Equation 48 · A Chatbot Confessed to Being Built by a Company That Never Trained It
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol bar I_V
bar is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
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What the article says around this equation
No sealed trial of the kind proposed later in this article has been run, and every number in this section is invented to show what the construction predicts, not what it has found. Suppose a population of N=30 models: ten fine-tuned directly on a seeded source’s outputs ( ), ten exposed only to a scaffold template and a handful of the source’s outputs recirculated through an unrelated synthetic-data pipeline ( ), and ten trained on the same task distribution with no contact with the source at all ( ), each tested against a k=200 -probe battery for one seeded, low-prior trait. Suppose =0.03 , a 3 percent spontaneous rate, and \bar…
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No sealed trial of the kind proposed later in this article has been run, and every number in this section is invented to show what the construction predicts, not what it has found. Suppose a population of N=30 models: ten fine-tuned directly on a seeded source’s outputs ( ), ten exposed only to a scaffold template and a handful of the source’s outputs recirculated through an unrelated synthetic-data pipeline ( ), and ten trained on the same task distribution with no contact with the source at all ( ), each tested against a k=200 -probe battery for one seeded, low-prior trait. Suppose =0.03 , a 3 percent spontaneous rate, and =0.61 , =0.22 . Then =0.598 and =0.196 : on this invented population, vertical exposure would explain roughly 60 percent of the gap between baseline and observed incidence, horizontal exposure roughly 20 percent — smaller, as one would expect from a noisier, more indirect channel, but not zero.
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