Sharma et al. (2023): Assembly Theory Explains and Quantifies Selection and Evolution

What the work establishes

Sharma et al. present assembly theory as a framework that leaves physics unchanged while redefining the object on which physical laws act. Objects become entities defined by their possible formation histories. This definition makes selection measurable through two observables: the assembly index of an object and its copy number. The assembly index counts the minimal recursive steps needed to build the object from elementary building blocks. Copy number counts identical instances. Their product, called assembly, quantifies the selection required to produce the observed ensemble.

The paper shows that high assembly values appear only when a copying or selection process has operated. Random physical processes rarely generate many identical high-index objects. The theory therefore supplies a forward account of how novelty and selection together produce open-ended complexity without invoking new physical laws.

Core results

The authors define an object as finite, distinguishable, persistent, and breakable. They construct assembly spaces by recursive combination of prior objects. The shortest path in such a space yields the assembly index. They demonstrate the measure on molecules, strings, and discrete component systems. Mass spectrometry can read the index for molecules because it records bond formation history.

Assembly rises sharply when both index and copy number are large. This signature distinguishes evolved or selected ensembles from unselected ones. The framework applies across scales from chemistry to biology and technology. It predicts that functional, copyable objects require prior selection of the mechanisms that produce them.

Exact passages

From the abstract: "We present assembly theory (AT) as a framework that does not alter the laws of physics, but redefines the concept of an ‘object’ on which these laws act."

From the introduction: "In AT, objects are not considered as point particles, but are defined by the histories of their formation as an intrinsic property."

From the assembly theory section: "An object is finite, is distinguishable, persists over time and is breakable such that the set of constraints to construct it from elementary building blocks is quantifiable."

From the assembly index section: "For each object, the most important feature is the assembly index a_i, which corresponds to the shortest number of steps required to generate the object from basic building blocks."

Convergence patterns touched

The work addresses flow networks and memory. Assembly paths are branching structures that record prior construction steps. The assembly index functions as stored history that later steps can reuse. Selection amplifies certain paths, producing the scale-invariant patterns of increasing complexity observed in chemistry and biology. The ladder from difference through structure to memory and life receives a quantitative physical description at the chemical scale.

Distance from the full OIP/GRAIN synthesis

The paper supplies a mechanistic bridge between physics and selection-driven complexity. It quantifies how structural patterns arise and persist without design. It stops short of the mirror layer. It does not model the observer inside the system or address how mind reads the grain. The synthesis therefore extends the framework by adding the reader as an object whose own assembly history participates in the ledger.

Honest limits and disconfirming edges

The measure applies to discrete, breakable objects with well-defined building blocks. Continuous fields and fundamental particles lie outside its current scope. Experimental validation remains strongest for molecules; extension to cells, organisms, or artifacts requires further calibration. The theory does not yet predict which specific objects will be discovered next, only that high-assembly objects indicate prior selection. Reductionist accounts that treat all structure as epiphenomenal remain compatible at the level of fundamental laws; assembly theory adds a higher-order description rather than replacing those laws.