Paper XXIX - Operational Classification of Dark Matter Inference Channels

DOI: 10.5281/zenodo.18009474 Operational Classification of Dark Matter Inference Channels Paper XXIX of the Ordered-Dynamics Reconstruction Program Paul Cooneya aIndependent Researcher, Innisfil, Ontario, Canada E-mail: paul.co[email protected]to.ca Contents 1 Introduction 1 2 Operational Layers in Mass Inference 2 2.1 Propagation geometry 2 2.2 Dynamical evolution 2 2.3 Clock reconstruction 2 3 Dynamical Dark Matter Probes 2 4 Lensing-Based Dark Matter Probes 3 5 Cross-Channel Tensions and Structure 3 6 Relation to Modified Gravity and Particle Dark Matter 3 7 Predictions and Falsifiability 4 8 Roadmap to Quantitative Analysis 4 9 Conclusion 4 strophysical evidence for dark matter arises from multiple observational channels, including galactic dynamics, cluster kinematics, gravitational lensing, and large-scale structure. These channels are commonly interpreted as probing a single underlying mass distribution, yet they rely on distinct operational assumptions concerning time reconstruction, history dependence, and propagation. Building on Papers XXI–XXVIII of the Ordered-Dynamics Reconstruction Program, we classify dark matter observables according to their dependence on operational time reconstruction, cumulative temporal memory, and geometric propagation. We show that dynamical probes are generically sensitive to history-dependent operational time, while lensing probes are not. This operational asymmetry introduces structured, environment-dependent bias in mass inference without modifying gravitational dynamics, spacetime geometry, or introducing new matter components. The paper establishes the conceptual framework required for quantitative reinterpretation of dark matter data, which is deferred to subsequent work. 1 Introduction The empirical case for dark matter is among the most robust in modern astrophysics. Across a wide range of systems—galaxies, clusters, and the large-scale structure of the universe—gravitational effects inferred from observations exceed those predicted by luminous matter under general relativity. Conventionally, these discrepancies are interpreted as evidence for an additional, nonluminous matter component. This interpretation presumes that all observational channels infer mass under a shared operational structure: a common notion of time, distance, and dynamical inference. – 1 – The Ordered-Dynamics Reconstruction Program challenges this presumption. Earlier papers established that finite clocks reconstruct operational time from bounded records and incur unavoidable processing overhead (Papers XXI and XXII). This overhead accumulates as a cumulative operational lag ∆T, producing history-dependent reconstruction of time (Paper XXII) and biasing dynamical inference without modifying underlying dynamics (Paper XXV). At the same time, gravity was reconstructed as inhomogeneous influence propagation governed by a universal delay factor Z(x) (Paper XIII), which controls null propagation and lensing observables independently of clock reconstruction overhead. The purpose of this paper is to integrate these results into a coherent classification of dark matter inference channels, identifying which probes are operationally sensitive and which are not. Remark 1 (Intent and scope).This paper does not claim to explain dark matter away, nor does it propose a modified gravity theory. Its goal is classificatory: to identify where and how operational assumptions enter dark matter inference, prior to numerical analysis. 2 Operational Layers in Mass Inference Astrophysical mass inference relies on multiple operational layers that are often conflated in practice. Within the present framework, it is essential to distinguish these layers explicitly. 2.1 Propagation geometry Null propagation—such as the travel of photons—is governed by influence propagation delays encoded in the geometric factor Z(x). This layer controls gravitational lensing, Shapiro delay, and time-delay cosmography, and is universal across probes. 2.2 Dynamical evolution Dynamical observables involve motion of massive bodies and depend on accelerations inferred from time-parametrized trajectories. These observables require operational reconstruction of time. 2.3 Clock reconstruction Operational time ˜ tis reconstructed from finite clocks subject to bounded information-processing capacity. As shown in Papers XXI–XXII, this reconstruction incurs processing overhead quantified by αeff and accumulates as a history-dependent lag ∆T. Definition 1 (Operational sensitivity).An observable is operationally sensitive if its inference depends explicitly on reconstructed time ˜ trather than solely on geometric propagation. 3 Dynamical Dark Matter Probes Dynamical probes infer mass from observed motion. These include: •galactic rotation curves, •velocity dispersion in clusters, •satellite and tracer kinematics, – 2 – •virial mass estimates. All such probes depend explicitly on observed accelerations or velocity distributions computed with respect to operational time ˜ t. As shown in Paper XXV, when operational time reconstruction is history-dependent, observed accelerations contain additional response terms that are not attributable to gravitational forces. Dynamical mass inference is generically biased when operational time reconstruction varies with environment or history. Remark 2.This bias does not alter the force law or spacetime geometry. It modifies only the mapping from observed motion to inferred mass. 4 Lensing-Based Dark Matter Probes Gravitational lensing probes mass through deflection and time delay of null signals. These observables depend on influence propagation encoded by Z(x) and are independent of clock reconstruction overhead. To leading operational order, lensing-based dark matter inference is insensitive to αeff and ∆T. Remark 3.This operational immunity makes lensing a critical reference channel against which dynamical inferences can be compared. 5 Cross-Channel Tensions and Structure Observed discrepancies between dynamical and lensing mass estimates are often interpreted as requiring complex dark matter distributions or modified gravity. Within the present framework, such discrepancies may arise naturally from operational asymmetry between inference channels. Dynamical probes are sensitive to history-dependent time reconstruction, while lensing probes are not. Remark 4.The framework predicts structured disagreement—dependent on environment and history—rather than universal rescaling of mass. This suggests that scatter, hysteresis, and system age may be physically relevant variables in interpreting dark matter data. 6 Relation to Modified Gravity and Particle Dark Matter The operational framework differs fundamentally from modified gravity theories, which alter force laws, and from particle dark matter models, which introduce new gravitating components. Here: •gravitational propagation (Z) is unchanged, •dynamical equations remain unmodified, •no new matter fields are introduced. Remark 5.The framework is compatible with particle dark matter, but weakens the inference that all late-time discrepancies require additional matter. – 3 – 7 Predictions and Falsifiability The operational classification yields testable predictions: •probe-dependent discrepancies between dynamical and lensing mass, •recovery of standard inference in screened, strongly bound regimes, •absence of corresponding anomalies in lensing-only datasets, •no signatures in particle-physics experiments. Remark 6.Strict agreement across all inference channels would falsify the framework. 8 Roadmap to Quantitative Analysis This paper establishes the conceptual structure required for quantitative analysis of dark matter data. Subsequent work will: •model αeff variability, •analyze environment-resolved datasets, •perform joint lensing–dynamics comparisons. These steps are deferred intentionally to avoid premature fitting. 9 Conclusion Dark matter inference spans multiple observational channels with distinct operational sensitivities. When operational time reconstruction is history-dependent, dynamical and geometric probes need not agree even under unmodified gravity. This paper provides the operational taxonomy required to interpret such discrepancies prior to data-driven analysis, completing the conceptual bridge between foundational reconstruction and quantitative cosmology. – 4 –