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Necessity of math justification/motivation in a patent?

I don't know if its appropriate question here...but I anyway want to try... I have an algorithm in which I have a finite data in which each element is assumed as an element of a metric space with a ...
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Keyword trends - Detecting trends in a stream of words using frequency analysis (Citizennet) - Patent Application - PRIOR ART REQUEST

AN OVERBROAD PATENT ON performing frequency analysis on the occurrence of target words in a stream of words - This application from Citizennet seeks to patent the idea of...Generating a discrete time ...
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Machine Learning - Detecting similar documents using entity extraction (Nhn) - Patent Application - PRIOR ART REQUEST

AN OVERBROAD PATENT ON Methods of detecting similar documents - This application from Nhn seeks to patent the idea of...Extracting an entity from two or more web documents, calculating weights based ...