This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the emergence of Hilbert-space structure and Schrödinger-type effective dynamics from the coherent two-field sector established in Paper 02. The work demonstrates that the global coherence constraints imposed on the discrete informational substrate naturally generate an effective complex representation endowed with linear superposition properties and unitary-preserving evolution. The analysis shows that the two-component coherent sector admits a mathematically stable reformulation equivalent to a Hilbert-space structure, and that the effective evolution of the coherent amplitudes leads to a Schrödinger-type dynamical equation without introducing quantum mechanics as an initial assumption. The article further derives the probabilistic interpretation associated with the effective amplitudes and clarifies how quantum-like statistical behavior emerges from the internal coherence conditions of the underlying discrete system. No quantum postulates are assumed at the foundational level. The purpose of the article is to demonstrate that the formal structures associated with quantum mechanics can emerge as effective consequences of coherence-preserving informational dynamics. The article does not assume quantum mechanics as a foundational theory and does not postulate the Hilbert-space formalism a priori. Instead, the work demonstrates that, within the internal hypotheses and coherence constraints of the proposed discrete informational framework, structures mathematically equivalent to Hilbert-space representations and Schrödinger-type evolution can arise as effective emergent descriptions. The purpose of the derivation is therefore not to reproduce standard quantum mechanics by assumption, but to show that quantum-like formal structures may consistently emerge from deeper coherence-preserving informational dynamics.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the emergence of Hilbert-space structure and Schrödinger-type effective dynamics from the coherent two-field sector established in Paper 02. The work demonstrates that the global coherence constraints imposed on the discrete informational substrate naturally generate an effective complex representation endowed with linear superposition properties and unitary-preserving evolution. The analysis shows that the two-component coherent sector admits a mathematically stable reformulation equivalent to a Hilbert-space structure, and that the effective evolution of the coherent amplitudes leads to a Schrödinger-type dynamical equation without introducing quantum mechanics as an initial assumption. The article further derives the probabilistic interpretation associated with the effective amplitudes and clarifies how quantum-like statistical behavior emerges from the internal coherence conditions of the underlying discrete system. No quantum postulates are assumed at the foundational level. The purpose of the article is to demonstrate that the formal structures associated with quantum mechanics can emerge as effective consequences of coherence-preserving informational dynamics. The article does not assume quantum mechanics as a foundational theory and does not postulate the Hilbert-space formalism a priori. Instead, the work demonstrates that, within the internal hypotheses and coherence constraints of the proposed discrete informational framework, structures mathematically equivalent to Hilbert-space representations and Schrödinger-type evolution can arise as effective emergent descriptions. The purpose of the derivation is therefore not to reproduce standard quantum mechanics by assumption, but to show that quantum-like formal structures may consistently emerge from deeper coherence-preserving informational dynamics.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the emergence and structural uniqueness of the effective two-field representation arising from the coherent sector identified in Paper 01. The work demonstrates that the coherence-preserving dynamics of the discrete informational framework admit a minimal effective structure based on two coupled components, and that this structure emerges as the unique stable representation compatible with the global coherence constraints. The analysis establishes the conditions under which the two-field sector becomes dynamically unavoidable within the effective description and prepares the mathematical framework developed in Paper 03, where Hilbert-space structure, Schrödinger-type dynamics, and probabilistic emergence are derived. No quantum-mechanical or geometric assumptions are introduced at the foundational level. The purpose of the article is to derive the minimal effective representation required by the internal consistency of the coherent informational dynamics.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article develops the axiomatic foundation of the framework and introduces the discrete informational system underlying the construction. The paper defines the admissible configuration space, the local update structure, the global coherence constraint, and the dynamical selection principles leading to the emergence of a coherent sector. The analysis establishes the existence, invariance, and structural uniqueness of the coherent sector, together with the effective restrictions that prepare the minimal two-component structure developed in Paper 02 and the emergent quantum framework constructed in Paper 03. No quantum-mechanical, geometric, or probabilistic structure is assumed at the foundational level. The purpose of the work is to establish the minimal structural and dynamical layer from which the later effective constructions emerge.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework’s effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article introduces the general structure, scope, and current status of the framework. The work provides an organized overview of the results developed in the first articles of the series, clarifies the overall logic of the theoretical construction, and situates the framework within a broader research program dedicated to the emergence of quantum, thermodynamic, and geometric structures from informational coherence constraints. The article does not introduce new specific physical postulates, but serves a methodological and introductory role: it defines the conceptual setting of the series, the relation between the different levels of the derivation, and the interpretative and theoretical limitations currently assumed within the framework.
This series presents a structured and logically sequential formulation of a discrete informational framework governed by global coherence constraints. Although it originates from the same research program developed in the earlier exploratory preprint series (P-series), the works presented here constitute an autonomous and self-contained series, organized in a progressively axiomatic form and focused on the explicit derivation of the framework's effective structures. The goal of the construction is to investigate whether structures commonly associated with quantum mechanics, thermodynamics, and geometry may emerge from a discrete relational substrate without being introduced as fundamental postulates. Each article addresses a specific level of the theoretical derivation and forms part of a progressive logical structure based on results established in the preceding works of the series. This article derives thermodynamics as the unique coarse-grained consequence of coherence loss within the informational framework established in Papers 01–03. Starting from the coherence-selected physical sector and its effective quantum description, the work introduces coarse-graining as a constructive mechanism and studies the emergence of irreversible macroscopic behavior from an underlying coherence-preserving dynamics. The analysis derives entropy as the unique information-loss functional compatible with the structural constraints of the framework, proves the second law as a monotonicity consequence of the induced semigroup evolution, and establishes the relation between quantum coherence reduction and thermodynamic behavior. Equilibrium, temperature, and thermodynamic potentials are obtained as structural consequences rather than independent postulates. No thermodynamic laws are assumed at the foundational level. The purpose of the article is to show how thermodynamic structure may emerge as an effective macroscopic description of the same informational dynamics that gives rise to quantum mechanics.
This work presents an axiomatic and structural reconstruction of core elements of quantum mechanics. Starting from minimal principles — symmetry under vanishing preference, normalization, consistency of probability assignments, and coherence-preserving dynamics — we derive several central features of the quantum formalism rather than postulating them. Key results include: A geometric derivation of the constants 1/21/\sqrt{2}1/2 and 1/21/21/2 from symmetry and normalization. A theorem-level derivation of the Born rule (including the qubit case) from noncontextuality and additivity. A reconstruction of Schrödinger dynamics from reversible norm-preserving structure. A derivation of the tensor-product structure for composite systems from composition axioms and local tomography, with entanglement emerging as a necessary consequence. Formal treatment of Bell–CHSH nonlocality, Tsirelson’s bound, and no-signalling. A conditional reconstruction of complex Hilbert space structure from intrinsic phase dynamics and compositional consistency. The manuscript is self-contained and framed in standard mathematical-physics language. It does not propose modifications to quantum mechanics, but instead clarifies why many of its defining structures arise inevitably from deeper structural constraints. Prior computational and model-based work by the authors (including diagnostic toy models exploring phase locking, coherence stabilization, and recursive-time dynamics) is acknowledged but intentionally not reproduced here, in order to keep the present work focused on axiomatic structure rather than model-specific architecture. This upload is intended as a foundations and reconstruction contribution, suitable for readers interested in the mathematical and conceptual structure of quantum theory.
We develop a derivation of dynamics of Quantum Mechanics and measurement within a fundamentally timeless and scale-invariant framework. Building on a prior reconstruction of quantum kinematics from renormalization consistency, we extend the analysis to dynamical evolution and the measurement process using three minimal principles: a global constraint (timelessness), a variational formulation, and resolution independence. We show that relational time emerges through conditional decomposition of the global state, leading to an effective Schrödinger evolution under suitable conditions on clock subsystems. Renormalization group (RG) transformations, treated as maps on the state space induced by coarse-graining, generate an effective non-unitary dynamics for reduced states. Under standard assumptions of weak coupling and scale separation, this dynamics takes Lindblad form, providing a structural origin for decoherence. A central result of this work is the formulation of a stability selection principle: configurations contributing to observable physics correspond to those that are simultaneously stationary under the action and stable under RG flow. This principle unifies dynamical selection (via the variational structure) and structural selection (via renormalization), and provides a mechanism for the emergence of classical behavior. Measurement is described as an effective sector dynamics arising from decoherence and coarse-grained evolution. The Lindblad equation admits a stochastic representation in which the system evolves between dynamically independent sectors, leading to an effective description of definite outcomes without introducing a fundamental collapse postulate. The Born rule follows from the unique quadratic measure consistent with refinement structure and is realized dynamically within this framework. Together, these results provide a structural account under minimal assumptions of quantum dynamics, decoherence, and measurement as emergent features of a timeless, renormalization-consistent theory governed by stability across scales.