---
slug: paper-marshall-s-m-murray-a-r-g-cronin-l-2017-a-probabilistic-framework-for-identifyin
title: Marshall, Murray & Cronin 2017: Pathway Complexity as a Biosignature Threshold
canonical: https://miscsubjects.com/a/paper-marshall-s-m-murray-a-r-g-cronin-l-2017-a-probabilistic-framework-for-identifyin
---

## What the work establishes

Marshall, Murray and Cronin define Pathway Complexity as the length of the shortest sequence of joining operations that assembles a target object from a set of basic subunits. The measure counts the minimum joins required while allowing reuse of intermediate structures. An object reaches a biosignature threshold when its abundance exceeds the probability of forming via any abiotic pathway of that length.

The framework models assembly as a graph process. Subunits are vertices. Joins add edges. The Pathway Complexity equals the minimum steps across all possible assembly sequences. High values combined with observed abundance indicate a non-random trajectory through state space.

Core result: living systems and their products produce objects whose formation probability falls below any reasonable abiotic expectation once Pathway Complexity exceeds a calculable bound. The bound derives from the combinatorial explosion of alternative structures at each join step.

## Exact primary passages

Abstract: "In this paper, we present a new type of complexity measure, Pathway Complexity, that allows us not only to threshold the abiotic-biotic divide, but to demonstrate a probabilistic approach based upon object abundance and complexity which can be used to unambiguously assign complex objects as biosignatures."

Section on Pathway Complexity as a Biosignature: "The motivation for the formulation of Pathway Complexity is to place a lower bound on the likelihood that a population of identical objects could have formed abiotically from an initial pool of starting materials, i.e. without the influence of any biological system or biologically derived agent."

Same section: "If we find anything significantly above the threshold then this, we propose, is a general biosignature. By searching for complexity alone, whether of molecules, objects, or signals, we don’t have to make any assumptions about the details of the biology or its relation to our own biology."

## Convergence patterns touched

The measure formalizes selection on assembly pathways. Energy-driven flows generate structures; only certain pathways sustain abundance against combinatorial dilution. This maps to branching and flow-network patterns in chemical state space. It quantifies the step from raw difference (subunit variety) to structured memory (reused intermediates) without presupposing life.

## Distance from the full synthesis

The paper supplies a concrete metric for the transition from abiotic flow to selectable structure. It remains silent on later Ladder stages such as explicit memory encoding or observer participation. It treats the detection problem from outside the system and does not address the Mirror Layer.

## Honest limits and disconfirming edges

The model assumes idealized joining rules and uniform probability across pathways. Real chemistry includes energetic biases and kinetic traps that can alter effective thresholds. The 2017 framework is theoretical; experimental calibration appears in later assembly-theory papers. No empirical dataset of abiotic versus biotic samples is presented here. Reductionist objections note that any threshold remains model-dependent until exhaustive enumeration of alternative pathways is feasible.

## Claims

- Pathway Complexity counts the shortest sequence of joining operations from defined subunits. [mechanistic]
- Abundance of high-Pathway-Complexity objects supplies a probabilistic biosignature. [mechanistic]
- The approach requires no assumptions about specific biochemistry. [anecdotal]
- Living systems sustain non-trivial trajectories in state space. [speculative]
- The bound derives from combinatorial explosion at each assembly step. [mechanistic]
