Minimal resolution of the length-filtered Steenrod module

Construct the beginning of a minimal resolution of the Steenrod-algebra module $(\mathcal{A}/\mathcal{A}\beta)_{\geq k+1}$.

Background

The mod-p cohomology of the symmetric product spectrum \mathbb{Sp}{pk} is expressed using the length filtration on \mathcal{A}/\mathcal{A}\beta. The paper computes initial homotopy groups indirectly through multiplication in the Steenrod algebra and notes that an explicit minimal resolution would provide a more conceptual calculation.

References

What does the beginning of a minimal resolution of the module $(\mathcal{A}/\mathcal{A}\beta)_{\geq k+1}$ look like?

— An abelian model for the Goodwillie tower of the circle  (2609.31269 - Nervo, 25 Sep 2026) in Section 2, subsection “Symmetric products”