This paper develops a theory-neutral structural result concerning relational descriptions in physics. Many modern frameworks assign physical meaning through interactions rather than observer-independent intrinsic properties. This raises a general composition problem: if facts are generated locally within interaction contexts, what determines their coherent comparison across later chains or networks of interactions? Within a minimal framework of interacting systems, locally assigned relational facts, and maps between fact contexts, the paper establishes an interface necessity theorem: local fact assignments together with bare accessibility structure are not, in general, sufficient to determine unique cross-context composition outcomes whenever later comparison, inheritance, or aggregation of records is permitted. Some additional structure governing admissibility, translation, filtering, compatibility, or equivalence between relational fact spaces is generically required. This additional layer is termed interface structure and is used operationally rather than ontologically. No new force, hidden variable, or replacement dynamics is proposed. Instead, the result identifies a structural requirement linking local relationality to broader coherence. The paper discusses implications for relational quantum mechanics, decoherence-based narratives of record formation, Wigner-type multi-observer scenarios, and broader network descriptions of physical information. This work is related to the broader Horizons-as-Dynamical-Interface Framework (HDIF) program.
This paper develops a theory-neutral structural result concerning relational descriptions in physics. Many modern frameworks assign physical meaning through interactions rather than observer-independent intrinsic properties. This raises a general composition problem: if facts are generated locally within interaction contexts, what determines their coherent comparison across later chains or networks of interactions? Within a minimal framework of interacting systems, locally assigned relational facts, and maps between fact contexts, the paper establishes an interface necessity theorem: local fact assignments together with bare accessibility structure are not, in general, sufficient to determine unique cross-context composition outcomes whenever later comparison, inheritance, or aggregation of records is permitted. Some additional structure governing admissibility, translation, filtering, compatibility, or equivalence between relational fact spaces is generically required. This additional layer is termed interface structure and is used operationally rather than ontologically. No new force, hidden variable, or replacement dynamics is proposed. Instead, the result identifies a structural requirement linking local relationality to broader coherence. The paper discusses implications for relational quantum mechanics, decoherence-based narratives of record formation, Wigner-type multi-observer scenarios, and broader network descriptions of physical information. This work is related to the broader Horizons-as-Dynamical-Interface Framework (HDIF) program.
This preprint develops a level-dependent interpretation of admissibility and compositional constraints within relational physical frameworks. Building on prior work establishing that local relational assignments together with accessibility structure are generally insufficient to determine unique cross-context composition outcomes, the paper examines how additional compositional constraints may be interpreted operationally across different descriptive levels. Rather than introducing new dynamical entities or modifying established physical theories, the framework treats admissibility and compositional constraints as structural conditions governing how relational information may be propagated, filtered, translated, and consistently composed across multiple interaction contexts. The work situates this interpretation relative to relational quantum mechanics, decoherence-based descriptions, gauge-theoretic transition structure, quantum information theory, relativistic causal structure, and distributed systems frameworks. Representative physical constraint classes discussed include causality, consistency, stability, equivalence preservation, and information-theoretic limitations. The framework is intentionally structural, interpretive, and ontology-neutral in scope. Its primary contribution is to clarify the role of admissibility and compositional constraints in maintaining compositionally consistent relational descriptions across distributed interaction contexts.
(This version has been superceeded, see v.3) Contemporary approaches to physical unification typically emphasize dynamical laws, interpretive frameworks, or information-theoretic reconstructions. Less attention is given to the structural constraints that determine which physical descriptions can remain coherent and stable under interaction, scale transition, and aggregation. This paper develops a constraint-first analysis of coherence, arguing that persistence and unification require restrictions on admissible physical continuations that are not reducible to dynamics alone. Within the framework referred to here as Quantum Coherence Theory (QCT), coherence is treated not as a fragile quantum resource but as a structural property governed by interaction geometry and constraint density. On this view, classical behavior emerges when accumulated constraints sufficiently narrow admissible evolution, while quantum behavior re-emerges when constraints are relaxed. The account does not introduce new dynamics, collapse mechanisms, or modifications of quantum formalism, but instead clarifies the conditions under which existing formalisms yield stable, unified descriptions. The resulting constraints distinguish QCT from observer-centric, intrinsic-collapse, and purely descriptive decoherence accounts, while remaining compatible with globally unitary dynamics. Formal analysis in later sections develops operational redundancy conditions, admissibility constraints on joint states, and rigidity-style arguments linking redundant record structure to the stability of classical descriptions. These results do not constitute a complete theory of unification, but they narrow the space of physically admissible descriptions and clarify the structural role of coherence in bridging quantum and classical regimes.
AbstractWe investigate the minimal structural conditions under which relational accessibility organization admits a topological representation within physical description. Starting solely from the existence of distinguishable states and admissible comparison relations, we analyze how accessibility structures arise without introducing prior notions of space, geometry, metric structure, probability, or dynamics.Within the present framework, comparison between states is interpreted as a structural relation governing the accessibility of distinctions. The consistency requirements imposed on admissible comparisons induce preorder-like relational organization on the state space. We show that such comparison-induced accessibility structures admit neighborhood-like representations and may be organized in a form compatible with topological description.Importantly, the present framework does not interpret topology as a primitive geometric entity. Rather, topological structure is treated as a mathematical representation of relational accessibility induced by admissible comparison structure. In this perspective, neighborhood relations characterize accessibility coherence among distinguishable states rather than spatial proximity in a preexisting geometric manifold.We further show that equivalence structures associated with comparison naturally introduce classes of states that are indistinguishable within a given accessibility framework while remaining structurally distinct in the underlying state space. This provides a relational interpretation of local accessibility organization without invoking observer-dependent notions or externally imposed representational scales.The present work does not introduce new mathematical constructions. Instead, it identifies structural conditions under which topological representation becomes compatible with a minimal relational framework of physical description.
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.
This paper develops an interpretive and operational framework in which physical “memory” is defined as persistent relational constraint rather than as an internal record carried by an isolated object. The proposal is motivated by three established facts: quantum interactions can generate correlations that survive spatial separation; open-system dynamics redistribute locally accessible information into system–environment correlations; and spacetime geometry in general relativity constrains later motion through a dynamical field determined by matter and energy. These facts do not imply that particles remember, that entanglement is a communication channel, or that curvature literally stores a semantic history. They do, however, motivate a precise cross-domain question: when does a past interaction leave a measurable relational structure that continues to constrain future observables? We distinguish this operational notion from stronger metaphysical claims and from biological or cognitive memory. Standard correlation measures, including mutual information and correlation functions, are proposed as candidate observables for quantifying persistence, while a persistence timescale separates transient correlation from durable relational structure. The framework is then applied cautiously to quantum systems, fields, spacetime, biology, and cognition. Speculative ideas such as frequency-selective persistence and curvature–coherence coupling are reformulated as hypotheses that must predict deviations from standard theory to become new physics. The resulting account is not presented as a replacement for quantum mechanics, quantum field theory, general relativity, or neuroscience, but as a disciplined vocabulary and research program for comparing information persistence across scales.
We develop a rigorous categorical and topological framework for Relational Quantum Dynamics (RQD), formalizing a dynamic network of observers as a relational graph enriched with quantum-theoretic structure. In RQD, quantum systems and observers have no intrinsic properties, only relationships: we prove via category theory (Yoneda’s lemma) that each object (observer/system) is uniquely determined (up to isomorphism) by its web of morphisms to all others, with no additional absolute identity. This network of interactions is formalized as a structured graph of observers – mathematically, a category (and higher-dimensional generalizations) enriched with weights capturing interaction strength. We show how quantum correlations and information flow can label the graph’s edges, yielding a rich combinatorial structure. Crucially, quantum contextuality and entanglement impose topological constraints on the observer network. Using presheaf topos theory and sheaf cohomology, we prove that the absence of a global assignment of outcomes (no single “God’s-eye” view) corresponds to a nontrivial cohomology class on the relational graph. In particular, in contextual scenarios the first Čech cohomology H1 of the presheaf of local measurement outcomes is nonzero, providing a rigorous obstruction to global consistency. These results endow the relational graph with a “twisted” topology reflecting quantum connectivity constraints. We present theorem-proof developments of these ideas and discuss implications: how RQD’s relational ontology naturally explains Bell inequality violations without spooky action, how multi-observer paradoxes (Wigner’s friend) are resolved by higher-category structures, and potential links to models of consciousness via integrated information.