We propose a preliminary mathematical framework for physical theories based on experimentally grounded constraints. A physical theory is represented as a structured object (S, O, D) consisting of a state space, a set of observables, and a dynamical law. We introduce constraint operators acting on the space of candidate theories, encoding symmetry, causality, quantum, and dynamical requirements. The space of physically admissible theories is defined as the intersection of constraint-defined subsets, leading to a constraint-based interpretation of physical laws as consistency conditions. This framework provides a unified mathematical perspective in which classical mechanics, relativity, and quantum theory can be understood as different realizations within a common structure. This work presents a preliminary but structured conceptual and mathematical framework.
We propose a preliminary mathematical framework for physical theories based on experimentally grounded constraints. A physical theory is represented as a structured object (S, O, D) consisting of a state space, a set of observables, and a dynamical law. We introduce constraint operators acting on the space of candidate theories, encoding symmetry, causality, quantum, and dynamical requirements. The space of physically admissible theories is defined as the intersection of constraint-defined subsets, leading to a constraint-based interpretation of physical laws as consistency conditions. This framework provides a unified mathematical perspective in which classical mechanics, relativity, and quantum theory can be understood as different realizations within a common structure. This work presents a preliminary but structured conceptual and mathematical framework.
We propose a constraint-based formalism in which physical systems are characterized by operators acting on a state space. In this framework, constraint operators encode admissibility, projection, and structural restriction in a unified manner. We analyze the algebraic properties of these operators and show that, under natural conditions, they form a projection-based structure. This perspective provides a common structural language that accommodates diverse physical theories. In particular, projection operators in quantum mechanics may be interpreted as instances of constraint operators, and measurement processes may be viewed as constraint-driven transformations. In statistical and information-theoretic contexts, entropy can be interpreted as a coarse-grained measure of the size of constraint-compatible state spaces. The proposed formalism does not aim to replace existing theories, but to provide a minimal and theory-independent framework for describing how physical structure may arise from constraints. This work provides a structural bridge between constraint-based formulations and projection structures in quantum mechanics.
This work presents a continuous, constraint-based interpretive framework for physical systems that unifies quantum behavior, classical structure, and cosmological evolution without introducing new forces or modifying established equations. Rather than treating quantum mechanics, electromagnetism, and general relativity as fundamentally separate domains, the paper proposes that these regimes can be understood as consistent descriptions of a shared underlying structure. The framework is built on three foundational elements: a non-geometric substrate (P_0) defining admissible configurations, interaction as the propagation of constraint, and geometry as the macroscopic record of accumulated interaction. Within this perspective, physical structure emerges through a continuous progression: distinctions enable gradients, gradients enable interaction, interaction accumulates as constraint, and constraint stabilizes into persistent configurations. The quantum–classical transition is interpreted as a continuous increase in interaction-induced constraint, while spacetime curvature reflects the large-scale organization of these interactions. The framework does not replace existing theories, but instead provides a unified conceptual interpretation that remains fully consistent with established physics across known regimes. Its value lies in clarifying relationships between domains, offering a continuous ontology of physical systems, and suggesting potential directions for further formalization.
Foundational problems in physics—including quantum measurement, spacetime emergence, gravitational dynamics, nonlocality, the arrow of time, and the status of physical existence—are typically addressed in isolation, via model-dependent extensions or interpretive assumptions. This work proposes a different approach. We introduce a constraint-based framework, the Closure Admissibility Principle (CAP), which specifies minimal structural conditions any physical description must satisfy in order to be globally consistent. CAP is formulated in operational terms, using admissibility of states, recoverability under refinement, and stability of closed records, without assuming spacetime, dynamics, or ontology a priori. We show that enforcing these constraints induces a unifying closure structure on law-space, from which several persistent foundational puzzles are resolved as structural consequences rather than postulates. In particular, collapse is reclassified as record selection, spacetime and gravity emerge only in compressible regimes, General Relativity appears as an infrared universality class rather than a fundamental law, singularities correspond to failures of admissible description, and null (“nothing”) models are excluded as inadmissible fixed points. The framework is explicitly falsifiable via operational and weak-field tests, and its scope and limits are stated precisely. The results suggest that many foundational paradoxes arise not from incomplete dynamics, but from admitting globally incoherent physical descriptions.
This paper presents a continuous structural ontology in which quantum mechanics, field theory, and general relativity are interpreted as regime-specific descriptions of a shared underlying system. Rather than introducing new forces or modifying established equations, the framework identifies three minimal and persistent structural elements across physical regimes: admissible configuration space, propagating constraint, and geometry as the macroscopic record of accumulated interaction. The work is intentionally interpretive rather than revisionary. It proposes that physical evolution can be understood as the propagation of constraint over admissible configurations, with increasing restriction giving rise to stable structure, classical behavior, and geometric curvature. Established mathematical formalisms—including Hilbert space, field equations, and general relativity—are preserved and reinterpreted within a common structural language. This framework aims to improve conceptual continuity across quantum, field, and geometric domains while remaining fully consistent with existing empirical results. It does not claim a complete formal unification, but instead offers a minimal ontological foundation that may clarify relationships between currently distinct theoretical descriptions. This paper forms part of the broader Communication Matrix research program.
Modern physics relies on multiple theoretical frameworks that successfully describe phenomena at specific scales, yet remain conceptually fragmented when addressing the relations between quantum mechanics, general relativity, thermodynamics, and measurement. This work introduces the Agreement-Based State-Space Framework (ABSSF), an operational interpretative model in which physical reality is described in terms of admissible states, constraints, and transitions rather than fundamental objects. Within this framework, particles are interpreted as stable trajectories in state space, interactions as quantized permissions for transitions, time as an ordering of realized transitions, and entropy as a measure of accessible configurations. The framework does not propose new physical laws or numerical predictions; instead, it provides a unifying language capable of consistently interpreting phenomena ranging from quantum measurement and confinement to cosmological structures, vacuum behavior, and information flow. ABSSF is intended as a conceptual bridge between existing theories, offering structural clarity while remaining fully compatible with established physical models.
We introduce a unified framework in which system validity, dynamics, and evolution are governed by constraint-defined admissibility. A system state is admissible if it satisfies a set of constraints, and deviation from admissibility is quantified by a residual function α(S). We show that system evolution can be expressed as a gradient-driven process minimizing α(S), providing a unified description of physical motion, computational optimization, and control systems. We further extend the framework to a variational formulation and demonstrate that α(S) acts as a generalized potential. A quantum formulation is derived in which α(S) appears as a constraint-based potential term in the Schrödinger equation. Measurement is interpreted as constraint injection, and apparent probabilistic behavior emerges from admissibility structure. The theory provides a unified description across classical mechanics, quantum systems, and computational processes, reframing dynamics as the minimization of inconsistency with respect to constraint-defined admissibility.