We present a restriction-based reconstruction framework in which physical form is derived from aminimal ontology of admissible restriction on a realizability space. From a restriction filtration and itsnonempty core, we define a cumulative restriction-work functional and an associated information-time.A locality/factorization hypothesis yields an effective action functional, while stabilization of restrictedmeasures separates geometric and contextual representational regimes. In the contextual regime, apresheaf of local Boolean algebras is glued into a global orthomodular event structure supporting aconsistent probability valuation. Under standard regularity conditions, Hilbert-space representation isobtained via classification results for orthomodular lattices, and the associated valuation admits the Bornform. In the geometric regime, covariance and boundary-localization conditions constrain the effectiveaction to the Einstein--Hilbert class. A restriction dynamics operator is introduced via variationalselection, generating an irreversible restriction flow. Extensions for defects, matter, and gauge structureare formulated as programmatic developments within the same core framework. The aim is structuralreconstruction rather than a complete predictive physical theory.
We present a restriction-based reconstruction framework in which physical form is derived from aminimal ontology of admissible restriction on a realizability space. From a restriction filtration and itsnonempty core, we define a cumulative restriction-work functional and an associated information-time.A locality/factorization hypothesis yields an effective action functional, while stabilization of restrictedmeasures separates geometric and contextual representational regimes. In the contextual regime, apresheaf of local Boolean algebras is glued into a global orthomodular event structure supporting aconsistent probability valuation. Under standard regularity conditions, Hilbert-space representation isobtained via classification results for orthomodular lattices, and the associated valuation admits the Bornform. In the geometric regime, covariance and boundary-localization conditions constrain the effectiveaction to the Einstein--Hilbert class. A restriction dynamics operator is introduced via variationalselection, generating an irreversible restriction flow. Extensions for defects, matter, and gauge structureare formulated as programmatic developments within the same core framework. The aim is structuralreconstruction rather than a complete predictive physical theory.
We propose Stratified Causal Actualization (SCA), a generative framework in which physical reality is not presupposed as spacetime populated by matter, nor as probabilistic outcomes governed by dynamical laws, but as the irreversible actualization of causally constrained possibility. Beginning from primitive events and a causality relation devoid of geometry, time, or metric structure, we construct an ordinally stratified latent causal space encoding structured potentiality. We show that physics cannot be written directly on this space: realization requires an epistemic projection that discards internal causal structure while preserving distinguishability, yielding a realizability domain Ω. On Ω we derive admissibility, filtration, valuation, and variational actualization, closing the schema (Ω,A,⪯,ρ,TA,W,Φ,JA,D) governing consistent realization. A central result is the identification of a universal causal saturation invariant: the ratio of actual to maximal admissible causal restructuring. This invariant underlies the observed invariance of light propagation without presupposing spacetime geometry or kinematic postulates, and generates causal horizons as structural, rather than geometric, phenomena. Within this framework, time emerges as restriction depth, distance as constraint-mediated reachability, matter as stable restriction cores, and physical law as the fixed-point structure of permissible actualization. General relativity and quantum mechanics arise as complementary representational regimes encoding different projections of the same underlying causal stratification. SCA does not modify existing physical theories; it identifies the landscape from which their core structures necessarily arise.
This paper develops a reconstruction of probability that does not begin by assuming a probability space, a probability simplex, or the Born rule. Instead, it asks a prior foundational question: under what physical and mathematical conditions are a set of alternatives entitled to carry positive, additive probabilities at all? The construction begins with lawful histories, future interfaces, and retained records. It distinguishes coherent alternatives from exclusive empirical events, preventing multiple interfering routes from being mistaken for separate probabilistic outcomes. A future-sufficient quotient identifies distinctions that no admitted future test can detect, while a record-qualification step determines when alternatives have become genuine empirical events. Dagger-compatible comparison and positive record factorization then produce a positive comparison kernel, from which normalized event probabilities arise only after the relevant record sectors are certified as exclusive. The framework is extended beyond individual measurements. Compatible finite record refinements generate a global probability measure under explicit realizability conditions; stochastic kernels provide a compositional calculus for carrying probabilistic information through unresolved future structure; and locally classical measurement contexts are assembled into a single positive state on a generally non-Boolean effect structure. This allows globally coherent probability to exist even when no context-independent deterministic assignment of outcomes exists. On a reflection-positive Hilbert-space branch, admissible future contexts are represented by positive effects and positive normalized states by density operators. The Born state-effect law then appears as the finite-dimensional representation of a probability structure that has already been earned through record qualification, positivity, exclusivity, refinement, and contextual consistency rather than introduced as a primitive postulate. The paper also separates two mechanisms that are often conflated: quadratic Born-type weighting arises from dagger self-comparison, whereas equal probabilities for symmetric alternatives arise from symmetry of the outcome structure. A further state-effect bridge analysis classifies residual coordinate freedom and identifies an exceptional rank-two adjugate transformation with Lorentzian signature, which is removed when positive self-dual identification is required. The central interpretation is that probability can function as a lawful form of global completion: it can carry future-relevant law through unresolved structure even when deterministic uniqueness is unavailable. The paper does not derive a mechanism selecting one actual outcome and does not claim that every physical sector satisfies the stated hypotheses. Instead, it provides an explicit dependency-controlled architecture connecting lawful completion, reflection positivity, event qualification, contextuality, stochastic continuation, Hilbert reconstruction, and the Born rule.
The same position need not imply the same future: observing an address may discard information about past events, active memory, and records. This work determines the data needed to reconstruct a temporal law and reconcile its spatial, coherent, and record readouts. Admissible extensions of a history define a graded generator of actualization; marked event rates specify its dynamics in physical time. We establish separate criteria for recovering the event count from an address and for the predictive sufficiency of that address. A distinguishing future test yields a sharp lower bound on the error of a purely spatial description. On a finite strongly connected state space, marked cycle probabilities classify strictly positive laws up to local changes of clock. For factorized first-event records, outcome fractions form a complete metric invariant after a common reparametrization of age has been factored out. On a finite irreducible state space, zero configurational entropy production characterizes the unitary continuation of the same temporal form. Its invariant complex sectors realize all finite-dimensional autonomous Hamiltonian dynamics, up to a global phase. Preparation, probabilistic readout, and retention of a sector require separate operational conditions. The zero-support condition for address jumps acquires the precise meaning of preserving the admissible state space, provided that the continuous evolution is also checked. For a phase-pure QND writer, an independently calibrated rate of record discrimination predicts transition suppression and a sufficient event-count budget on a finite interval. The joint pressure of transport and recording distinguishes realizations with identical separate marginals. Marked irreversibility may persist even when the configurational dynamics is reversible. These results define a testable sequence: reconstruct the event law, determine its sufficient readouts, and compare predictions across instruments. Equilibrium event algebras, protected phase constructions, and local clocks for infinite systems extend this sequence under explicitly stated assumptions. This preprint develops the temporal sector of the Theory of Structural Articulation (TSA).
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.
For stationary, stable linear systems, quantum form (symplectic form, complex structure, Hilbert inner product) is not a set of external postulates but geometric architecture already carried by the classical action and its flow; read through a local projection, for which decoherence is the explicit candidate, only one postulate remains: that states are sections. The Born measure is not derived here. This is a foundations paper. It adds no new dynamics, and most of its mathematics is known; its contribution is to arrange known results inside one ontology and to check what that ontology can and cannot carry. The ontology has a static space of consistent configurations, a single actualized history, a many-to-one projection Π and a selection operator A, and was proposed to account for quantum structure, the arrow of time and the Born rule. Taking each claim to the smallest system on which it can be computed, we find that the natural explicit candidate for Π, a projection onto locally accessible degrees of freedom, is standard decoherence theory; we do not show that Π must take this form. For linear systems with stable dynamics the quantum structure the ontology presupposes is reconstructed from the classical action: the symplectic form from the boundary term, the complex structure from the flow, and the Hilbert inner product from their combination. Stability of the linearized dynamics, rather than positivity of the action's Hessian, is the condition for quantum form to exist. Given the section postulate, the topological invariants of the ontology become the integrality conditions of geometric quantization; under the preservation assumption of Proposition 1, a dynamics that couples subsystems admits a single value of ħ; and if topology fixes dimensionless constants at all, it can do so only at a boundary, the measured values being images under renormalization-group flow (an illustrated pattern, not a derivation). The hidden sector splits into a gauge part and a temporally accessible part, which exposes a dilemma for structural accounts of irreversibility. A global selection cannot signal under three stated conditions, the central one being that its criterion reads only unconditioned reduced states in the causal past; we conjecture that selection is triggered by redundant environmental records. A hypothesis that the history begins at a regular horizon is tested against the Einstein equations in homogeneous models. Each result is labelled as known, synthesis or conjecture. The code-backed checks are listed in Tables 2–4 and reproduced by the attached scripts (run_all.py, with assertions on the quoted values; tested on Python 3.11/Linux and Python 3.14/Windows). Of the original framework's three predictions, one coincides with standard quantum mechanics in its safe form, one is withdrawn, and one lacks a mechanism and is bounded by binary-pulsar timing. How to check this paper: every result carries a status tag (known / synthesis / conjecture / withdrawn / scoped numerical evidence) collected in the ledger (Table 1). Code-backed claims are listed with their IDs in Tables 2–4. Unzip scripts_v15.zip and run python run_all.py (a few minutes; --rederive also redoes the symbolic Bianchi IX derivation); it asserts the numbers quoted in the text and exits non-zero on any mismatch. Corrections are welcome.
Abstract This paper introduces Existential Relativity (ER) as a context-indexed mathematical framework for physical existence and change. ER asserts that existence is not a context-free property of objects, fields, or excitations within an external container, but a locally defined in/out distinction generated by an internally specified basis-set, ruler, constraint system, complement, admissible transformation class, and boundary structure. Static existence is defined as a distinction that is a nontrivial partition of a context. Dynamic change is formalized as a lawful, interaction-conditioned transition from one context-indexed distinction to another. Transitions are generally not isolated, as they may be conditioned by static distinctions, boundaries, fields, apparatus settings, background structures, or simultaneous transitions of other contexts. Derivation, recovery, and reinterpretation constraints for the major models of physics are presented. Classical Hamiltonian mechanics and quantum field theory are recovered as special context structures. Born-rule probability, continuous Schrödinger evolution, Lorentzian signature, and gauge connection result from conditional derivations under stated auxiliary assumptions. General relativity is developed in greater depth through the Proposition of Metric-Stress-Energy Co-Admissibility, in which diffeomorphism covariance, shared variational closure, boundary consistency, covariant balance, and local second-order metric dynamics constrain the admissible coupling between a metric-ruler context and a matter context to the Einstein form within the declared regime. The paper also specifies admissibility conditions for contexts and transitions and proposes micro-to-macro emergence as the primary empirical application.