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Using Photoshop, when I change the document size from to 72.25cm x 54.19cm at 72ppi to 12cm x 9cm the resolution jumps to 433.493ppi.

How can I stop Photoshop from doing this?

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Is the image for print or screen? – Scott Mar 5 '13 at 23:17
The ppi flag is being "altered" so as to avoid changing the exact pixel dimensions. The size is derived from the pixels divided by the ppi; the ppi is derived from the pixels and the specified inches. In both cases the pixels remain fixed. – horatio Mar 6 '13 at 15:26

Immediate solution, check the "Resample Image" option in the Image size dialog window.

More importantly you need to explain the final output of the image. For print, you may want the 433ppi. You haven't provided enough detail in your question to thoroughly answer. You can edit your question to provide these types of detail.

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