Planck’s constant h has long been introduced axiomatically in quantum mechanics, with its numerical value fixed empirically. Yet its structural necessity and intrinsic relation to the topology of phase space remain unresolved. In this work we develop a phase-ontological framework — the Omega-model — in which monodromy provides the fundamental mechanism of quantization. The structural chain is established as: Topology → Monodromy → Quantization Rules → h as universal coherence threshold.Within this perspective, h is not derived as a numerical constant but identified as a universal unit of minimal coherent action that calibrates the model’s internal parameters. This formulation yields a unified topological explanation for (i) the inevitability of quantized action and (ii) the dichotomy of bosonic versus fermionic statistics, interpreted as trivial and nontrivial monodromy, respectively. Consistency of the coherence criterion with foundational quantum experiments and even recent high-energy anomalies demonstrates that the Omega-model offers a coherent bridge between topology, phase coherence, and the structural foundations of quantum theory.
Planck’s constant h has long been introduced axiomatically in quantum mechanics, with its numerical value fixed empirically. Yet its structural necessity and intrinsic relation to the topology of phase space remain unresolved. In this work we develop a phase-ontological framework — the Omega-model — in which monodromy provides the fundamental mechanism of quantization. The structural chain is established as: Topology → Monodromy → Quantization Rules → h as universal coherence threshold.Within this perspective, h is not derived as a numerical constant but identified as a universal unit of minimal coherent action that calibrates the model’s internal parameters. This formulation yields a unified topological explanation for (i) the inevitability of quantized action and (ii) the dichotomy of bosonic versus fermionic statistics, interpreted as trivial and nontrivial monodromy, respectively. Consistency of the coherence criterion with foundational quantum experiments and even recent high-energy anomalies demonstrates that the Omega-model offers a coherent bridge between topology, phase coherence, and the structural foundations of quantum theory.
The quantization of action, discrete energy levels, and finite phase-space resolution are among the most fundamental yet conceptually opaque features of quantum physics. In standard theory, the universal constant is introduced empirically, and canonical quantization rules are postulated without deeper ontological justification. In this work we present a first-principles derivation of quantization based on the Structural Unified Field (SUF) framework. By treating physical entities as layered “existence objects” characterized by a boundary parameter and an existence function , we argue that structural identity requires a minimal nonzero layer separation . This structural irreducibility implies a universal minimal distinguishability in all attribute domains, which, when projected into phase space, yields a minimal phase-space cell and thus a universal minimal action unit. Upon mapping to physical units, this structural minimal action corresponds to Planck’s constant . The SUF interpretation thereby promotes quantization from an empirical postulate to a necessary consequence of the ontological geometry of existence. The resulting framework naturally accounts for discrete spectra, uncertainty relations, action quantization, canonical commutation relations, topological quantization phenomena, and the universality of . We discuss broader implications for the foundations of quantum theory, the quantum–gravity interface, and potential avenues for testing structural deviations.
This paper presents a Coherence Geometry interpretation of Planck’s constant as a natural action scale arising from phase closure in structured coherence fields. Planck’s constant is traditionally introduced as an empirical constant. In this paper, a natural coherence action scale S0 arises from the requirement that stable μ-field structures close phase cycles in integral multiples of 2π. This quantizes action increments as S=2πnS0. The standard quantum relations follow once S0 is calibrated to laboratory data, yielding S0=ℏ. The result is structural rather than numerological: the paper does not claim to derive the measured numerical value of h without calibration. Instead, it argues that an action scale of the Planck type appears naturally from phase-constrained coherence geometry, with numerical value fixed by physical units and experimental comparison. Internal reference: CGI-RSR-000020.
Planck’s constant ℏ is usually introduced as a fundamental postulate of quantum theory. In this work, we derive ℏ analytically from a topological action principle, showing that it emerges as the minimal quantized action required to stabilize a coherent spinor phase configuration. We model the field as Ψ(x)=ρ(x)eiΘ(x), where Θ(x) is a compact scalar valued on S1. Within this framework, we define the class of minimal winding configurations C1/2, characterized by half-integer topological charge ∮γ∂μΘdxμ=π. We demonstrate that the least non-vanishing action over this class is finite, topologically invariant, and equal to ℏ. This implies that ℏ is not a postulate, but a phase-ontological consequence of topological fixation. We further analyze connections with Aharonov–Bohm phenomena, persistent phase currents, and quantized interference effects as physical manifestations of discrete winding. Our results open a new perspective on quantization grounded in global phase topology.
We extend the sphere-on-sphere geometric quantization mechanism of the Operator-Derived Dimension (ODD) framework to derive the full kinematical structure of quantum mechanics. Starting from the topological origin of Planck’s constant h as a winding invariant of the S1 intersection between the five-dimensional bulk and the four-dimensional causal horizon, we show that the symplectic form, canonical commutation relations, phase, spin, and the path-integral formulation arise uniquely and necessarily from the same geometry. Quantization is therefore not postulated but enforced by topology, while operator algebra emerges from the transverse slicing dynamics. This places the foundations of quantum mechanics on geometric and topological necessity rather than axiomatic assumption.
This accepted manuscript is structurally governed by THE META-INDEX (Zenodo DOI: 10.5281/zenodo.18169167) Quantum theory achieves unparalleled empirical success, yet it remains ontologically incomplete with respect to the nature of transitions between physical states. While quantum states are rigorously defined, the process by which a system moves from a potential state to a realized state is typically treated as instantaneous, probabilistic, or measurement-dependent, leaving the transition itself conceptually unexamined. This structural omission underlies several persistent foundational problems, including the measurement problem and the ambiguous status of probability. In this work, quantum behavior is reinterpreted not as an intrinsic property of discrete entities, but as the manifestation of threshold organization governing stable transitions between states. To formalize this perspective, the concept of an Organizational Field (OF) is introduced. The Organizational Field is defined as a topological–temporal regulatory structure that constrains admissible transitions without functioning as a force, energy carrier, or particle field. Within this framework, quantization emerges as a consequence of stability regulation during transitions rather than fundamental discreteness. The fine-structure constant α is accordingly reinterpreted not as a fundamental coupling parameter, but as the stability-band signature of the Organizational Field as projected onto electromagnetic processes. This interpretation accounts for the dimensionless character of α, its small but nonzero value, and its universality across physical scales, without attempting to derive its numerical magnitude. A conceptual distinction is drawn between π as a constant of static geometric form and α as a constant of dynamic transition stability. The framework yields falsifiable predictions, including the existence of micro-band structures in transition statistics and context-sensitive deviations under extreme conditions. The proposed model offers a structural completion of quantum theory by introducing an explicit ontology of transition grounded in threshold organization
This work presents a structural interpretation of the reduced Planck constant ℏ within the framework of the Structural Principle of Entanglement (PSE). In this theory, ℏ is not a fundamental physical parameter nor a quantum‑mechanical postulate. Instead, it emerges as the compressed image of a discrete action threshold selected by the regularized emergent structure. The PSE establishes a unidirectional ontological hierarchy: a prespatial structure without geometry, a fundamental reorganization governed by a coherence threshold, an emergent correlation that organizes continuity, a regularization process that filters coherent configurations, and a set of complexity thresholds that preserve discrete structural rigidity. Together, these elements produce a minimum action threshold that is structural rather than physical. Through a compressive and non‑invertible projection, this structural rigidity is formalized in the physical domain as the reduced Planck constant ℏ. As a result, the quantization of action, canonical non‑commutativity, precision limits, and the structure of the quantum state space are not primitive features of nature. They are consequences of the compressive projection and of the discrete rigidity selected in the emergent domain. Quantum physics therefore appears not as a set of fundamental axioms, but as an effective representation of a deeper emergent structure. In this view, ℏ is an ontological property of the PSE hierarchy: the physical signature of a discrete threshold rooted in the prespatial domain. Observable physical reality is a compressed representation of this emergent structure, and ℏ is its most fundamental imprint.