We describe the framework and strategy of the ^G infrared search for extraterrestrial civilizations with large energy supplies, which will use the wide-field infrared surveys of WISE and Spitzer to search for these civilizations waste heat. We develop a formalism for translating mid-infrared photometry into quantitative upper limits on extraterrestrial energy supplies. We discuss the likely sources of false positives, how dust can and will contaminate our search, and prospects for distinguishing dust from alien waste heat. We argue that galaxy-spanning civilizations may be easier to distinguish from natural sources than circumstellar civilizations (i.e., Dyson spheres), although Gaia will significantly improve our capability to identify the latter. We present a zeroth order null result of our search based on the WISE all-sky catalog: we show, for the first time, that Kardashev Type III civilizations (as Kardashev originally defined them) are very rare in the local universe. More sophisticated searches can extend our methodology to smaller waste heat luminosities, and potentially entirely rule out (or detect) both Kardashev Type III civilizations and new physics that allows for unlimited free energy generation.
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