Observer as a Substrate-Independent Realization Condition: A Cross-Disciplinary Framework for Observable State Formation

1 Observer as a Substrate-Independent Realization Condition: A Cross-Disciplinary Framework for Observable State Formation Veronika Pudsey Independent Researcher [email protected] Abstract Across machine learning, physics, quantum theory, and the biological sciences, many systems exhibit the same fundamental transition: a probabilistic representation of possible states gives rise to a single, externally accessible outcome. Although these processes differ in substrate, scale, and mechanism, they share a minimal structural form involving a description of alternative possibilities, constraints that determine when one becomes admissible, and the resulting realized state. This article develops a substrate-independent framework that formalizes this shared structure. We define a realization condition as the minimal set of constraints under which a probabilistic state description yields a definite, externally accessible outcome, and argue that the role traditionally attributed to an “observer” in quantum theory can be understood in these functional terms. We examine four distinct domains — large language models, information-based physical theories, quantum measurement, and biological decision making — and show that each instantiates this transition in a structurally homologous way without implying mechanistic or ontological equivalence. The framework clarifies the functional role of observation in quantum theory, provides a common vocabulary for cross-domain comparison, and identifies structural expectations that may guide empirical work on uncertainty resolution and outcome formation. The framework is deliberately limited to describing the form of this transition rather than its underlying mechanisms, but it offers a basis for interdisciplinary analysis and a foundation for further theoretical development. 2 1 Introduction Across scientific fields, many systems are described in terms of multiple possible states together with the conditions under which one of these states becomes actual. Large language models compute probability distributions over candidate tokens and emit one realized token. Informationtheoretic formulations of physics treat thermodynamic or entropic constraints as limiting physically admissible configurations. In quantum mechanics, measurement interactions map amplitude assignments to definite, externally accessible outcomes. In biological and cognitive systems, decision processes convert probabilistic neural population codes into discrete behavioral or neural states. These examples differ in mechanism, substrate, and theoretical background, yet they share the same structural transition: a probabilistic state description is resolved into a definite, observable outcome under a set of constraints. Despite this structural similarity, each domain uses its own terminology — “measurement,” “observer,” “decision rule,” “decoding” — and these vocabularies rarely align. As a result, conceptually identical transitions are analyzed as unrelated phenomena, making it difficult to identify what is genuinely shared and what is substrate-specific. This article develops a substrate-independent formulation of this transition. We propose that the role traditionally associated with an observer — particularly in quantum mechanics — can be recast as a realization condition: the minimal set of constraints under which a probabilistic state description Σ yields an externally accessible outcome σ. This definition is functional rather than ontological. It does not presuppose a specific physical mechanism, nor does it commit to any interpretation of quantum theory, theory of information, or model of neural computation. Instead, it isolates the abstract mapping Σ → 𝑅 𝜎, and examines how this mapping is instantiated in otherwise unrelated systems. We apply this framework to four domains: • probabilistic state formation and decoding in large language models, • information-theoretic constraints in statistical and classical physics, • quantum measurement across major interpretations, and • biological and cognitive decision mechanisms. The aim is not to claim mechanistic identity or to propose a unified physical theory. Rather, the goal is to show that these domains exhibit the same minimal structure for producing externally accessible outcomes from probabilistic specifications, and that this structure can be analyzed independently of the substrate in which it is realized. By making this structure explicit, the framework provides a common vocabulary for comparing realization processes that are typically studied in isolation and helps distinguish where parallels between domains reflect genuine structural equivalence rather than superficial analogy. 3 2 Background and Motivation Across scientific disciplines, many systems are described at two complementary levels: (1) a probabilistic state description specifying multiple possible outcomes, and (2) a realized outcome that becomes externally accessible through some process. Quantum measurement, neural decision-making, and probabilistic decoding in large language models (LLMs) all exhibit this basic transition. Yet despite this shared structure, these domains use incompatible terminologies and divergent conceptual frameworks for describing what selects an outcome and what makes it observable. In quantum theory, decades of debate concern the role of the observer, the ontology of collapse, and whether measurement should be understood as a physical, informational, or epistemic process. In cognitive science and neuroscience, decision-making is formalized through drift– diffusion models, attractor dynamics, or Bayesian inference, each with its own vocabulary for representing uncertainty and resolving it. In machine learning, next-token sampling in autoregressive LLMs is a fully operational mapping from a probability distribution to a selected token, but typically analyzed in terms of optimization or performance rather than as an instance of a more general realization process. These literatures differ dramatically in substrate and mechanism, yet they share a recurring structural pattern: a probabilistic state space gives rise to a definite, externally accessible state under some set of constraints. What is currently missing is a substrate-independent vocabulary for describing this transition itself — separately from the physical, computational, or biological machinery on which it is implemented. A unifying framework is difficult to construct directly from quantum or biological systems, because the relevant processes are experimentally constrained, partially inaccessible, or conceptually contentious. By contrast, LLMs provide a uniquely tractable reference system: their probabilistic state Σ (token distribution), realization condition R (decoding rule), and realized outcome σ (emitted token) are all explicit, measurable, and experimentally controllable. This transparency makes LLMs an ideal starting point for formalizing the minimal structure required for probabilistic descriptions to yield definite outcomes. Why this is not a trivial reformulation It is tempting to view any such abstraction as a restatement of the obvious — systems must satisfy some condition in order to produce an outcome. But in several domains, especially quantum theory, the nature of this condition has remained conceptually opaque for nearly a century. By reformulating the “observer” not as an agent or a physical subsystem but as a functional role defined by a realization condition R, the framework separates the structure of outcome formation from ongoing ontological debates. This shift provides a common analytical language across domains that are otherwise theoretically isolated, and enables comparison between constraints that look different physically but play the same structural role. 4 Motivation of this work The motivation of this article is therefore twofold: (1) to develop a substrate-independent description of state realization as a mapping Σ →ᴿ σ, where R denotes the minimal constraints under which a probabilistic state becomes externally accessible; and (2) to use LLMs as a computationally transparent reference system for articulating this structure and examining how analogous patterns appear in quantum measurement, information-based physical theories, and biological decisionmaking. This approach does not assert mechanistic equivalence across domains. It isolates the minimal form of the transition from probabilistic specification to observable outcome and provides a structural vocabulary for comparing realization processes across substrates, identifying both shared invariants and substrate-dependent constraints. 3 Terminology and Definitions This section introduces the core terminology used throughout the paper. All definitions are formulated in a substrate-independent manner and apply uniformly to computational, physical, and biological systems. Formal notation and domain-specific mathematical structure are deferred to the Framework section and Appendix A. 3.1 Probabilistic State Description A probabilistic state description is a representation of a system in terms of mutually exclusive possible states, each associated with a probability value. It specifies the likelihood of potential outcomes but does not determine which state, if any, will be realized as an observable outcome. 3.2 Observable State An observable state is a system state that is accessible beyond the internal transition dynamics of the system that produced it. An observable state must be stable or robust enough to be detected, recorded, or used as input by another system or process. 3.3 External Accessibility External accessibility is the condition under which a state is available to systems other than the one whose internal dynamics generated it. A state is externally accessible when it can influence, constrain, or modify another system or process. In quantum theory, external accessibility typically corresponds to the formation of environmentally robust pointer states through decoherence, where information about the system becomes redundantly encoded in the environment. 3.4 State Realization State realization is the transition in which a probabilistic state description yields a specific observable state. Realization marks the resolution of uncertainty, enabling one outcome to become externally accessible. 5 3.5 Realization Condition A realization condition is a set of constraints that is sufficient to transform a probabilistic state description into an observable state. Realization conditions may be computational, physical, or biological and do not require the presence of an agent, apparatus, or conscious observer. 3.6 Observer (substrate-independent) In this framework, an observer is defined functionally rather than as an entity. An observer is any configuration of interactions or constraints that enables a probabilistic state description to become an observable state. This definition does not assume that the observer is human, conscious, macroscopic, or localized. 3.7 Substrate-Independence A concept is substrate-independent when it can be applied across systems with different physical or computational realizations without implying mechanistic or ontological equivalence. Both state realization and realization conditions are treated in substrate-independent terms in this paper. 4 Probabilistic State Realization in Large Language Models Large language models (LLMs) provide a computational system in which every component of the probabilistic-to-definite transition can be explicitly specified, inspected, and experimentally varied. For this reason, LLMs constitute the clearest operational instance of the abstract structure introduced in Section 3. In LLMs, the probabilistic state description (Σ), the realization condition (R), and the realized observable state (σ) are mathematically defined and observable at each step of the autoregressive generation process. This section formalizes this correspondence and surveys empirical findings relevant to realization processes. (For mathematical details, see Appendix A.2.) 4.1 Probabilistic state description in transformer-based LLMs (Σ_LLM) Let 𝑥<𝑡 =(𝑥1,𝑥2,…,𝑥𝑡−1) denote the preceding token sequence. A transformer-based LLM computes logits 𝑧𝑡∈ℝ∣𝑉∣, which define a conditional probability distribution over the next token: ΣLLM(𝑡)≡𝑃(𝑥𝑡∣𝑥<𝑡)=softmax(𝑧𝑡). The distribution 𝑃(𝑥𝑡∣𝑥<𝑡) enumerates all mutually exclusive candidate outcomes, assigns each a probability but does not determine which outcome is realized. This satisfies the definition of a probabilistic state description from Section 3.1. Structural properties of these distributions — including entropy, calibration, and internal feature directions — are empirically measurable (Chang et al., 2024; Cao, 2023; Nanda et al., 2021). 6 4.2 Realization conditions implemented by decoding algorithms (R_LLM) A decoding rule specifies the constraints under which a single token is selected from the probabilistic distribution. Formally, a realization condition is a function 𝑅LLM:ΣLLM(𝑡) ⟶𝜎LLM(𝑡). Common decoding rules include: • argmax decoding 𝜎𝑡=arg⁡max⁡𝑖𝑃(𝑥𝑖∣𝑥<𝑡) • sampling-based decoding (categorical sampling) • top-k sampling (restricting support to the k highest-probability tokens) • nucleus sampling (restricting support to a cumulative probability mass p; Holtzman et al., 2020) • beam search, which deterministically expands high-probability continuations (Welleck et al., 2020) These procedures act as identifiable realization conditions: when held constant, they generate reproducible outcome statistics from the same probabilistic state description. 4.3 Observable state formation and external accessibility (σ_LLM) Once a token 𝑥𝑡has been selected, it becomes externally accessible through one of several operational channels: streaming to a user interface, API response delivery, or integration into downstream computation (Zhou, 2023). An emitted token meets the definition of an observable state (Section 3.2), as its value is available to systems outside the model’s internal dynamics and can influence subsequent processes. This satisfies the definition of external accessibility (Section 3.3). 4.4 LLMs as a tractable model system for state realization LLMs instantiate the abstract transition ΣLLM → 𝑅LLM 𝜎LLM in a fully specified and experimentally controllable form. Three properties make LLMs uniquely suited as a reference model for studying realization: 1. Full transparency of Σ. Next-token distributions are directly observable and can be compared across contexts (Chang et al., 2024; Mielke et al., 2021). 2. Full controllability of R. Realization conditions can be modified systematically (Holtzman et al., 2020), enabling experimental manipulation of outcome statistics. 3. Immediate external accessibility of σ. Realized tokens are encoded as stable, externally available states with well-defined operational meaning. 7 Because no biological or physical system offers simultaneous transparency of probabilistic state, controllability of the realization condition, and direct accessibility of realized states, LLMs function as a methodological baseline for analyzing realization processes across substrates. (For a formal comparison with quantum and physical systems, see Section 7.) 4.5 Empirical Signatures of Realization Processes in LLMs Empirical studies of transformer-based LLMs provide measurable evidence for each component of the probabilistic-to-definite transition described in this section. Although the internal computations of physical and biological systems may be partially inaccessible or distributed, LLMs offer a level of transparency that allows realization processes to be directly characterized, systematically varied, and replicated across experimental conditions. Published work supports three aspects of this claim: the structure of probabilistic state descriptions, the dependence of realized outcomes on decoding constraints, and the external accessibility of realized states. 4.5.1 Structure of probabilistic state descriptions Next-token distributions exhibit measurable statistical structure: entropy variation (Chang et al., 2024), calibration effects (Cao, 2023), logit-projection feature directions (Nanda et al., 2021; Olsson et al., 2022), and syntactic/semantic uncertainty patterns (Hu et al., 2023). 4.5.2 Dependence of realized outcomes on realization conditions Decoding constraints systematically shape realized outcomes: nucleus sampling restricts the realizable region (Holtzman et al., 2020); temperature scaling alters variance (Wang et al., 2020); beam search induces mode collapse (Welleck et al., 2020); constrained decoding restricts permissible continuations (Lu et al., 2021). 4.5.3 Stability and external accessibility of realized states Generated tokens are integrated into downstream applications (Moore et al., 2025), influence usermodel interaction dynamics (Moore et al., 2025), and participate in automated tool-use pipelines (Wu et al., 2023). 4.5.4 Summary Empirical work demonstrates that next-token distributions in LLMs have measurable internal structure, decoding procedures act as identifiable realization conditions and realized tokens are externally accessible system states. LLMs therefore provide the most analytically tractable system for studying realization processes in a substrate-independent framework. 5 Information in Physics and Computation: Toward a Unified State-Realization Framework This section examines how informational formulations of physical theory provide structural parallels to the realization processes analyzed in LLMs (Section 4). The goal is not to claim physical equivalence between computational and physical systems, but to identify shared abstract structure 8 in the mapping from informational possibilities to externally accessible outcomes. Formal details and mathematical definitions relevant to this section are summarized in Appendix A.4. 5.1 Historical Foundations of Physical Information Classical information theory was originally developed to quantify uncertainty in communication channels (Shannon, 1948). Although formulated for engineering purposes, entropy soon proved to have direct physical significance. Landauer (1961) established that erasing one bit of information incurs a minimum energetic cost of 𝑘𝐵𝑇ln⁡2, demonstrating that information processing has necessary thermodynamic implications. Bekenstein (1973) showed that black-hole entropy scales with horizon area, indicating that physical systems possess finite informational capacity. Wheeler (1990) later suggested that physical structure may arise from informational constraints; although conceptual rather than empirical, this idea reflects a broader shift toward informational formulations of physical theory. Across these developments, information is treated not merely as an epistemic quantity but as one that constrains physically realizable states. 5.2 Information, Constraints, and Physical State Formation In classical statistical mechanics, macroscopic observables emerge from ensembles of microscopic states subject to fixed constraints such as energy, particle number, or volume (Landau & Lifshitz, 1980). Jaynes (1957) reformulated this framework in explicitly informational terms: given a set of constraints, the macroscopic state corresponds to the distribution that maximizes entropy. Conceptually: microstate ensemble ⟶ constraints ⟶ macroscopic observable. Although the mechanisms differ from those in computational systems, the structural role of constraints in selecting observable states parallels the realization-condition framework introduced in Section 3. Contemporary approaches extend this informational perspective. Lloyd (2006) interprets the universe as performing elementary informational operations. Verlinde (2011) models gravity as an entropic force arising from underlying degrees of freedom. Davies (2019) proposes that laws of physics reflect informational regularities. These views differ in scope and empirical support, but all treat information and constraints as determinants of physically realizable states. A closely related structural limitation appears in the Bekenstein–Hawking entropy bound: the maximum informational content of a region scales with its boundary area (Bekenstein, 1973; Hawking, 1975). The holographic principle generalizes this observation by proposing that information within a spatial region is encoded on its boundary surface (’t Hooft, 1993; Susskind, 1995). In both cases, boundary conditions restrict the set of realizable physical configurations. 9 5.3 Substrate-Independent Interpretation Although physical and computational systems differ in ontology, both can be described using a space of informational possibilities (analogous to Σ), constraints determining which possibilities can be realized (analogous to R), and externally accessible outcomes (analogous to σ). In physics, Σ corresponds to microstate ensembles or quantum state spaces; R corresponds to macroscopic constraints, conservation laws, decoherence-selected bases, or boundary conditions; σ corresponds to macroscopic observables or stable measurement outcomes. This structural mapping does not assert that physical and computational systems share mechanisms or physical identity. It claims only that the form of the probabilistic-to-definite transition can be represented in a unified substrate-independent framework. This view aligns with Landauer’s assertion that information is physical (1961) and Vedral’s reciprocal claim that physics may be informational in nature (2012). 5.4 Summary Information-theoretic approaches to physics treat informational degrees of freedom as constraints on the space of realizable physical states. This provides a conceptual bridge between the computational realization processes analyzed in Section 4 and the quantum-measurement transition examined in Section 6. These structural parallels support a substrate-independent interpretation of realization that applies to physical, computational, and — later — biological systems. 6 Quantum Measurement as a Realization Process Quantum measurement provides a concrete physical instance of the transition from a probabilistic state description to an externally accessible outcome. Although interpretations differ on the ontology of this transition, its operational structure is well defined. This section characterizes quantum measurement in the substrate-independent terms introduced in Section 3, without appealing to specific interpretational commitments. A compact formal summary of quantum states, projective measurements, and POVMs is provided in Appendix A.3. 6.1 Quantum probabilistic state description (Σ_QM) Quantum systems are represented by density operators 𝜌acting on a Hilbert space ℋ. A measurement is specified by a set of positive operator-valued measure (POVM) elements {𝐸𝑖}, each corresponding to a possible measurement outcome (Nielsen & Chuang, 2000). Outcome probabilities are given by the Born rule: 𝑃(𝑖)=Tr(𝜌𝐸𝑖). In the terminology of this paper, the pair (𝜌,{𝐸𝑖}) constitutes a probabilistic state description: the possible outcomes are enumerated, their probabilities are well defined, but no specific outcome is determined. This is the quantum mechanical instance of Σ. 16 Under this reformulation R may be localized (LLM decoding, neural threshold), or distributed (environment-induced decoherence, population coding), may or may not involve conscious agents, and may be implemented by physical, computational, or informational processes. This definition is consistent with all major quantum interpretations (Copenhagen, decoherence, Everett, RQM, QBism) without committing to any of them. The observer becomes a structural role, not a physical object. 8.5 Entropy Requirement and System Boundaries The requirement 𝐻(Σ)>0 for non-trivial observation has direct implications for how we identify observer systems. Consider the commonly used example of a thermostat. An isolated thermostat controller — understood as a deterministic state machine transitioning between {ON,OFF} based on fixed threshold rules — has 𝐻(Σ)≈0 when analyzed as an autonomous mechanism. No probabilistic state description is represented within the controller itself; no uncertainty is resolved; and therefore, no observation occurs in the sense characterized by the mapping Σ →ᴿ σ. Observation emerges only when the thermostat is considered as part of a coupled system that includes the local thermal environment. The relevant Σ is then a joint probability distribution over: • the fluctuating air temperature near the sensor, • the sensor’s physical configuration (e.g., bimetallic curvature), • the actuator state of the switching mechanism. Because this joint system exhibits 𝐻(Σ)> 0 due to environmental and thermal variability, the realization condition 𝑅 — the thermostatic coupling linking sensor readings to actuator transitions — selects a specific realized state 𝜎 from among these possibilities. This illustrates a general principle: observation is not a property of an isolated mechanism, but a functional role instantiated within a coupled dynamical system that contains genuine uncertainty. Although the entropy condition 𝐻(Σ)> 0 depends on how the system boundary is drawn, this dependence is not arbitrary. In the Σ–R–σ formulation, the relevant boundary is determined by where the realization process actually occurs: the boundary encloses exactly those degrees of freedom that contribute to the probabilistic state description Σ and to its reduction under R. Thus, the framework does not shift the burden to subjective boundary choices; rather, it identifies system boundaries through the structure of the realization mapping itself. Observation is located wherever a probabilistic state is reduced to an externally accessible outcome, and the associated boundary is the minimal region in which this reduction is functionally instantiated. In practice, identifying the relevant system boundary is partly empirical. Although the Σ–R–σ framework specifies the structural requirement for observation (a non-zero-entropy probabilistic description reduced under R), the concrete boundary that supports this structure depends on domain-specific dynamical considerations. Thermodynamic systems use equilibration timescales to distinguish system from reservoir; neural systems rely on functional connectivity patterns to 17 delimit assemblies; quantum systems depend on decoherence timescales to separate apparatus from environment. The framework therefore does not eliminate empirical judgment in boundary selection, but it clarifies the structural role that any valid boundary must instantiate: it must enclose exactly those degrees of freedom whose interactions generate and resolve the uncertainty encoded in Σ. Frameworks that attempt to localize “the observer” within a fixed spatial boundary 𝐵 face a dilemma. If 𝐵 excludes environmental degrees of freedom, then 𝐻(Σ)≈0 and observation collapses into trivial state propagation. If 𝐵 includes the relevant environmental uncertainty, the observer–observed distinction becomes spatially diffuse or ambiguous. The substrate-independent formulation Σ⁡→ᴿ⁡σ avoids this dilemma by characterizing observation through relational structure rather than spatial partitioning. This makes it naturally applicable to systems in which boundaries are distributed, emergent, or context-dependent — including neural networks, quantum measurement chains, and engineered control systems. 8.6 Implications and Limits of the Framework This framework does not specify the physics of collapse or branching, does not assert equivalence between neural and computational mechanisms, does not reduce biological or quantum processes to computation, and does not claim an ontology of information. It identifies only the minimal structure required for any system to produce an externally accessible outcome: a probabilistic state description, a set of realization constraints, and a realized state. Because the framework characterizes observation through the relational structure Σ⁡→ ᴿ⁡σ, rather than through spatial boundaries or substrate-specific mechanisms, it enables systematic comparison across domains that would otherwise remain theoretically isolated. Section 9 discusses broader theoretical implications and potential directions for empirical and conceptual work. 9 Implications and Limitations The substrate-independent formulation introduced in Section 8 characterizes state realization across computational, quantum, physical, and biological systems using a minimal structural mapping Σ →ᴿ σ. This abstraction separates the form of the probabilistic-to-definite transition from the mechanisms that implement it. Below we outline the main implications of this view and clarify its limits. 18 9.1 Implications 9.1.1 Cross-Domain Formal Analysis of Outcome Formation Because the framework characterizes outcome formation in terms of probabilistic state descriptions (Σ), realization conditions (R), and externally accessible states (σ), it offers a shared vocabulary for comparing systems that are otherwise analyzed in isolation. This perspective supports structural comparison across LLM decoding, quantum measurement, neural decision making, and information-constrained physical processes without assuming mechanistic or ontological similarity. 9.1.2 Clarifying the Observer in Quantum Theory Reformulating the observer as a realization condition R — the minimal set of constraints under which a quantum probabilistic specification yields an externally accessible outcome — sidesteps commitments regarding consciousness, collapse, or branching. It describes quantum measurement using the same structural components that characterize computational and biological systems while leaving quantum dynamics and their interpretation fully domainspecific. 9.1.3 Applications to Artificial Systems and Model Analysis In artificial sequence models, realization conditions are implemented explicitly as decoding rules. Treating decoding as a realization condition highlights how systematic modifications of R (e.g., temperature, top-k constraints, beam search) reshape the distribution of realized outcomes σ. This provides a structural basis for analyzing sampling behaviour, uncertainty calibration, and decoding strategies, and suggests empirical tests based on how different classes of R modulate σ across contexts. 9.1.4 Linking Information-Based Physics and Computational Systems Several information-theoretic approaches in physics already describe macroscopic states as constraint-selected realizations from a space of informational possibilities. The present framework makes this structural parallel explicit: both physical and computational systems can be analyzed in terms of probabilistic state spaces and constraint-driven selection. This does not imply that physical processes implement computation; rather, it situates informational constraints within a broader class of realization structures. 9.1.5 Sequential and Dynamically Evolving Realization Conditions In many systems — autoregressive models, recurrent neural circuits, and iterative physical or biological processes — outcomes occur in sequences. In such cases, σₜ influences (and sometimes modifies) Σₜ₊₁ or Rₜ₊₁. The framework therefore accommodates systems whose realization conditions evolve over time, enabling analysis of sequential dependencies without altering the underlying structural mapping. 19 9.1.6 Distinguishing Structural from Superficial Similarities Because the framework isolates the minimal elements required for a probabilistic-to-definite transition, it helps distinguish cases where different systems are structurally analogous from cases where similarities arise only from surface-level terminology or intuitions. This discriminative role is particularly relevant for comparing quantum measurement with computational and biological processes, where analogies are often drawn informally but lack a precise structural basis. 9.1.7 Clarifying What the Framework Does Not Imply The framework does not assert that different systems share microphysical mechanisms, that quantum states have a particular ontology, that biological processes reduce to computation, or that a single unifying physical principle governs all realization processes. It isolates only the abstract structure of outcome formation, leaving mechanistic accounts to domain-specific theories. 9.2 Limitations 9.2.1 No Mechanistic Unification Structural similarity does not imply mechanistic identity. Σ →ᴿ σ abstracts away from internal dynamics and cannot derive quantum, biological, or computational processes from one another. 9.2.2 Agnosticism About Quantum Ontology The framework is compatible with all major interpretations but endorses none. It clarifies the functional role of measurement without addressing whether outcomes reflect collapse, branching, epistemic update, or decoherence-only accounts. 9.2.3 No Claims About Consciousness or Agency Although some realization conditions involve human observers, the framework does not treat consciousness as necessary or sufficient for state realization. It distinguishes functional roles from experiential or phenomenological ones. 9.2.4 No Ontological Commitment to Information The framework is compatible with (but does not require) information-based approaches to physics. It does not imply that physical reality is fundamentally informational or computational. 9.2.5 Limited Scope The framework addresses outcome formation only. It does not specify the origin or evolution of probabilistic state descriptions Σ, how realization conditions R are physically implemented, the internal dynamics of systems that satisfy R, or the physical laws governing their behavior. It isolates the structural form, not the underlying mechanism. 9.2.6 Abstraction as Strength and Limitation By abstracting away from substrate-specific details, the framework can unify formally similar systems — but cannot replace domain-specific theories. It identifies the boundaries of structural 20 analogy and makes clear where additional physical, biological, or computational detail is indispensable. 9.3 Summary The substrate-independent framework developed in this paper provides a formal structure for describing outcome formation across domains characterized by probabilistic state spaces and constraint-driven realization. Its value lies in clarifying functional roles, supporting crossdomain comparisons, and providing a neutral vocabulary for analyzing realization processes. Its limitations ensure that it remains a conceptual tool rather than a claim of mechanistic or ontological unification. 10 Conclusion Across computational models, information-theoretic physical frameworks, quantum measurement, and biological decision processes, observable outcomes arise through a transition from a probabilistic description of possible states to a definite, externally accessible one. Although the underlying mechanisms differ — transformer decoders, thermodynamic or entropic constraints, measurement interactions, or neural thresholds — the structural form of this transition is the same. This article formalized that shared structure through the substrate-independent mapping Σ → 𝑅 𝜎, where Σ specifies mutually exclusive possibilities, R denotes the minimal constraints under which one possibility becomes admissible, and σ is the resulting state available to other systems. Within this framework, the observer is not treated as a special entity but as the functional structure that implements the realization condition — whether carried out by an algorithmic decoding rule, a quantum measurement interaction, an environmental coupling, or a biological boundary mechanism. By reformulating the observer in functional terms, the framework situates quantum measurement within the same abstract class as computational sampling, neural decision making, and constraintdriven physical state formation. It provides a neutral vocabulary for comparing outcome-formation processes across domains that are typically analyzed in isolation, and clarifies when similarities between systems indicate genuine structural equivalence rather than superficial analogy. At the same time, the framework is deliberately limited. It does not address the physical mechanisms responsible for quantum state change, the origin or evolution of probabilistic descriptions, the biophysical details of neural computation, or the internal dynamics of artificial models. It captures only the minimal structure required for a probabilistic specification to yield an externally accessible outcome. By isolating this structural commonality, the framework may support interdisciplinary analysis of decision, measurement, and realization processes, and offer a foundation for further theoretical work. Potential directions include developing more formal criteria for realization conditions, 21 identifying empirical signatures that test cross-domain predictions, and refining domain-specific applications to determine where substrate-independent structure ends and where substratedependent mechanism begins. Appendix A — Formal Background and Mathematical Details This appendix provides the formal and mathematical details referenced in the main text. It includes: • formal notation for probabilistic state descriptions Σ, • formal notation and examples of realization conditions R, • quantum measurement operators (POVMs, density matrices), • neural decision models (drift–diffusion, population coding), • information-theoretic quantities used for uncertainty analysis. A.1 Probabilistic State Descriptions A probabilistic state description Σ represents a set of mutually exclusive candidate states together with their associated likelihoods. Discrete case: Σ={(𝑠𝑖,𝑝𝑖)},𝑝𝑖≥0,∑𝑝𝑖 𝑖=1. Continuous case: Σ=(𝑠,𝑝(𝑠)),∫𝑝(𝑠) 𝑑𝑠 =1. Examples include: • token-probability distributions in LLM decoders, • likelihood functions in neural population codes, • probability amplitudes in quantum systems (via Born’s rule after squaring), • informational microstates in physical systems. Σ is purely structural: it imposes no assumption about whether uncertainty is epistemic, physical, computational, or biological. A.2 Realization Conditions A realization condition 𝑅 is defined as the minimal set of constraints under which a probabilistic state description Σ produces an externally accessible outcome 𝜎. Formal structure: 22 𝑆:𝛴⁡→ᴿ⁡𝜎 where: • Σ is a probabilistic state description, • R is the minimally sufficient constraint structure, • σ is the resulting observable outcome, • S is the system undergoing state realization. Properties • Minimality: R contains only constraints necessary for selection. • Substrate independence: R may be computational (LLM), physical (quantum), neural (decision boundary), or thermodynamic. • External accessibility: σ must be observable by another system. A.2.1 Computational example (LLM decoding) Given a probability distribution over tokens {𝑝𝑖}: Greedy decoding: 𝜎 =argmax𝑝𝑖 𝑖. Sampling: 𝜎 ∼𝑝𝑖. Top-k / nucleus sampling (Holtzman et al., 2020): R restricts the support of Σ before sampling. These decoding rules instantiate R. A.3 Quantum Measurement Formalism Quantum measurements are represented by POVMs: 𝐸𝑘≥0,∑𝐸𝑘 𝑘=𝐼. For a system in state 𝜌: Outcome probability: 𝑝𝑘=Tr(𝜌𝐸𝑘), Post-measurement state (Kraus representation): 23 𝜌′=𝑀𝑘𝜌𝑀𝑘 † Tr(𝑀𝑘𝜌𝑀𝑘 †),𝐸𝑘=𝑀𝑘 †𝑀𝑘. Measurement interactions instantiate the realization condition in quantum systems: they map a probabilistic description (amplitudes → probabilities) to a definite, externally accessible result. A.4 Decision Models in Biological Systems A.4.1 Drift–Diffusion Model (DDM) Neural decision processes can be described as noisy accumulation of evidence: 𝑑𝑥𝑡=𝑣 𝑑𝑡+𝜎 𝑑𝑊𝑡, where 𝑣 is drift (evidence), 𝜎diffusion (noise), and 𝑊𝑡 a Wiener process. The decision is realized when 𝑥𝑡reaches a boundary (threshold): 𝑥𝑡=±𝐵 ⇒ 𝜎 (choice). The decision boundary functions as the realization condition. A.4.2 Neural Population Coding Population responses encode likelihood functions of stimulus variables. For neurons 𝑖with tuning curves 𝑓𝑖(𝑠): 𝑝(𝑠 ∣𝑟)∝ ∏exp 𝑖 ⁣(−(𝑟𝑖−𝑓𝑖(𝑠))2 2𝜎𝑖2), which forms the probabilistic state description over sensory variable 𝑠. A.5 Information-Theoretic Measures A.5.1 Shannon entropy 𝐻 =−∑𝑝𝑖log⁡𝑝𝑖 𝑖. A.5.2 Von Neumann entropy 𝑆(𝜌)=−Tr(𝜌log⁡𝜌). These are used to quantify uncertainty in classical, computational, quantum, and biological systems. 24 References Arieli, A., Sterkin, A., Grinvald, A., & Aertsen, A. (1996). Dynamics of ongoing activity: Explanation of the large variability in evoked cortical responses. Science, 273(5283), 1868–1871. Bekenstein, J. D. (1973). Black holes and entropy. Physical Review D, 7(8), 2333–2346. Bohr, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 48(8), 696–702. Cao, S. (2023). On the Entropy Calibration of Language Models. OpenReview preprint. Chang, H.-S., Peng, N., Bansal, M., Ramakrishna, A., & Chung, T. (2024). REAL Sampling: Boosting Factuality and Diversity of Open-Ended Generation via Asymptotic Entropy. arXiv preprint arXiv:2406.07735. Churchland, A. K., Kiani, R., Chaudhuri, R., Wang, X.-J., Pouget, A., & Shadlen, M. N. (2011). Variance as a signature of neural computations during decision making. Neuron, 69(4), 818–831. Davies, P. C. W. (2019). The demon in the machine: How hidden webs of information are solving the mystery of life. Penguin. Elhage, N., Nanda, N., Olsson, C., et al. (2021). A mathematical framework for transformer circuits. Anthropic technical report / arXiv preprint. Everett, H. (1957). “Relative state” formulation of quantum mechanics. Reviews of Modern Physics, 29(3), 454–462. Fiser, J., Berkes, P., Orbán, G., & Lengyel, M. (2010). Statistically optimal perception and learning: from behavior to neural representations. Trends in Cognitive Sciences, 14(3), 119–130. Friston, K. (2005). A theory of cortical responses. Philosophical Transactions of the Royal Society B: Biological Sciences, 360(1456), 815–836. Friston, K. (2010). The free-energy principle: a unified brain theory? Nature Reviews Neuroscience, 11(2), 127–138. Fuchs, C. A., & Schack, R. (2013). Quantum-Bayesian coherence. Reviews of Modern Physics, 85(4), 1693–1715. Gold, J. I., & Shadlen, M. N. (2007). The neural basis of decision making. Annual Review of Neuroscience, 30, 535–574. Hawking, S. W. (1975). Particle creation by black holes. Communications in Mathematical Physics, 43(3), 199–220. Holtzman, A., Buys, J., Du, L., Forbes, M., & Choi, Y. (2020). The curious case of neural text degeneration. In Proceedings of the International Conference on Learning Representations (ICLR 2020). 25 Hu, J., Zhang, B., Sun, Q., Hu, Z., & Dong, Y. (2023). A survey on uncertainty in natural language processing. arXiv preprint arXiv:2306.04459. Jaynes, E. T. (1957). Information theory and statistical mechanics. Physical Review, 106(4), 620–630; 108(2), 171–190. Knill, D. C., & Pouget, A. (2004). The Bayesian brain: The role of uncertainty in neural coding and computation. Trends in Neurosciences, 27(12), 712–719. Landau, L. D., & Lifshitz, E. M. (1980). Statistical physics. Part 1 (3rd ed.). Pergamon Press. Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5(3), 183–191. Lloyd, S. (2006). Programming the universe: A quantum computer scientist takes on the cosmos. Alfred A. Knopf. Lu, X., Yu, M., Zhou, J., Ren, X., Zhang, M., & Dong, Y. (2021). Neurologic decoding: (Un) constrained text generation with neurosymbolic methods. Advances in Neural Information Processing Systems, 34, 8964–8977. Ma, W. J., Beck, J. M., Latham, P. E., & Pouget, A. (2006). Bayesian inference with probabilistic population codes. Nature Neuroscience, 9(11), 1432–1438. McFadden, D. (2001). Economic choices. American Economic Review, 91(3), 351–378. Moore, K., Roberts, J., Watson, D., & Wisniewski, P. (2025). Human-Alignment and Calibration of Inference-Time Uncertainty in Large Language Models. arXiv preprint arXiv:2508.08204. Nielsen, M. A., & Chuang, I. L. (2000). Quantum computation and quantum information. Cambridge University Press. Olsson, C., Elhage, N., Nanda, N., et al. (2022). In-context learning and induction heads. Anthropic technical report / arXiv preprint. Pouget, A., Beck, J. M., Ma, W. J., & Latham, P. E. (2013). Probabilistic brains: Knowns and unknowns. Nature Neuroscience, 16(9), 1170–1178. Raj, A., & van Oudenaarden, A. (2008). Nature, nurture, or chance: Stochastic gene expression and its consequences. Cell, 135(2), 216–226. Ratcliff, R., & McKoon, G. (2008). The diffusion decision model: Theory and data for two-choice decision tasks. Neural Computation, 20(4), 873–922. Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics, 35(8), 1637–1678. Rovelli, C. (2021). Helgoland: Making sense of the quantum revolution. Penguin. Schlosshauer, M. (2007). Decoherence and the quantum-to-classical transition. Springer.