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Decomposing

The dead body of Francis reeked of corruption. She reached forward searching through the slimy remains of what was once flesh. Something hard found her fingers. With trepidation she pulled out a credit-card sliver of plastic with some sort of code printed on it. How was this going to get her the password to the Professor's secret research?

Solution

author: Rich Wareham (rjw57)

The picture is a QR code which, when scanned, resolves to:
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The == at the end is a dead giveaway that this is Base64-encoded data. Decoding it results in the following PNG file:

Examining each colour channel, we find that the red channel appears to just be random noise, the green channel is upper-triangular and the blue channel appears to be a QR code.

More careful examination shows the QR code to have range 0 to 127 rather than 0 to 255 as might be expected. This is a clue to treat the values as signed 8-bit integers.

Decoding the QR code gives "Householder", a reference to Householder transformations which are used to compute the QR decomposition of a matrix.

It turns out the other two channels are quite literally a "QR decomposition" as they are the QR decomposition of a QR code. Treating them as signed integers and multiplying together gives a QR code which decodes to "prophase deep", the solution.