We present a structural framework for analyzing dynamics in background-independent theories based on admissible transport on configuration spaces. The approach reformulates canonical evolution not in terms of a fixed Hamiltonian, but via constrained transport maps acting on an admissible subspace of states, preserving constraint closure and covariance by construction. Within this setting, we show that admissible dynamics admit a dual description in terms of state transport and observable transport, related by an adjoint pairing, and we establish conditions under which validation metrics are invariant under this duality. We further prove that admissibility enforces contraction bounds on accumulated deviations under composition, providing a structural explanation for stability without specifying a particular microscopic dynamics. The framework is applied to canonical Loop Quantum Gravity as a consistency analysis rather than as a proposal for new dynamics. We clarify how transport-based formulations relate to existing spin- network and spin-foam constructions, and we identify precise conditions under which such formulations remain anomaly-free. No claim is made to resolve the full dynamics problem or to derive novel physical predictions. Instead, the results provide a controlled language for distinguishing structurally stable evolutions from inadmissible ones in background-independent quantum theories. This work is an information-theoretic framework concerned with admissible transport and stability of information under composition. Physical theories, including Loop Quantum Gravity (LQG), are used solely as structured test cases rather than as the primary object of study. LQG serves as a representative background-independent information system. This manuscript is information theory under constraints, not physics. CIFT is an information-theoretic framework in which conserved quantities are measured in bits and are conditional on explicit admission and boundary exchange.
We present a structural framework for analyzing dynamics in background-independent theories based on admissible transport on configuration spaces. The approach reformulates canonical evolution not in terms of a fixed Hamiltonian, but via constrained transport maps acting on an admissible subspace of states, preserving constraint closure and covariance by construction. Within this setting, we show that admissible dynamics admit a dual description in terms of state transport and observable transport, related by an adjoint pairing, and we establish conditions under which validation metrics are invariant under this duality. We further prove that admissibility enforces contraction bounds on accumulated deviations under composition, providing a structural explanation for stability without specifying a particular microscopic dynamics. The framework is applied to canonical Loop Quantum Gravity as a consistency analysis rather than as a proposal for new dynamics. We clarify how transport-based formulations relate to existing spin- network and spin-foam constructions, and we identify precise conditions under which such formulations remain anomaly-free. No claim is made to resolve the full dynamics problem or to derive novel physical predictions. Instead, the results provide a controlled language for distinguishing structurally stable evolutions from inadmissible ones in background-independent quantum theories. This work is an information-theoretic framework concerned with admissible transport and stability of information under composition. Physical theories, including Loop Quantum Gravity (LQG), are used solely as structured test cases rather than as the primary object of study. LQG serves as a representative background-independent information system. This manuscript is information theory under constraints, not physics. CIFT is an information-theoretic framework in which conserved quantities are measured in bits and are conditional on explicit admission and boundary exchange.
Covariant Information Field Theory (CIFT) provides a formal, axiomatic framework for admissibility-governed inference that is independent of physical realization. In this work, we present the Harlow Conduit / Loop-Quantum-Gravity (HC/LQG) construction as a realization-level theory that instantiates CIFT admissibility constraints within a gapped, cascaded operator system. We show that admissibility is not merely a structural filter but induces predictive, falsifiable convergence behavior when implemented in such systems. In particular, HC/LQG yields explicit thresholds, exponential screening bounds, and laboratory-verifiable observables, while preserving strict separation from CIFT’s core axioms. This establishes HC/LQG as the first predictive theory to emerge from CIFT: one that derives measurable consequences from admissibility without importing physical assumptions back into the foundational framework. A key feature of this work is the principled reuse of high-precision experimental results traditionally reported as null within Loop Quantum Gravity (LQG)–adjacent test programs. Experiments designed to probe vacuum dispersion, polarization rotation, or refinement-induced spectral drift—while reporting no positive signal—nevertheless establish stringent upper bounds on admissible transport behavior. Within the Covariant Information Field Theory (CIFT) framework, these null results are reinterpreted not as failures of detection but as empirical constraints defining the boundary of admissible corridors. When applied to cascaded, gapped holonomic systems, these constraints predict the emergence of stability-selected transport channels—realized here as Harlow Conduits—whose convergence thresholds and screening behavior are quantitatively consistent with the reported null bounds. In this sense, HC/LQG constitutes the first realization-level theory to extract predictive structure from CIFT using existing experimental null data, without reclassifying those results as detections or modifying the underlying experimental claims. From a canonical perspective, the present construction may be read as a controlled realization of kinematical admissibility rather than a proposal for gravitational dynamics. To the best of our knowledge, This manuscript is the first rigorously predictive, admissibility-based, foundation on which a complete quantum gravity theory can actually be built.
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 provides a purely formal and technical development of the mathematical structures underlying a correlational framework for physics. It introduces no ontological assumptions, no physical interpretation, and no experimental claims. All constructions are independent of primitive notions of space, time, dynamics, causality, or physical law. The paper rigorously defines correlational configuration spaces, admissibility conditions, representational equivalence classes, and quotient structures. A central object is the consistency functional, together with its Hessian operator, treated as a (possibly unbounded) self-adjoint operator on infinite-dimensional spaces. Detailed attention is given to domains, spectral properties, stability, and variational structure. Projection operators onto observable subspaces are introduced as mathematically irreversible restrictions, with explicit treatment of information loss and consistency of reduced descriptions. The canonical correlational flow is defined as a gradient flow of the consistency functional, with proofs of local existence, uniqueness, reparametrization freedom, and dissipative character, all without invoking time or dynamics. The paper also analyzes fixed points, attractors, metastable configurations, and the precise formal relations between flow, Hessian, and projection. Finally, the intrinsic limits of the framework are made explicit, including configurations without physical interpretation, breakdowns of projection, and ill-defined spectral structure. This work is intended as a technical companion to foundational, canonical, and applied papers. Its sole purpose is to eliminate formal ambiguity and provide a mathematically explicit backbone for subsequent physical realization and application.
This work develops the structural consequences of the Closure Admissibility Principle (CAP), a constraint-based framework for analyzing the internal consistency of physical descriptions across quantum theory, spacetime models, and information-theoretic formulations. We formalize closure completeness, admissible observer classes, refinement stability, and irreversible operations, and demonstrate that paradox-generating constructions arise from structurally forbidden transformations rather than physical inconsistency. The paper proves a closure trichotomy governing admissible physical claims and establishes conditions under which apparent contradictions reduce to violations of admissibility constraints. Canonical examples from irreversibility, information flow, and foundational physics are analyzed within a unified operator-structural setting.
This paper introduces the Relativity of Information Frames (RIF), a foundational framework that precedes and constrains dynamical theories. RIF treats information frames—σ-algebras of distinguishable events—as the fundamental objects of physical description, and formulates interaction as the joint realization of such frames subject to a symmetry principle: no information frame may be privileged over another. From this principle alone, the framework derives a canonical restriction on joint event structures. We prove the existence of a distinguished σ-algebra—the pointer algebra—which is the unique maximal event algebra compatible with perspectival symmetry and the existence of consistent probability assignments. Any empirical model admits a global probability measure on this algebra, while any strict extension generically fails to do so, reintroducing contextuality. These results impose non-trivial structural constraints that any admissible dynamics must respect. The framework is applied to quantum theory, not by postulating dynamics, but by showing how its core structures arise necessarily from informational consistency. Observables appear as perspectival maps, state update corresponds to interaction-induced coarse-graining, the Born rule follows from a martingale structure on the induced σ-algebra filtrations, Wigner-type scenarios are consistent, and unitary evolution is reinterpreted as gauge freedom in joint descriptions rather than ontic time evolution. RIF does not replace dynamical theories; it delimits them. It identifies which event structures, probability assignments, and symmetries are admissible prior to dynamics, and therefore clarifies what features of quantum theory are structural necessities rather than contingent dynamical postulates. The framework further implies intrinsic irreversibility, a relational notion of locality, and constraints on emergent geometric structure, which any subsequent dynamical formulation must accommodate.
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.