---
slug: paper-marshall-s-m-moore-d-g-murray-a-r-g-walker-s-i-cronin-l-2022-formalising-the-pat
title: Formalising the Pathways to Life Using Assembly Spaces: Marshall et al. 2022
canonical: https://miscsubjects.com/a/paper-marshall-s-m-moore-d-g-murray-a-r-g-walker-s-i-cronin-l-2022-formalising-the-pat
---

## What the work establishes

Marshall, Moore, Murray, Walker and Cronin formalise assembly spaces as mathematical structures that track the minimum steps needed to build complex objects from basic parts. The work shows how selection in non-equilibrium systems produces objects whose assembly index exceeds what random processes alone can achieve at observable abundances.

Core result: an object carries extrinsic information when its shortest assembly pathway in the space is long and the object appears in high copy number. This combination marks selection rather than chance.

## Exact primary works and passages

The 2022 paper is Marshall, S.M., Moore, D.G., Murray, A.R.G., Walker, S.I. & Cronin, L. Formalising the Pathways to Life Using Assembly Spaces. Entropy 24(7):884.

Key passage from the abstract of the closely related 2019 arXiv precursor (arXiv:1907.04649, which the 2022 paper formalises): "We have developed the theory of pathway assembly to explore the extrinsic information required to distinguish a given object from a random ensemble. To quantify the assembly in an agnostic way, we determine the pathway assembly information contained within such an object by deconstructing the object into its irreducible parts, and then evaluating the minimum number of steps to reconstruct the object."

Another passage: "The Pathway Assembly index (PA) of an object is the length of the shortest pathway to construct the object starting from its basic building blocks."

The 2022 paper supplies the rigorous definitions of assembly spaces as acyclic quivers with reachability relations and proves bounds on the assembly index.

## Convergence patterns touched

The formalism captures branching through combinatorial joining operations. It captures memory through the historical record encoded in the assembly index. It captures selection as the mechanism that populates high-index objects at observable abundances. These patterns align with the grain of reliable structural emergence across scales.

The work stays at the level of objects and their construction histories. It does not yet model the full Ladder from raw difference through flow to mind.

## Distance from the full OIP/GRAIN synthesis

The paper supplies a mechanistic account of how selection produces complex objects inside assembly spaces. This directly supports the OIP unit as work object and the ledger as cumulative assembly history. It remains silent on the Mirror Layer in which the reader participates in the same system. The distance is therefore one of scope, not contradiction.

## Honest limits and disconfirming edges

The model is classical and combinatorial. It assumes permitted joining operations are given in advance. Quantum or continuous dynamics fall outside its current statements. Abundance is required to distinguish selection from rare random events; single high-index objects carry no signature. No empirical threshold for life is derived here; later experimental papers address measurement.

A reductionist objection notes that the assembly index remains a descriptive statistic until tied to specific physical dynamics. The authors leave that linkage for future work.

## How assembly spaces support the synthesis

Assembly spaces make the emergence of structure from selection countable and comparable. An object with high assembly index and high copy number must have traversed a narrow pathway. That pathway records the action of selection on prior objects. The result is a ledger of construction steps that can be replayed and repaired by further selection. This matches the OIP loop at the level of chemical and physical objects.

The work therefore supplies one concrete formal layer beneath the claim that energy flows produce a narrow family of patterns. Branching appears in the quiver edges. Memory appears in the retained sub-objects. Selection appears in the abundance filter.

## What remains open

The formalism does not yet incorporate the reader as participant. It does not address how assembly spaces themselves arise or evolve. It does not quantify the transition from object to agency or to reflective mind. These gaps keep the paper at mechanistic tier for its mathematical claims and leave higher tiers of the synthesis untouched.

Claims in this article are addressable. Readers and models can test the assembly index on new objects, tighten the abundance requirement, or extend the quiver to dynamical systems. Each test either repairs or disconfirms the stated bounds.
