5. Conceptual Illustration

This section introduces no new theory. It fulfills a promise made at the close of Section 3 and the opening of Section 4: to build complete task cards for the two Argus examples already described, and to actually compute $TCI_\ell$, $n_{\text{mixed}}(\ell)$, and $\Delta TCI$. The numbers that follow are illustrative constructions by the author, not measurements from Argus's real telemetry — they serve to expose the index's mechanics, not to report an empirical result. That distinction matters: a case study with real data is the program of Article 5, not this one.

Before filling in any card, a question Section 4 left implicit must be resolved: how should properties Section 2 classified as purely surface be treated at the physical-ecology level? "Number of cues" and "presentation of cues" describe a representation — how many cues reach someone, how they are shown to them. The physical ecology does not represent anything to anyone; it therefore has no value of its own on these two properties. The convention adopted here, and applied consistently, is this: the seven properties classified as pure depth in Section 2 are inherited across levels — the value computed at the physical-ecology level carries over to the AI's representation and to the supervisor's, barring explicitly documented distortion; the two mixed properties (organizing principle, decision duration) may diverge, since their depth component and their surface component can legitimately come apart; the two purely surface properties (number of cues, presentation of cues) have no value at the physical-ecology level, and $TCI_{\text{eco}}$ is computed over only the remaining nine properties.

5.1. Thermal anomaly detection

The task is the one already described in Section 3: few calibrated sensors, a stable thermal trend, known engineering thresholds, a comprehensible physical relationship, enough time to confirm — but potentially quasirational if load, ventilation, and operating cycle alter how temperature is interpreted. Four cards are built here: physical ecology, AI representation, and two variants of the supervisory representation — one that preserves trend and context ("rich"), another that reduces everything to a binary alert ("poor").

Brief justification: distribution and certainty are "mixed" at the ecology level because the raw reading mixes regimes (load, ventilation, cycle) before any contextualization — the AI and the rich panel resolve that ambiguity by contextualizing the signal (hence rising to $+1$), the poor panel does not resolve it, it merely hides it (hence regressing to $0$). The cue-criterion relation stays at $-1$ across all levels, being a purely depth property — thermal degradation is physically linear or it isn't, regardless of who observes it. Organizing principle and presentation diverge only in the poor variant, exactly as Section 2 predicted for the two "mixed" properties.

$$TCI_{\text{eco}} = \frac{5}{9} \approx 0.56 \quad (n_{\text{mixed}} = 2)$$ $$TCI_{\text{AI}} = \frac{9}{11} \approx 0.82 \quad (n_{\text{mixed}} = 0)$$ $$TCI_{\text{sup-rich}} = \frac{9}{11} \approx 0.82 \quad (n_{\text{mixed}} = 0) \implies \Delta TCI_{\text{AI-sup}} = 0$$ $$TCI_{\text{sup-poor}} = \frac{2}{11} \approx 0.18 \quad (n_{\text{mixed}} = 3) \implies \Delta TCI_{\text{AI-sup}} \approx 0.64$$

The result confirms, with numbers, Section 4's qualitative narrative: when the panel preserves context, $\Delta TCI_{\text{AI-sup}} = 0$; when it reduces the task to a binary alert, $\Delta TCI_{\text{AI-sup}}$ jumps to $0.64$ — more than half of the total possible range.

The case marked with an asterisk. The "number of cues" property for the poor panel resists clean classification. The classical polarity says few cues favor analysis — but a single binary alert is not a task with few cues to analyze; it is a task with no cues left, one that does not invite analysis but invites blind trust in the recommendation. Classical CCT, formulated for human judges who always have access to some raw cue, does not distinguish "few analyzable cues" from "no cues, just a conclusion." This section does not force an answer to that distinction — it flags it as a limit of the property as inherited from the literature, and assigns $0$ by convention, not by conviction. This is, notably, exactly the kind of situation Article 2 already described as automation complacency through institutional void: the absence of cues strips the supervisor of the possibility of deciding, not merely the ease of doing so.

5.2. Bearing-failure prediction from vibration

The second example, harder by design: high-frequency signals, dozens of derived attributes, strong redundancy among measurements, interaction with load and speed, multiple failure modes, scarcity of positive events — even when the human interface is reduced to a single risk score.

$$TCI_{\text{eco}} = \frac{1}{9} \approx 0.11 \quad (n_{\text{mixed}} = 0)$$ $$TCI_{\text{AI}} = \frac{-1}{11} \approx -0.09 \quad (n_{\text{mixed}} = 0)$$ $$TCI_{\text{sup}} = \frac{-2}{11} \approx -0.18 \quad (n_{\text{mixed}} = 1) \implies \Delta TCI_{\text{AI-sup}} \approx 0.09$$

Here, unlike the thermal example, $n_{\text{mixed}}$ stays low across all levels — not because the task is simple, but because properties point confidently in opposite directions: four toward the intuitive pole (distribution, redundancy, decomposability, certainty), four toward the analytical pole (measurement, relation, weighting, duration), plus the number/presentation pair tilting slightly toward intuition at the AI level. This is genuine quasirationality, exactly as Section 4 anticipated. And $\Delta TCI_{\text{AI-sup}}$ stays small ($0.09$) — reducing the task to a single score does not visibly shift the index, because the task was already, at depth, resistant to decomposition.

This is precisely where the most important point of this section lies: the index stays low, but the problem has not disappeared. The organizing principle drops from $+1$ to $-1$ at the supervisor level — the score does not explain what it is based on, it only communicates it — but that single signal, diluted among the remaining ten properties, does not perceptibly move $\Delta TCI$. A supervisor receiving this score is just as much in the dark as in the thermal example with the poor panel — but here the index does not flag it. $\Delta TCI_{\text{AI-sup}}$ detects structural displacement of mode; it does not detect the opacity of a principle when that opacity does not displace the rest of the task. This is not a calculation failure — it is exactly the boundary of application already declared in Section 4, now visible in numbers, not just in prose.

The "number of cues" asterisk repeats deliberately across both examples — not as redundancy, but to show that the problem lies with the property itself as inherited from classical CCT, not with a particular case. CCT was formulated for human judges who always have access to some raw cue; it does not distinguish "few analyzable cues" from "no cues, just a conclusion." This section does not force that distinction — it flags it as a point for future refinement, visible precisely because it appears twice, in tasks of different natures, with the same result.

5.3. A structural limit of the index, discovered while calculating

The convention adopted at the start of this section — seven inherited depth properties, four (two surface, two mixed) free to diverge — implies an upper bound on $\Delta TCI_{\text{AI-sup}}$ that is not obvious from Section 4's formula alone. If only four of the eleven properties can, by convention, differ between the AI's representation and the supervisor's, and each can swing at most between $-1$ and $+1$ (a range of $2$), then:

$$|\Delta TCI_{\text{AI-sup}}| \leq \frac{4 \times 2}{11} = \frac{8}{11} \approx 0.73$$

This is not a universal law of CCT — it is a direct consequence of the inheritance convention adopted in this section, and it would change if that convention were abandoned (for instance, if the AI itself were allowed to operate on a distorted estimate of a depth property, rather than on its true value). But within the terms in which this article defines $TCI_\ell$, the limit is real: $\Delta TCI_{\text{AI-sup}}$ will never approach the extremes of $2$, even when the supervisor's interface is reduced to the absolute minimum — the thermal example, at $\Delta TCI \approx 0.64$, already sits close to that ceiling.

This limit has direct implications for the design of authority architectures: even minimalist supervisory interfaces cannot, by construction, produce divergences above roughly $0.73$ — which places a structural ceiling on the kind of risk $\Delta TCI$ can detect. The consequences of this ceiling for the distribution of authority between AI and supervisor are explored in Article 4, which asks whether architectures operating near this limit demand different forms of governance than those operating near zero.

The two examples, read together, show what this article can and cannot deliver to Articles 4 and 5: a comparable, auditable, and explicitly bounded number — one that detects a specific kind of structural risk well, has a known mathematical ceiling, and fails predictably exactly where Section 2 already warned it would.

(Bibliographic note: this section introduces no new citations. All numeric values, tables, and the theoretical $8/11$ limit are original, illustrative constructions of this trilogy, developed to demonstrate the mechanics of $TCI_\ell$ and $\Delta TCI$ as defined in Section 4; they do not correspond to measurements from Argus's real telemetry, which remain reserved for the empirical case study in Article 5.)