This paper establishes the structural uniqueness of a phase-to-action conversion scale within an admissibility-first framework. Starting from a quotient-defined principal phase and its real cover, it proves that any admissible action representative possesses a constant monodromy, while linear conversion follows only under separately declared history-composition and single-phase sufficiency conditions. The resulting scale is universal only across commissioned, cycle-consistent comparison channels, with disconnected sectors remaining Undefined. Applied to the wider framework, the theorem supplies the missing formal justification for the common factor identified empirically with (\hbar), without claiming to derive its numerical value or the full structure of quantum mechanics.
This paper establishes the structural uniqueness of a phase-to-action conversion scale within an admissibility-first framework. Starting from a quotient-defined principal phase and its real cover, it proves that any admissible action representative possesses a constant monodromy, while linear conversion follows only under separately declared history-composition and single-phase sufficiency conditions. The resulting scale is universal only across commissioned, cycle-consistent comparison channels, with disconnected sectors remaining Undefined. Applied to the wider framework, the theorem supplies the missing formal justification for the common factor identified empirically with (\hbar), without claiming to derive its numerical value or the full structure of quantum mechanics.
This paper gives a first-principles structural derivation of Planck’s constant within the completion-locked closure framework. The derivation begins from a completion-locked phase–time–energy structure in which admissible phase-frequency comparisons are fixed before energy observables are compared. It does not assume the numerical value of Planck’s constant, the Planck–Einstein energy–frequency law, the standard Hamiltonian phase convention, or canonical commutator normalization. Instead, the action scale is derived from a projective phase carrier, a strongly continuous time-translation representation with Stone angular-frequency generator, an admissible class of energy observables for the same deformation, a sector-rich and spectrally exhaustive comparison structure, and, for dimensional reporting only, a unit convention. The main representation theorem proves that any admissible energy observable satisfying spectral affiliation, direct-sum naturality, tensor-product additivity, zero normalization, continuity, positivity orientation, spectral exhaustivity, and common-source descent must be linear in the Stone generator. This yields a unique reduced action scale, from which the full-cycle quantum of action follows by circle normalization. The Planck–Einstein energy–frequency law is then derived as a consequence of the same structure rather than assumed as an input. The paper also establishes conditional action-unit closure pathways. A certified electromagnetic response branch supplies one action-unit closure path, while a certified curvature–vacuum branch supplies a second through an independently derived source vacuum invariant. A single certified dimensional branch determines the action unit within its unit convention; two same-source certified branches overdetermine the same action unit and therefore must agree. Since Planck’s constant is dimensional, its decimal value becomes meaningful only after an action-unit convention or certified dimensional branch has been specified. Under the post-2019 SI convention, the numerical value of Planck’s constant is exact by definition. The structural contribution of the paper is to identify Planck’s constant not as an empirical insertion into quantum dynamics, but as the derived action-conversion invariant relating phase-frequency generation to physical energy observables, with independent electromagnetic and curvature–vacuum closure paths for the same action unit. License note: Distributed under CC BY-NC-ND 4.0.
The Admissibility of Natural Physics, Part I begins where an admissibility-first reconstruction of single-system quantum mechanics ends. Its central question is not whether the familiar tensor-product formalism can be assumed, but whether any physical composition law can be derived without importing composite systems, global state spaces, entanglement, locality, or signalling as primitives. The book develops a disciplined reconstruction of binary quantum composition from operational and structural requirements. It first records the exact content and limitations of the inherited single-system closure, establishes dependency and non-circularity statutes, and introduces the possible object of natural physics only as a provisional target ledger rather than as an assumed ontology. It then examines joint preparation, product states and effects, marginal consistency, operational no-signalling, minimal and maximal probabilistic composites, local tomography, and the classification of admissible tensor-product representations. Particular attention is given to the distinction between a mathematical representation theorem and the uniqueness of a physical composition rule. Real, complex, quaternionic, Jordan-algebraic, minimal, maximal, restricted, and non-tomographic alternatives are compared under explicitly declared admissibility conditions. The complex Hilbert-space tensor product is recovered only on branches satisfying the required factorization, coherence, scalar, and operational closure conditions. Where several inequivalent composites survive, the result is a classified family rather than a falsely asserted uniqueness theorem. Entanglement is introduced only after composition has been commissioned. It is defined as the failure of an admitted joint state to belong to the convex closure of admitted product preparations. The analysis proves, within the resulting predictive grammar, that entanglement is a property of composite-state geometry, not an additional force, substance, interaction mechanism, or signalling channel. Throughout, the argument enforces quotient primacy, refinement stability, finite diagnostic closure, regeneration stability, explicit dependency receipts, local termination, and the possibility of Undefined as a legitimate scientific outcome. Part I therefore supplies neither a speculative ontology nor a presupposed many-world formalism. It provides a conditional classification theorem for binary physical composition and identifies precisely what remains to be established before interaction, repeated composition, particle identity, locality, fields, symmetries, and particle content may be addressed.
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 Admissibility of Natural Physics, Volume II extends the admissibility-first reconstruction from physical composition to interaction, open dynamics, identical carriers, exchange structure, and occupation grammar. It derives interaction as failure of commissioned factorization, complete positivity as stability under ancillary extension, and dilation only under explicitly admitted environmental structure. It then treats carrier identity as quotient equivalence, constructs permutation actions on repeated composites, classifies symmetric, antisymmetric, para, reducible, and projective exchange sectors, and determines the additional premises required for Fock-like occupation spaces. The resulting framework remains branch-valued: unique closure, classified family, missing premise, or (\Undefined). Bose, Fermi, braid, and para statistics are retained as conditional possibilities pending the derivation of regional topology and locality.
Action principles, phase accumulation and quantized closure appear across classical mechanics, quantum theory, semiclassical dynamics, superfluidity and geometric phase phenomena. Their coexistence is familiar; their structural relationship is usually taken as part of the established formalism. Here we reconstruct that relationship in the opposite direction. Starting from persistent relational dynamics, we show how a real two-component rotation supplies a phase coordinate without assuming a primitive complex number, how a relational canonical one-form can connect phase increments to action-like increments, and how stationary phase and global phase consistency impose two distinct selection conditions. The local condition yields stationary action, δA_R = 0. The global condition yields integral symplectic periods. Under the explicit convention F_R = −iΩ_R/κ_A for a U(1) connection curvature, global compatibility requires [Ω_R/(2πκ_A)] ∈ H²(M_R,Z), equivalently ∫_Σ Ω_R = 2πnκ_A on closed two-cycles. This separates the origin of discreteness from the origin of the dimensionful conversion scale. Topology fixes integer classes; it does not determine κ_A. We therefore identify a precise remaining problem: what selects a unique, universal and non-zero κ⋆ across coherently composable sectors? The framework makes this question falsifiable by requiring cross-scale closure, causal ancestry, intervention consistency and independence from observer compression. It also distinguishes a universal phase–action conversion scale from scale-dependent effective couplings. The result is a sharpened bridge from relational phase to stationary dynamics and quantized closure, with a mathematically explicit boundary between what is derived, what is inherited from established geometry, and what remains to be selected dynamically. The revision formalizes an Action-Scale Factorization Theorem together with Exact-Action and Curvature-Compatibility no-go results, thereby separating the existence of quantized closed-path sectors from the still-open physical selection of a universal non-zero scale such as ħ.
Barrios Hita et al. [Phys. Rev. Lett. 136, 240202 (2026)] proposed a quotient-space formulation of quantum mechanics over the real numbers and concluded that complex numbers are only a convenience. A preceding analysis [arXiv:2607.05865] showed that, when the construction is empirically equivalent to complex quantum mechanics, its real flag is protected by a hidden complex structure J^ and its composition rule is the balanced tensor product over that structure. Here we ask what would follow from the stronger operational reading that the flag is an accessible real degree of freedom. The answer is a direct clash with overlap-determinability (OD), introduced in [arXiv:2601.14638], and with standard no-go theorems. A readable or coherently controllable flag fixes a representative of each ray, and hence supplies precisely the phase convention that OD identifies as the missing resource for universal superposition of unknown states. Once promoted to a generic phase-access primitive, this resource enables probabilistic cloning of a linearly dependent set, steering-based signaling, and logarithmic-query unstructured search. Thus the quotient construction has a sharp follow-up interpretation: as a protected gauge representation it is standard complex quantum mechanics in real notation; as an accessible real theory it leaves the quantum operational framework.