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Being lossless is a function of the whole pipeline from an input image to an output image. The last step being encode to PNG doesn't guarantee anything about losslessness.

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Lossless means that the file encodes the exact same information that was given to the encoder. This is a property of the format.

Yes but people add pre-preprocessor steps to image formats, like blurring jpegs or lowering bit depth in PNGs to make them more compressible.

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