This document presents a fully expanded and jointly developed version of the universal-wave framework first proposed by Jean-Charles J. C. Tassan, now integrated with the information-theoretic architecture of the QSOL program. The resulting monograph provides a unified theoretical model in which all particles emerge as structured local excitations—qutrit codons—within a single global wave function Ψ. Time is treated as discrete, space remains continuous and relativistic, and the evolution of Ψ proceeds through a structured unitary operator enriched with resonance transformations and manifold patching. The integration introduces an internal algebra for each excitation, enabling amplitude, phase-group, and contextual data to be encoded directly into ψᵢ(x, tₙ). Local perturbations are reformulated as QEC-style correction dynamics acting on excitation lineage, offering a computational interpretation of how local interactions modify the global wave. Entanglement is represented as a dual-layer phenomenon, combining global coherence with shared codon-state synchronization. This merged framework remains compatible with standard quantum mechanics, while extending the descriptive capacity of particle–wave behavior and providing a foundation for future simulation work, resonance-based modeling, and sonification research. The monograph consolidates both authors’ approaches into a coherent information-geometric structure, offering a flexible platform for ongoing theoretical development. The attached document contains the full expanded manuscript, including revised sections, integrated formulations, and updated discussion.
This document presents a fully expanded and jointly developed version of the universal-wave framework first proposed by Jean-Charles J. C. Tassan, now integrated with the information-theoretic architecture of the QSOL program. The resulting monograph provides a unified theoretical model in which all particles emerge as structured local excitations—qutrit codons—within a single global wave function Ψ. Time is treated as discrete, space remains continuous and relativistic, and the evolution of Ψ proceeds through a structured unitary operator enriched with resonance transformations and manifold patching. The integration introduces an internal algebra for each excitation, enabling amplitude, phase-group, and contextual data to be encoded directly into ψᵢ(x, tₙ). Local perturbations are reformulated as QEC-style correction dynamics acting on excitation lineage, offering a computational interpretation of how local interactions modify the global wave. Entanglement is represented as a dual-layer phenomenon, combining global coherence with shared codon-state synchronization. This merged framework remains compatible with standard quantum mechanics, while extending the descriptive capacity of particle–wave behavior and providing a foundation for future simulation work, resonance-based modeling, and sonification research. The monograph consolidates both authors’ approaches into a coherent information-geometric structure, offering a flexible platform for ongoing theoretical development. The attached document contains the full expanded manuscript, including revised sections, integrated formulations, and updated discussion.
This monograph presents the complete theoretical formulation of the Universal Resonance Field Theory (UR), a unified geometric framework connecting informational geometry, quantum measurement, critical phenomena, and gravitational structure. The work integrates Fisher-information dynamics, hazard-modified Ricci flow, an extended Einstein–Maxwell sector, and a renormalization-group derivation of the universal critical exponent α ≈ 1.27. The framework provides a single-outcome quantum measurement mechanism, a geometric generalization of the Born rule (GWBR), and a predictive informational mass tensor applicable across physical, biological, and cosmological scales. This document serves as the foundational reference for all UR-related empirical and theoretical research.
EE_V05 represents a significant refinement and extension of the continuum‑geometric framework for electron entanglement within the Monistic Continuum Model (MCM). Compared to EE_V04, this version improves the mathematical clarity, structural consistency, and conceptual accessibility of the model. The continuum field, operator definitions, and correlation structures have been streamlined and unified across all sections. The main updates include : • A revised and more coherent formulation of the continuum field 𝐶 and the organization space ΛΩ.• A clearer and more precise description of the nonlocal operator 𝐷nl and its role in generating non‑separable kernel structures.• An expanded and reformulated main theorem, providing a transparent spectral argument for continuum‑induced entanglement.• A newly added abstract summarizing the core contributions of EE_V05.• A comprehensive glossary of symbols and concepts to support readability and formal consistency.• Refined discussion and conclusion sections, offering improved comparisons with QM, QFT, GR, GRW, Everett, and relational QM.• Harmonized LaTeX structure and section ordering aligned with the conventions of the MCM series. EE_V05 therefore provides a more complete, coherent, and technically precise presentation of electron entanglement as a geometric and dynamical phenomenon emerging from the continuum substrate of the MCM. MCM – Master Document (10.5281/zenodo.22128163)
The PSE framework develops a fully structural description of physical phenomena, where space‑time, fields, particles and constants arise as geometric projections of a deeper prespatial correlation network. The theory replaces ontological entities with structural invariants defined by a fundamental reorganization operator 𝔇, which selects admissible modes of coherence through discrete internal operators (rigidity, symmetry, internal transformations). In the PSE, space‑time is not fundamental: it emerges from structural distance via the map Φ, compressing and projecting prespatial geometry. Coherence configurations generate both localized modes (particles) and diffuse modes (fields), while interactions correspond to structural variations of internal invariants rather than dynamical forces. Key physical quantities—mass, energy, spin, charge, c, ℏ, probability—are reinterpreted as emergent geometric effects: mass as minimum rigidity, energy as total rigidity, c as the upper bound of admissible structural variation, ℏ as minimum granularity of admissible modes, probability as structural compatibility between system and detector, entanglement as structural co‑immersion, decoherence as loss of compatibility. The PSE provides a unified structural explanation for quantum statistics, uncertainty, interactions, causal structure, and emergent constants. It also clarifies the limits of the emergent description: space‑time cannot represent co‑immersion, internal operators, structural compatibility, or prespatial geometry. These appear only indirectly as amplitudes, probabilities, apparent collapse, non‑locality and dynamical interactions. This document presents the complete A–P formulation of the PSE, detailing the structural foundations, emergent phenomena, and the geometric origin of the laws of physics. Andrea ToricelliWith the help of Artificial Intelligence systemsa.toricelli@Hotmail.it
This monograph develops a particle-first framework for many-particle quantum mechanics based on finite topological carriers, their actual causal histories, and a physical spacetime–vacuum substrate. The construction retains three physical axioms: microscopic ontic definiteness with finite localization, the physical reality of the substrate, and persistent causal source–response coupling. Euclidean self-return is treated as a geometric condition of a specified substrate realization rather than an additional matter axiom. The framework connects covariant parent dynamics and finite-energy carrier configurations to stratified many-particle configuration spaces, joint histories, preparation measures, probability currents, and conditional phase and Hilbert-space representations. Fixed- and variable-particle-number dynamics are formulated within a common sector-resolved description. Particular attention is given to finite-core interactions, historical memory, collision-induced changes in carrier decomposition, scattering, bound states, resonances, creation, annihilation, and decay. The manuscript presents scattering constructions for specified short-range interaction classes, together with multichannel and three-cluster formulations. Exchange statistics, entanglement, measurement records, kinetic reduction, and collective phenomena are examined as related aspects of the enlarged carrier–substrate dynamics. Local fields, propagators, diagrammatic expansions, and other effective computational tools are introduced downstream as representations on explicitly restricted domains. Their use does not assign independent ontic status to operator-valued fields or internal diagram lines. Mathematical results, physical-realization assumptions, numerical calculations, and empirical validation are distinguished throughout. A complete computational replacement for quantum field theory is not claimed: model-specific interaction kernels, reproducible many-particle calculations, and quantitative comparisons between particle and effective-field descriptions remain central tasks. Owing to the integration of material developed through successive stages of research and revision, the present draft contains some uneven organization, repetition, and discontinuities in its logical presentation. A simplified and reorganized version, with a clearer logical sequence and more concise exposition, is planned for subsequent publication. Keywords Finite topological carriers; causal histories; many-particle quantum mechanics; stratified configuration spaces; historical memory; collision and scattering; variable particle number; quantum reactions; exchange statistics; effective field representations.
New Subquantum Information Mechanics (NMSI) is a unified theoretical framework that extends quantum mechanics and classical field theory by introducing a deeper informational substrate underlying all physical processes. NMSI proposes that the vacuum is not empty but a structured subquantum medium composed of oscillatory informational units ("infobits"), whose coherent interactions generate observable matter, energy, and spacetime geometry. In this model, particles, fields, and forces emerge as stable oscillatory patterns in a multidimensional informational manifold. Mass is interpreted as the amount of structured subquantum information stored in the vacuum; photons represent freely propagating oscillatory modes that carry information without storing it. Gravitational interaction arises from gradients in informational density, producing curvature-like behavior consistent with Einstein’s equations but without singularities. NMSI provides a mathematically consistent reinterpretation of key physical concepts, including: Subquantum resonances as generators of particle states Oscillatory duality as the mechanism behind wave–particle behavior Informational conservation replacing classical energy conservation at the deepest scale Coherent cyclicity explaining cosmological evolution without expansion Lie-symmetry foundations linking subquantum dynamics with macroscopic structure The project develops: 1. A formal axiomatic system for NMSI 2. Analytical and numerical models of subquantum oscillatory networks 3. Applications to cosmology (non-expanding Universe, baryonic cycle), condensed-matter systems, atmospheric coherent structures, and computational architectures (TQC – Twin Quantum Computing) 4. Testable predictions that differentiate NMSI from standard quantum mechanics and ΛCDM cosmology The NMSI framework aims to provide a deeper, symmetry-based understanding of physical reality, reconciling mathematical rigor with observational coherence and offering new pathways toward unified physics.
This monograph develops a consistent formulation of quantum mechanics on the cyclic algebra C3C_3C3, replacing the traditional complex imaginary unit iii with the unique anti-Hermitian axis j+j2j + j^2j+j2. This replacement yields a two-channel (visible–hidden) generalization of Schrödinger evolution and extends the standard complex formalism into a richer phase geometry. The resulting framework exhibits a natural decomposition into Hermitian and anti-Hermitian directions, enabling a multi-carrier interpretation of wave dynamics. The aim of this volume is not to present a finalized or definitive theory, but to consolidate a fast-expanding set of technical results—operator identities, geometric arguments, phase-projection methods, and algebraic constructions—into a unified reference document. Much of this material originated from scattered manuscripts, research notes, and exploratory derivations. The present edition gathers these components systematically, offering a coherent foundation for more optimized and fully structured future versions. The monograph should therefore be regarded as a developmental edition. Several chapters contain preliminary proofs or interim formulations; the C₃ trigonometric system, the multi-carrier interpretation of the wavefunction, and the visible–hidden projection formalism are presented in their earliest integrated form. Future editions will refine the conceptual hierarchy, provide additional examples, and extend the framework to relativistic domains, CnC_nCn operator algebras, and geometric interpretations of phase curvature. Keywords:C₃ algebra, cyclic complex numbers, multi-carrier quantum mechanics, two-channel Schrödinger equation, anti-Hermitian axis, visible–hidden phase geometry, phase curvature, generalized Born rule, operator algebra on CnC_nCn, extended trigonometric systems. Notes: This is a working research monograph; subsequent versions will reorganize and expand several sections and incorporate additional applications.