The term "connective spectrum" is not widely recognized in established scientific literature or common terminology as of my last training cut-off in October 2023. It might be a specialized term from a specific field or a colloquial phrase used in a particular context.
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A connective spectrum has for . This makes the homological Atiyah-Hirzebruch spectral sequence first quadrant for a based space, and prevents negative coefficient degrees from affecting its first nonzero represented homology theory.