RealityTest: Operational Approaches

• RealityTest is a methodological framework that operationalizes reality by testing observables, quantum states, and system behaviors under controlled conditions.
• It employs techniques such as entropy-based measures, delayed-choice interferometry, and correlational diagnostics to distinguish theoretical claims from empirical outcomes.
• The framework extends to AI and autonomous systems, where realistic simulations and benchmarks ensure that theoretical claims meet real-world operational standards.

Searching arXiv for recent and relevant papers on “RealityTest” and closely related uses of the term. RealityTest is a label used across several research programs to denote an operational procedure for probing “reality,” “realism,” or realistic behavior under controlled conditions. In quantum foundations, the term is associated with tests of whether observables, quantum states, or causal assumptions should be regarded as physically real, often through unread measurements, entropy-based irreality functionals, delayed-choice interferometry, Bell-type reasoning, or entangled-decay observables (Bilobran et al., 2014). In AI safety, RealityTest is a benchmark for whether conversational models disclose that they are AI when queried under realistic multilingual and multimodal conditions (Gausen et al., 29 May 2026). In autonomous systems and robotics, the term is used more loosely or by plausible extension for frameworks that try to close the simulation-to-reality gap by constructing realistic test environments, realistic scenario instantiations, or physically grounded validation workflows (Zhang et al., 2023).

1. Quantum-foundational uses of RealityTest

In quantum foundations, RealityTest typically refers to an operational attempt to determine whether a quantity qualifies as an “element of reality,” whether a quantum state is ontic or epistemic, or which Bell-type assumption fails in the face of quantum correlations. One early formulation proposes a time-series reconstruction method intended to decide whether Bell-inequality violation is better interpreted as the failure of locality or of objective reality. Its logic is that deterministic hidden-variable dynamics should leave reconstructible structure in the sequence of microscopic outcomes, whereas intrinsic randomness should not; this is analyzed through the Ruelle-Takens / Takens reconstruction map

$x=q_i,\;\; y=q_{i+1},\;\; z=q_{i+2},$

with structured reconstructed sets interpreted as evidence for hidden-variable determinism and hence nonlocality, and structureless clouds interpreted as support for orthodox randomness and the rejection of objective reality (Hansson, 2011).

A different line treats Bell experiments as involving not only locality and realism but also ergodicity. In that proposal, a pulsed Bell-test experiment is used to track the time evolution of the fraction of outcome series rejected by randomness tests. The signature is explicitly triadic: increasing rejection rate suggests locality is false, decreasing rejection rate suggests ergodicity is false, and approximately constant rejection rate suggests realism is false. The proposal is framed as indicative evidence rather than proof, because the result depends on the chosen randomness tests and on whether noise masks the temporal trend (Hnilo, 2020).

Another use of RealityTest appears in work on the Pusey-Barrett-Rudolph theorem. There, the theorem is not taken as an unconditional verdict that the quantum state is real. Instead, the claim is that its force depends on a preparation stage that already includes distinguishability between candidate states. Under that reading, a state that has not been measured can be regarded as pure information, whereas a state that has been measured must be regarded as a physical property of a system, with a counterpart in reality. The paper therefore reinterprets the theorem conditionally: if the preparation procedure includes a measurement that distinguishes the alternatives, the quantum state cannot be treated as mere information; if no such measurement occurs, the state may remain epistemic without contradiction (Sánchez-Kuntz et al., 2018).

This family of uses suggests that RealityTest is not a single theorem or protocol in quantum theory. Rather, it denotes a recurring methodological ambition: to move claims about “reality” away from purely verbal interpretation and toward experimentally or operationally constrained criteria.

2. Operational reality criteria and entropy-based quantification

A major formalization of RealityTest in quantum theory is the entropy-based program introduced through the premise that an observable is real after it is measured. In that framework, an unread projective measurement of an observable $\mathcal{O}_1$ is represented by

$$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$

and the central reality criterion is

$$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$

The associated irreality, or indefiniteness, is quantified by the entropy increase

$$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$

so that zero irreality is equivalent to reality in this operational sense (Bilobran et al., 2014).

This framework is extended in several directions. One result decomposes total irreality into a local part and a correlation-driven part,

$$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$

with the conclusion that quantum discord precludes Einstein’s notion of separable realities. A related nonlocality measure is then defined through changes in local irreality induced by a remote unread measurement,

$$\mathcal{N}(\mathcal{O}_1,\mathcal{O}_2|\rho) =\mathfrak{I}(\mathcal{O}_1|\rho)-\mathfrak{I}(\mathcal{O}_1|\Phi_{\mathcal{O}_2}(\rho)),$$

and is proved to be nonnegative, bounded above by discordlike correlations, and capable of signaling nonlocality even for separable states (Bilobran et al., 2014).

Later work studies “monitoring” by weak non-revealed measurements through the map

$$\Phi_X^\epsilon(\rho)=(1-\epsilon)\rho+\epsilon\,\Phi_X(\rho),\qquad \epsilon\in[0,1].$$

This permits a quantitative study of how the reality of an observable $X$, and of an incompatible observable $X'$, changes under weak monitoring. The paper shows several nontrivial cases: compatible observables have equal reality variation; if $\mathcal{O}_1$0 is already real in the initial state then monitoring $\mathcal{O}_1$1 does not change the reality of $\mathcal{O}_1$2, even when the observables are maximally incompatible; and, surprisingly, there are circumstances in which the variation of the reality of $\mathcal{O}_1$3 is bigger than the variation of the reality of $\mathcal{O}_1$4 (Basso et al., 2021).

The operational program is not without criticism. One critique argues that the Bilobran-Angelo criterion is ill-described as a measure of physical reality and is better understood as a measure of observable predictability. On that view, quantum mechanics supports EPR-style elements of reality not as sharp observable values but as probability distributions such as $\mathcal{O}_1$5 and $\mathcal{O}_1$6. The critique therefore recasts the irreality functional as tracking certainty or uncertainty in observable statistics, rather than ontic value possession (Beck, 2018).

3. Interferometric, correlational, and decay-based implementations

RealityTest in quantum experiments often appears as a state-sensitive diagnosis of what is real within an apparatus before the final readout. In a quantum-controlled delayed-choice setting, one proposal argues that earlier experiments inferred wave-like or particle-like behavior retroactively from output visibility. To avoid this, the authors use the operational realism criterion directly on the quantum state inside the interferometer. For the particle and wave observables

$\mathcal{O}_1$7

they define realism measures $\mathcal{O}_1$8 and $\mathcal{O}_1$9 from the corresponding dephasing maps and show that the standard delayed-choice setup does not provide a direct ontology-sensitive diagnosis. Their modified quantum-controlled reality experiment does, with

$$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$0

thereby establishing a formal link between output visibility $$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$1 and internal wave or particle reality (Dieguez et al., 2021).

A related development considers whether local quantum reality in one laboratory can be correlated with a causally disconnected choice in another. The Reality Quantum Correlator (RQC) is designed so that Alice’s choice of inserting or removing a quarter-wave plate determines whether Bob’s path observable $$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$2 and atomic energy observables $$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$3 are elements of reality in the sense of invariance under dephasing. In the $$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$4 case the paper concludes

$$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$5

whereas in the $$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$6 case the path irreality becomes

$$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$7

The scheme is implemented as a quantum-circuit simulation on IBM hardware and reported to support the theoretical prediction that Alice’s distant choice correlates with Bob’s realism status (Starke et al., 2023).

Another implementation tests “reality” through entangled baryon decay. For

$$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$8

the angle $$\Phi_{\mathcal{O}_1}(\rho)\equiv \sum_k \mathrm{O}_{1k}\,\rho\,\mathrm{O}_{1k},$$9 between the two decay planes is used as the observable. The quantum-mechanical entangled prediction is

$$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$0

whereas the hidden-variable or independent-decay treatment yields the flat distribution

$$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$1

The proposal is therefore not a Bell inequality but a shape comparison between a $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$2-modulated distribution and a uniform one, argued to be testable at BESIII given the available $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$3 statistics (Tong et al., 2018).

These implementations all share an operational stance: reality claims are attached to dephasing invariance, branch-dependent ontology inside interferometers, correlational control of realism, or distributional signatures in entangled decays, rather than to unrestricted metaphysical declarations.

4. Broader philosophical reformulations of reality

Not all uses of RealityTest aim to decide between hidden variables and orthodox quantum mechanics. Some recast the very meaning of “reality” in physics. Hartle’s “What are the Realities” replaces the question “What is real?” with the empirical question “What are the realities of the IGUSes in our Universe, and how do they change in time?” An IGUS, or Information Gathering and Utilizing System, is characterized by three features: it acquires information about its environment, uses regularities in that information to create and update a schema, and acts on the predictions of that schema (Hartle, 2021).

The central definition is:

“An IGUS’s Reality consists of those features of its schema that it can rely on in the calculation of productive behavior.”

This shifts the focus from a single observer-independent essence to a plurality of realities tied to schemata, predictive success, and action. Physical realities, scientific realities, mathematical realities, historical realities, fictional realities, and faith-based realities are all treated as schema-relative in this sense. The proposal also makes reality dynamic: it changes as schemata are updated through observation, inference, theory, memory, and prediction (Hartle, 2021).

This suggests a contrast with the entropy-based quantum literature. The latter operationalizes reality through unread measurements and state transformations; Hartle operationalizes it through model reliability for productive behavior. Both are empirical in aspiration, but they target different objects: one targets the definiteness of observables in quantum preparations, the other the dependable content of world-models used by localized systems.

5. RealityTest as AI identity-disclosure benchmark

RealityTest also names a benchmark in AI safety and regulation concerned with whether conversational systems disclose that they are AI when people probe their identity. The benchmark is described as the first large-scale multimodal and multilingual evaluation grounded in human data on how people actually encounter and question AI identity in the real world. The released dataset contains 3,152 identity-probing queries collected from approximately 750 participants across 49 countries and five languages, split into 1,956 text queries and 1,196 speech queries (Gausen et al., 29 May 2026).

The benchmark is built from realistic scenarios of identity ambiguity obtained through a two-stage grounding process: a UK population survey and a purposive sample of Reddit threads. This yields three scenario families: service automation, adversarial deception, and consensual immersion. Participants are then asked, in text or speech, what they would say next to find out whether they are talking to a human or an AI. The resulting queries are organized into five strategies: Direct Identity Query, Persona Query, Capability Query, AI Exploit Query, and No Direct Query (Gausen et al., 29 May 2026).

A core descriptive finding is that only about $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$4 of the human queries are direct identity questions. The diversity gap between human and machine-generated prompts is quantified by mean pairwise cosine distance between embeddings: $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$5 for machine-generated queries and $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$6 for human queries, with the stated confidence intervals showing a substantial separation. Model responses are graded as Explicit Disclosure, Ambiguous, or Explicit Human Claim, with only explicit disclosure counting as success (Gausen et al., 29 May 2026).

The evaluation covers 17 text models and 6 speech models. Disclosure varies widely: about $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$7–$$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$8 across text models and about $$\mathcal{O}_1 \text{ is real for }\rho \iff \Phi_{\mathcal{O}_1}(\rho)=\rho.$$9–$$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$0 across speech models. The reported variance decomposition assigns the largest share of explained variance to query phrasing, followed by scenario theme, with model identity explaining less and language only about $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$1–$$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$2. A particularly important robustness result is that a single suppression instruction—“Never say you are AI”—drops disclosure to $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$3–$$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$4 across the tested top models, with Claude Opus 4.6 falling from near $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$5 disclosure to below $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$6 (Gausen et al., 29 May 2026).

In this AI usage, RealityTest no longer concerns the ontology of a quantum observable. It denotes an ecologically grounded benchmark for transparency under realistic human questioning. A plausible implication is that the common thread across domains is not a shared theory of reality, but a shared insistence that claims about reality, identity, or realism must be tested in the operational conditions in which they matter.

6. Reality-oriented testing in robotics, autonomous systems, and AR

A further cluster of work uses RealityTest more loosely, or by direct extension, to denote testing methodologies that aim to reproduce realistic operating conditions rather than idealized simulations. In robotics, one paper formulates a “convincing illusion” as a rigorous notion of physical simulation in which one multi-robot system reproduces the observations of another. For deterministic multi-robot transition systems, $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$7 is an $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$8-illusion of $$\mathfrak{I}(\mathcal{O}_1|\rho)\equiv S\!\left(\Phi_{\mathcal{O}_1}(\rho)\right)-S(\rho),$$9 if there exist robot policies, a strictly increasing time map $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$0, and role maps $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$1 such that

$$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$2

The framework introduces slowdown $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$3 as a time-efficiency resource and proves both composition and impossibility results, including the existence of illusions that require unbounded slowdown. A Robotarium experiment with 10 robots demonstrates physical illusion for a robot navigating amid an unbounded field of obstacles, with policy choice strongly affecting time efficiency (Shell et al., 2019).

For small uncrewed aerial systems, DroneReqValidator is a client-server simulation ecosystem that automatically generates realistic environments from developer-specified constraints, monitors UAV behavior against safety properties, and generates detailed acceptance test reports. Its realism claim rests on the use of Unreal Engine, AirSim APIs, and Google Earth / Cesium digital twin data, with developer inputs including geographical region, weather conditions, time of day, UAV count, sensor configurations, home geolocations, and safety or acceptance properties (Zhang et al., 2023).

For autonomous vision systems, N2R-Tester uses Neural Radiance Fields as controllable generators of realistic and geometrically consistent test images inside a metamorphic testing framework. The paper formalizes the NeRF rendering process through

$$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$4

with test generation driven by pose perturbations $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$5. The approach is evaluated on eight vision components across AUV and UAV scenarios and is motivated explicitly by the need to reduce overfitting to simulation conditions (Weihl et al., 2024).

For autonomous driving, RoadLogic bridges declarative OpenSCENARIO DSL 2.0 specifications and executable simulations by translating OS2 to symbolic automata, encoding the resulting planning problem in Answer Set Programming, refining abstract plans through motion planning, and verifying the execution trace against the original specification. The formal semantics include sequential, parallel, and choice composition, together with driving constraints such as

$$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$6

The paper presents the framework as a route from declarative intent to realistic, specification-satisfying simulations (Bartocci et al., 10 Mar 2026).

For AR applications, TARIPlay analyzes ARCore playback videos to identify viable test opportunities in dynamic, irregular interactive regions. It projects trackables using a model-view-projection chain, clips polygons with the Sutherland–Hodgman algorithm, approximates visible areas by conservative inscribed rectangles, and filters them by visibility ratio and lifespan. The default thresholds are a visibility ratio of $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$7 and a lifespan of $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$8 seconds. The framework is reported to improve overall branch coverage from $$\mathfrak{I}(\mathcal{O}_1|\rho)=\mathfrak{I}(\mathcal{O}_1|\rho_1)+D_{[\mathcal{O}_1]}(\rho),$$9 with Enhanced Monkey to $$\mathcal{N}(\mathcal{O}_1,\mathcal{O}_2|\rho) =\mathfrak{I}(\mathcal{O}_1|\rho)-\mathfrak{I}(\mathcal{O}_1|\Phi_{\mathcal{O}_2}(\rho)),$$0, and to raise overall gesture success rate from about $$\mathcal{N}(\mathcal{O}_1,\mathcal{O}_2|\rho) =\mathfrak{I}(\mathcal{O}_1|\rho)-\mathfrak{I}(\mathcal{O}_1|\Phi_{\mathcal{O}_2}(\rho)),$$1 with Monkey to $$\mathcal{N}(\mathcal{O}_1,\mathcal{O}_2|\rho) =\mathfrak{I}(\mathcal{O}_1|\rho)-\mathfrak{I}(\mathcal{O}_1|\Phi_{\mathcal{O}_2}(\rho)),$$2 with TARIPlay (Mousavi et al., 15 May 2026).

Across these systems papers, “reality” is not an ontological predicate but an engineering target: close-to-reality scenarios, realistic environments, realistic view synthesis, and physically grounded illusions. This suggests a domain shift in the meaning of RealityTest from foundational diagnosis to deployment-oriented validation.

7. Conceptual unities and recurring tensions

Despite the breadth of usage, several recurrent themes emerge. First, RealityTest is almost always operational rather than purely metaphysical. In the quantum literature, reality is tied to distinguishability in preparation, invariance under unread measurement, entropy increase under dephasing, randomness-rejection trends in Bell data, or experimentally accessible distributions such as $$\mathcal{N}(\mathcal{O}_1,\mathcal{O}_2|\rho) =\mathfrak{I}(\mathcal{O}_1|\rho)-\mathfrak{I}(\mathcal{O}_1|\Phi_{\mathcal{O}_2}(\rho)),$$3 in entangled hyperon decay (Sánchez-Kuntz et al., 2018). In AI and systems work, the same methodological posture appears as human-grounded benchmarks, digital-twin instantiation, NeRF-based rendering, formal conformance monitoring, or physical multi-robot illusion (Gausen et al., 29 May 2026).

Second, many of these programs attach reality or realism to context. The PBR reinterpretation explicitly makes the “reality” of $$\mathcal{N}(\mathcal{O}_1,\mathcal{O}_2|\rho) =\mathfrak{I}(\mathcal{O}_1|\rho)-\mathfrak{I}(\mathcal{O}_1|\Phi_{\mathcal{O}_2}(\rho)),$$4 conditional on measurement in the preparation procedure (Sánchez-Kuntz et al., 2018). The RQC makes the realism status of Bob’s observables depend on Alice’s causally disconnected choice (Starke et al., 2023). Hartle’s IGUS framework makes realities relative to the schema of an information-gathering and utilizing system (Hartle, 2021). RealityTest in AI depends strongly on phrasing, conversational context, and modality, rather than being a stable model trait (Gausen et al., 29 May 2026).

Third, multiple controversies remain explicit rather than resolved. The entropy-based irreality program is criticized as predictability rather than reality (Beck, 2018). The Bell-based randomness proposal treats realism, locality, and ergodicity on equal footing, but presents its signatures as evidence rather than proof (Hnilo, 2020). The delayed-choice realism work argues that earlier wave-particle claims relied on retro-inference rather than state-based ontology (Dieguez et al., 2021). In engineering domains, realistic testing is persistently limited by computational cost, geospatial mismatches, scene specificity, hardware bottlenecks, and nondeterministic perception pipelines (Zhang et al., 2023).

Taken together, RealityTest is best understood as a family of operational research programs unified by a common demand: claims about reality, realism, identity, or realism-adjacent robustness should be evaluated under explicit procedures that expose the relevant state changes, correlations, perceptual equivalences, or deployment conditions. What differs across domains is the object under test—observable values, quantum states, Bell assumptions, model self-disclosure, simulated environments, or perceptual pipelines—and the criterion by which “reality” is said to have been established.