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Establish that Assembly A quantifies the total amount of selection required

Determine whether the Assembly quantity A, computed from assembly indices di and copy numbers ni of each distinguishable object in an ensemble via the assembly equation, captures the total amount of selection required to produce the observed configuration of complex matter.

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Background

Assembly Theory introduces a quantity called Assembly, A, that aggregates contributions from the assembly indices and copy numbers of distinguishable objects in a sample. The authors propose A as a formalization of selection and evolution in assembly space.

They explicitly conjecture that A measures the total amount of selection required to produce the observed objects, making it an open problem to rigorously establish this relationship between A and selection.

References

For an observed configuration of complex matter (e.g., a system that can be broken apart to more basic building blocks), taking account of both the number of copies of distinguishable objects and their assembly indices allows quantifying its Assembly, A, which we conjectured captures the total amount of selection required to produce it.

— Assembly Theory and its Relationship with Computational Complexity (2406.12176 - Kempes et al., 18 Jun 2024) in Assembly Theory, paragraph defining Assembly A (around Eq. 1)