The Intrinsic Observability Framework (IOF) distinguishes structural decomposition from operational decomposition as complementary levels of organization. Structural decomposition establishes the observable and hidden domains as the architecture of observability, whereas operational decomposition assigns the latent structure to these domains under a given observational interaction. The present work extends this framework by introducing two complementary forms of totality: structural totality and operational totality. Structural totality represents the completeness of the structural architecture established through structural decomposition, consisting of the observable and hidden domains. Operational totality, in contrast, represents the completeness of the latent structure as operationally assigned across these domains through operational decomposition. The distinction therefore concerns different objects of completeness: structural totality refers to the architecture within which assignment is possible, whereas operational totality refers to the content completely assigned within that architecture. Operational totality is consequently neither an incomplete portion nor a degraded representation of structural totality. Different observational interactions may establish different operational totalities within a common structural totality. Such observer dependence does not imply incompleteness or mutually isolated operational worlds. Each operational totality is complete with respect to its own operational assignment, while the admissible relations among independently established operational totalities are constrained by the Global Consistency Rule (GCR). The resulting framework therefore distinguishes structural completeness, operational completeness, and global consistency, providing an organizational interpretation of how distinct observer-dependent totalities can coexist while collectively supporting a shared and coherent operational reality without modifying the mathematical formalism or empirical predictions of quantum mechanics.
The Intrinsic Observability Framework (IOF) distinguishes structural decomposition from operational decomposition as complementary levels of organization. Structural decomposition establishes the observable and hidden domains as the architecture of observability, whereas operational decomposition assigns the latent structure to these domains under a given observational interaction. The present work extends this framework by introducing two complementary forms of totality: structural totality and operational totality. Structural totality represents the completeness of the structural architecture established through structural decomposition, consisting of the observable and hidden domains. Operational totality, in contrast, represents the completeness of the latent structure as operationally assigned across these domains through operational decomposition. The distinction therefore concerns different objects of completeness: structural totality refers to the architecture within which assignment is possible, whereas operational totality refers to the content completely assigned within that architecture. Operational totality is consequently neither an incomplete portion nor a degraded representation of structural totality. Different observational interactions may establish different operational totalities within a common structural totality. Such observer dependence does not imply incompleteness or mutually isolated operational worlds. Each operational totality is complete with respect to its own operational assignment, while the admissible relations among independently established operational totalities are constrained by the Global Consistency Rule (GCR). The resulting framework therefore distinguishes structural completeness, operational completeness, and global consistency, providing an organizational interpretation of how distinct observer-dependent totalities can coexist while collectively supporting a shared and coherent operational reality without modifying the mathematical formalism or empirical predictions of quantum mechanics.
Operational decomposition has been introduced within the Intrinsic Observability Framework (IOF) as the structural process through which observation establishes the operational assignment of the latent structure within the observable and hidden domains. However, once multiple observations independently establish their respective operational decompositions, an important question arises: why do these independently established operational assignments remain mutually coherent rather than producing incompatible operational realities? In the present work, we address this problem by introducing the Global Consistency Rule (GCR) for operational decomposition. The GCR states that independently established operational decompositions need not be identical, but their mutual relations must satisfy common consistency conditions that preserve the coherence of operational reality. From this perspective, Relational Access Symmetry (RAS) is interpreted as an ideal relational consistency principle governing the organization of observational structures, whereas Access Transformation Symmetry (ATS) provides the operational consistency realized among physically accessible decompositions. Together, these complementary principles provide the structural basis of the GCR and constrain operational decomposition without eliminating its observational and accessibility dependence. The present formulation does not modify the mathematical formalism or empirical predictions of quantum mechanics. Instead, it provides a structural interpretation of why independently established operational decompositions can differ while remaining mutually coherent. The proposed framework therefore extends the IOF from a theory describing the establishment of operational decomposition to one in which the admissible relationships among multiple operational decompositions are explicitly constrained by a global consistency rule, allowing them to collectively constitute a coherent operational reality.
We extend the Intrinsic Observability Framework (IOF) by introducing a symmetry structure underlying observer-dependent descriptions of quantum systems. In previous works, probabilistic outcomes were formulated as a consequence of restricted access to the full quantum state, and observable predictions were shown to be invariant under admissible transformations of a fixed decomposition. In the present work, we relax the assumption of a fixed decomposition and allow the partition of the Hilbert space into observable and hidden sectors to depend on the observer. To relate such descriptions, we introduce Access-Transformation Symmetry (ATS), which characterizes invariance under transformations between observer-dependent decompositions. We show that, although the assignment of observable and hidden degrees of freedom may vary between observers, all observable predictions—such as probability distributions and expectation values—remain invariant. This establishes a consistent framework in which observer-dependent representations coexist with observer-independent empirical content. The present formulation reveals that observation is inherently asymmetric, while the underlying access structure exhibits a symmetry under transformations between observers. In this way, the IOF is extended from a structural framework to one that incorporates relational aspects of observability, while preserving its empirical consistency.
Operational decomposition was introduced in the preceding paper as the process through which the latent structure is operationally assigned to the observable and hidden domains under a given interaction. However, the condition under which this operational assignment becomes established has not yet been clarified. In this paper, we propose that observation induces operational decomposition. Observation is treated as the operational interaction through which the assignment of the latent structure to the observable and hidden domains becomes established, rather than as a process of information acquisition. From the observational perspective, this principle corresponds to the previously introduced statement that measurement grants accessibility. These two principles are interpreted as complementary descriptions of the same operational interaction, viewed respectively from structural and observational perspectives. The present work thereby clarifies the conceptual role of observation in establishing operational decomposition while intentionally leaving its detailed dynamical mechanism outside the scope of the paper.
We propose a framework, referred to as the Intrinsic Observability Framework (IOF), in which the probabilistic structure of quantum mechanics arises from an intrinsic decomposition of the Hilbert space into observable and hidden degrees of freedom. The total system is described by a pure state evolving unitarily, while observable states are obtained by restricting the description to the observable sector via a partial trace over the hidden sector. A key assumption of the present approach is that this decomposition is a fundamental and non-contextual feature of the system, rather than a modeling choice or a consequence of environmental interactions. The hidden degrees of freedom introduced here are not interpreted as unmeasured physical variables, but as components that are fundamentally excluded from the space of observable quantities. Within the IOF, mixed states and probabilistic outcomes emerge from incomplete access to the full state, without invoking intrinsic randomness, external environments, or branching worlds. This distinguishes the present formulation from decoherence-based approaches, hidden-variable theories, and many-worlds interpretations. The proposed framework provides an alternative structural perspective on the origin of quantum probabilities while preserving the standard unitary formalism. We discuss its conceptual implications and outline directions for future work.
We investigate the invariance structure of observable predictions in the Intrinsic Observability Framework (IOF), building on the Access-Induced Reduction Principle (ARP) introduced in Ref. [1]. While IOF allows for non-unique decompositions of a quantum system into observable and hidden degrees of freedom, physical predictions must remain invariant under admissible transformations of such decompositions. We formalize admissible transformations as those that preserve observable probability distributions derived from reduced states. Furthermore, we clarify the distinction between invariant statistical structures and non-invariant configurations of individual measurement outcomes. This establishes a consistent framework in which structural freedom coexists with empirical determinacy.
This work develops an ontological framework underlying contemporary physical theories, addressing a gap between formal admissibility and physical realization. Modern physics—quantum field theory, special relativity, and general relativity—successfully constrains admissible states, relations, and transitions, yet remains largely silent on how admissible structures become realized physical facts. This paper argues that the limitation is ontological rather than dynamical or epistemic. Two complementary notions are introduced. Structural indifference is the principle according to which physical structure distinguishes roles and invariants, but not the individual identity of the carriers realizing those roles. The coherence operator enforces relational compatibility among admissible roles, ensuring that realized parameter assignments are mutually consistent without fixing absolute numerical values. Together, these notions explain how observable universality can arise without global uniformity of laws or constants. Local variability of parameters becomes compatible with stable structure, while identical observational patterns emerge through coherence and translatability rather than numerical identity. Quantum mechanics is shown to be complete at the level of admissibility but ontologically incomplete with respect to realization. Gravity is interpreted as a global modulator of structural indifference, shaping large-scale regimes of realization without altering quantum formalism. The framework does not modify existing physical theories, introduce new dynamics, or rely on probabilistic selection. Instead, it articulates an ontological layer beneath current formalisms, clarifying why physical description works, how realization occurs, and why identity fixation is unnecessary.