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Equation 6 · Part 5 · Every Test Changed the Scene and Kept the Chair Red

fraction

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] .
fraction

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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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