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Equation 4 · Part 1 · The Hardest Unsolved Problems in Open-Weight AI

Symbol P

P(at least one surviving copy)=1−qN.P(\text{at least one surviving copy}) = 1 - q^{N}.
PP

What this part means

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

Its job in the formula

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

The passage around this formula

…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,…

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Learn the underlying idea

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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