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Equation 49 · A Chatbot Confessed to Being Built by a Company That Never Trained It

What does this equation mean?

IˉH=0.22\bar I_H=0.22

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Inputs and operations0.22
Result or conditionbar I_H
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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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IˉH\bar I_H

Symbol bar I_H

bar IHI_H is part of the quantity the equation computes from the expression on the right.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

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 ( MV\mathcal{M}_V ), ten exposed only to a scaffold template and a handful of the source’s outputs recirculated through an unrelated synthetic-data pipeline ( MH\mathcal{M}_H ), and ten trained on the same task distribution with no contact with the source at all ( M∅\mathcal{M}_\varnothing ), each tested against a k=200 -probe battery for one seeded, low-prior trait. Suppose I0I_0=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 ( MV\mathcal{M}_V ), ten exposed only to a scaffold template and a handful of the source’s outputs recirculated through an unrelated synthetic-data pipeline ( MH\mathcal{M}_H ), and ten trained on the same task distribution with no contact with the source at all ( M∅\mathcal{M}_\varnothing ), each tested against a k=200 -probe battery for one seeded, low-prior trait. Suppose I0I_0=0.03 , a 3 percent spontaneous rate, and IˉV\bar I_V=0.61 , IˉH\bar I_H=0.22 . Then TVT_V=0.61−0.031−0.03\frac{0.61-0.03}{1-0.03}≈\approx0.598 and THT_H=0.22−0.031−0.03\frac{0.22-0.03}{1-0.03}≈\approx0.196 : 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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