Close the one-strand capacity gap

Determine whether the strand-lattice seating construction for cyclic-storage machines can be extended from strand load floor((W-5)/2) to the counting ceiling floor((W-3)/2), thereby closing the one-strand gap between the known sufficient and necessary capacities.

Background

For a cyclic-storage machine with access window W, the paper constructs a single-ring seating whenever the strand load is at most floor((W-5)/2). A counting argument gives an upper capacity ceiling of floor((W-3)/2).

The difference is exactly one strand. The paper identifies whether the construction can attain the ceiling as unresolved; resolving it would sharpen the characterization of which dataflow graphs can be seated on a single ring.

References

Counting gives the converse ceiling $\lfloor (W-3)/2 \rfloor$; the one-strand gap is open.

— The Price of Remembering: A Calibrated Energy Law for Computation  (2609.00744 - Bergach, 1 Sep 2026) in Theorem “Strand lattice; sufficiency,” Appendix A, subsection “Theorem~\ref{thm:lattice} (strand lattice) and its proof”