Abstract This paper records a structural result: under the CODES / SO2 axioms, probability cannot be ontological. If evolution from the full state is deterministic—i.e., a function—then genuine stochastic branching from identical states is logically excluded. Probability survives only as a measurement, compression, or ignorance language over a deterministic, PAS_h–ordered substrate. This elimination is not an additional hypothesis or interpretive stance; it is a direct corollary of deterministic causation plus the choice of full state space.
Abstract This paper records a structural result: under the CODES / SO2 axioms, probability cannot be ontological. If evolution from the full state is deterministic—i.e., a function—then genuine stochastic branching from identical states is logically excluded. Probability survives only as a measurement, compression, or ignorance language over a deterministic, PAS_h–ordered substrate. This elimination is not an additional hypothesis or interpretive stance; it is a direct corollary of deterministic causation plus the choice of full state space.
This paper argues that probabilistic structure should not be treated as ontologically primitive. Instead, probability is defined relative to conditions of recordability: it organizes spaces of possible records rather than properties of events as such. The analysis distinguishes between events, records, and probabilistic structures, and shows that probability acquires meaning only when stable, distinguishable, and reproducible records are available. In this view, Kolmogorovian probability theory provides a formally consistent framework, but does not specify how probabilistic domains arise from empirical observation. As a result, probabilistic formalism underdetermines ontology. Different ontological models can generate identical probabilistic structures, which implies that probability cannot serve as a direct guide to the nature of reality. The paper critically examines Ontic Structural Realism (OSR), arguing that it risks conflating representational structure with ontological structure. It concludes that any ontological interpretation of probabilistic or correlational structures requires independent justification beyond formalism.
A logical physical ontology is code theory, wherein reality is neither deterministic nor random. In light of Conway and Kochen’s free will theorem [The free will theorem, Found. Phys. 36(10) (2006) 1441–1473] and strong free will theorem [The strong free will theorem, Not. Am. Math. Soc. 56(2) (2009) 226–232], we discuss the plausibility of a third axiomatic option — geometric language; the code-theoretic axiom. We suggest that freewill choices at the syntactically-free steps of a geometric language of spacetime form the code-theoretic substrate upon which particle and gravitational physics emerge.
The shift from classical deterministic prediction to quantum distributions does not by itself decide whether the real is intrinsically probabilistic. The argument begins with both the force and the limit of Laplace’s ideal: deterministic dynamics can coexist with incomplete knowledge of the initial conditions, and classical physics already employs probability. The uncertainty relation then requires a distinction between preparation uncertainty, measurement error, and disturbance, preventing a single formula from serving as an ontological verdict. Bell inequalities tighten the constraints by excluding a specific family of local explanations without ruling out deterministic nonlocal dynamics. The objectivity of probability therefore arises from the explanations that the distributions rule out, not from turning probability into substance. An unexpected detector pulse then allows us to follow the transition from a physical record to knowledge: the material configuration may persist while the act of discrimination is ephemeral; only recognition under a protocol requires a distinction between trace, singular inscription, passive mark, and symbol. Finally, the laser shows why technical fruitfulness increases a theory’s epistemic weight, even though rival ontologies may share the same formalism. The remaining interpretative openness is not arbitrary: it is bounded by results that any future account must accommodate.
Abstract This paper develops a metaphysical interpretation of quantum probability under the title Distributed Presence (DP). The central claim is that quantum probabilities should not be understood as measures of ignorance, nor merely as formal devices for predicting measurement outcomes, but as expressions of an objective mode of being: a system’s structured distribution of presence across mutually available channels of realization. On this view, a quantum system prior to measurement is neither fully actual in one determinate outcome nor reducible to a set of hidden definite properties. Rather, it exists in a non-binary mode, articulated by normalized presence fractions associated with the possible outcomes defined by a given interaction context. The Born rule is accordingly not replaced, but reinterpreted: the standard probability assignment is read as the operational expression of an underlying ontological distribution. The paper argues that this framework provides a unified reading of several familiar quantum features. Superposition is understood as a real distribution of presence rather than as epistemic indeterminacy; measurement is interpreted as single-channel actualization rather than as the physical destruction of alternatives; wave-particle duality is recast as the relation between distributed structure and localized realization; and quantum randomness is treated as intrinsic yet structurally constrained. The proposal remains fully compatible with the standard Hilbert-space formalism and introduces no hidden variables, additional collapse dynamics, or many-world branching. Its aim is interpretive rather than revisionary. Beyond its relevance to the foundations of quantum theory, DP is advanced as a contribution to the ontology of probability more broadly. It seeks to show how probability may be objective, physically meaningful, and ontologically basic without collapsing into determinism on the one hand or epistemicism on the other. In that sense, the paper offers a realist, single-world, structurally articulated account of quantum chance.
Supersession Note — May 2026 This CODES-era work is an exploratory predecessor and is no longer the canonical statement of the author’s program. It has been superseded by the identity-persistence stack: https://zenodo.org/records/20127331. Claims in this record concerning replacement of probability, unrestricted universality, ontology, physics, intelligence, biology, governance, or reality should be read as developmental framing, not as the current formal claim. The current claim is restricted to identity persistence under transformation within explicit admissibility constraints. Abstract: This work demonstrates that the Everett (Many-Worlds) interpretation of quantum mechanics, while claiming full unitarity, introduces irreversibility without cause. Decoherence is governed by the same unitary operator U(t) and its inverse U†(t); treating branch separation as permanent therefore imposes an unmotivated non-unitary constraint. Logical audit shows that the transition from approximate to exact orthogonality re-inserts collapse by assumption. The paper concludes that a genuinely deterministic formulation must permit lawful recoherence, consistent with Structured Resonance Dynamics.
Various physical examples are displayed in which the probability distribution can be traced back to its causal origin. It is argued that probability is never irreducible, but is, in principle, always derivable from a deterministic process which determines its numerical value. It is suggested that deterministic and probabilistic theories are interlocked, each presenting a different aspect of reality, yet that no description of the laws of nature in terms of either of these concepts will ever be ultimate.