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Equation 4 · Part 2 · Ten Failure Modes That Define the Open-Weight AI Ecosystem

superscript

pnp^n
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

None of these ten is exotic. Each is a specific, dated, sourced instance of a general property: an open-weight release multiplies the number of places a given property of the model can fail, without multiplying the number of parties responsible for checking it. A safety-trained closed model has one deployment surface a provider monitors; a safety-trained open model has as many deployment surfaces as there are people who downloaded it, and monitoring responsibility does not travel with the file. If a base model preserves a given desirable property — genuine safety training, license compliance, unmodified provenance — with independent probability p at each of n downstream forks, the…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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