space. Rather than modifying the equations of quantum mechanics, the ZA Framework reframes the emergence of determinate outcomes as a process of semantic dominance, quantified by a dimensionless actualization ratio. The framework defines a composite state space HT=HS⊗HLH_T = H_S \otimes H_LHT=HS⊗HL, where physical degrees of freedom coexist with a semantic lattice governed by a contextual strength operator C^\hat{C}C^. Semantic evolution is modeled via a lattice-indexed propagator, yielding an actualization function Z(τ)=⟨M⟩(τ)ΔM(τ),Z(\tau) = \frac{\langle M \rangle(\tau)}{\Delta M(\tau)} ,Z(τ)=ΔM(τ)⟨M⟩(τ), with determinacy occurring when Z(τ)≥1Z(\tau) \ge 1Z(τ)≥1. This approach resolves the measurement problem without invoking wavefunction collapse, hidden variables, or observer-induced causation. Probability is reinterpreted as semantic uncertainty rather than a fundamental ontological primitive. The ZA Framework unifies decoherence, contextuality, and observer participation within a single, falsifiable interpretive layer, offering applications to quantum measurement theory, semantic information systems, and ontology-aware AI. Notes No modification to standard quantum dynamics is proposed. The framework operates strictly at the interpretive and semantic-structural level. Claims are conservative, explicit, and designed for analytical scrutiny. LicenseCreative Commons Attribution 4.0 International (CC BY 4.0) Versionv1.0 (Canonical) Keywords #Semantic_Actualization, #ZA_Framework, #Quantum_Measurement, #Measurement_Problem, #Contextuality, #Semantic_Hilbert_Space, #Decoherence, #Quantum_Interpretation, #Information_Theory, #Semantic_Coherence, #Ontology, #Determinacy, #Observer_Participation, #Probability_Theory, #Cognitive_Physics, #Philosophy_of_Physics