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The Conceptual Move
An object’s complexity is not what it is made of or how it behaves but how many steps were needed to construct it from basic building blocks. The move is structural and specific: complexity is relocated from the properties of the finished object to the trajectory that produced it.
Sara Walker’s formulation: “The information is in the path, not the initial conditions.”
The starting observation is Cronin’s: complex molecules cannot just emerge into existence because the combinatorial space of possible constructions is too vast. A molecule of moderate complexity could in principle be assembled through an astronomically large number of different sequences of operations; most of those sequences will never be traversed. The fact that a particular complex molecule exists in quantity tells you something about the history that produced it — a history of selection, retention, and reuse.
The formal apparatus implements this move. Each element directly encodes the claim that construction history is what is being measured.
Assembly index (A)
The minimum number of joining operations required to construct an object from elementary building blocks. A molecule with an assembly index of 12 requires at least twelve joining steps; no shorter path exists. The index measures the depth of construction — how far from basic building blocks the object sits.
Assembly pathway
The actual sequence of operations that constructs the object. Multiple pathways may yield the same object; the assembly index is the length of the shortest. The distinction matters: what the theory measures is the minimum historical depth, not the actual route taken.
Copy number (n)
How many copies of an object are present in a sample. Multiple copies require having found and reused the construction route — they carry memory of the pathway. A single copy of a complex molecule could be a fluke; many copies of it indicate that the construction route has been retained and repeated.
Assembly equation
Total assembly increases with both index and copy number, weighted as defined in the theory. The combination encodes how much historical depth a population of objects carries. High index with high copy number indicates deep construction history that has been reliably reproduced.
The apparatus gives the conceptual move its formal teeth. What follows from it — the biosignature claim that high assembly index signals selection, and the metaphysical extension that time is a material property of objects — each builds on this foundation.