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Equation 7 · Part 1 · The Hardest Unsolved Problems in Open-Weight AI

Symbol P

P(at least one surviving copy)P(\text{at least one surviving copy})
PP

What this part means

P is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

P is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

This is a deliberately simplified model — real retention decisions are not independent, and q is not a single fixed number — but it isolates the right variable. Because copying an already-downloaded checkpoint costs approximately nothing, N grows with every re-share, and P(at least one surviving copy\text{at least one surviving copy}) climbs toward one almost as soon as distribution starts, for any q short of certainty. This is a restatement, in one line of algebra, of what NTIA’s 2024 report and RAND’s 2024 report both conclude in prose: monitoring and mitigation are the available tools, and recall is not among them [ 2 , 3 ] .

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A function assigns an output to each allowed input. The expression f(x) means “apply f to x”.

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Sources cited in the article section

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