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Equation 6 · Part 7 · Every Test Changed the Scene and Kept the Chair Red

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CAI(π)=1N∑i=1N1[trial i converges on the recolored true target, not the red decoy, within the paper’s own 2-meter success radius].\mathrm{CAI}(\pi) = \frac{1}{N}\sum_{i=1}^{N} \mathbb{1}\left[\text{trial } i \text{ converges on the recolored true target, not the red decoy, within the paper's own 2-meter success radius}\right] .
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

A countermodel earns its keep only once it points at a specific, buildable measurement nobody has taken. Define, for any policy π\pi , a Causal-Alignment Index under a cue-decorrelation intervention that repaints the true target a color other than red while placing an unmodified red decoy elsewhere in the same frame region class the paper’s own Urban Patio protocol already uses: CAI(π)=1N∑i=1N1[trial i converges on the recolored true target, not the red decoy, within the paper’s own 2-meter success radius]\mathrm{CAI}(\pi) = \frac{1}{N}\sum_{i=1}^{N} \mathbb{1}\left[\text{trial } i \text{ converges on the recolored true target, not the red decoy, within the paper's own 2-meter success radius}\right] . Pair it with a Recolor Robustness Ratio , comparing that score against the architecture’s own already-published performance on the paper’s hardest matched-appearance site:

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the article section

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