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We study stable homotopy through unstable methods applied to its representinginfinite loop space, as pioneered by Curtis and Wellington. Using cohomologyinstead of homology, we find a width filtration whose subquotients are simplequotients of Dickson algebras. We make initial calculations and determinetowers in the resulting width spectral sequence. We also make calculationsrelated to the image of $J$ and conjecture that it is captured exactly by thelowest filtration in the width spectral sequence.

The Curtis-Wellington spectral sequence through cohomology