General semi-analytic evaluation algorithm for higher-treewidth construction graphs

Develop a general algorithm and semi-analytic implementation for evaluating graph-zeta construction graphs containing loops, particularly those associated with graph blocks of treewidth at least three.

Background

The graph-zeta framework evaluates series-parallel blocks through rooted construction graphs and a product/convolution algebra. Construction graphs for higher-treewidth blocks contain loops and therefore cannot be evaluated by the same rooted traversal. The paper illustrates a loop-opening and loop-closing procedure for the K4 graph, using additional momentum channels, but does not provide a general semi-analytic implementation for arbitrary higher-treewidth construction graphs.

References

A general algorithm and semi-analytic implementation remains as future work.

— Exact and fast series expansions for quantum models with long-range interactions  (2609.18761 - Duft et al., 16 Sep 2026) in Section 6.4, “Evaluation of construction graphs with loops for highly connected blocks”