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Equation 6 · Part 8 · Every Test Changed the Scene and Kept the Chair Red

Numerator: 1

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] .
11

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

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

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the article section

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