This manifesto is a living document. Last updated on 2026-05-30.

Infrageometry Manifesto

The purpose of this manifesto is to distinguish Infrageometry from ordinary discrete geometry. The primary question is not how to discretize aspects of a smooth manifold and encode as much geometry as possible combinatorially, or how to associate a geometry to a graph based on its embedding, manifold learning, and coarse equivalence. Even though understanding this pipeline, implementing it, and building bridges to it, for example through bounds that make the associated geometry less fuzzy, are also part of the work, that is not the central question.

Instead, the question is which notions of geometry are native to the discrete substrate and which notions would be developed by a discrete, computationally bounded observer within it. To do that, the existing mathematics that arose historically from macro-observers modeling the macroworld through abstract, idealized, and utterly uncomputable notions is intentionally set aside, and only what is needed and natural at the discrete observer’s scale on sufficiently large graphs is considered. The aim is to explain geometric aspects of the universe, such as dimension, gauge degrees of freedom, observer independence, and relativity, as emergent and persistent aggregate properties of particular (hyper)graphs along certain rewriting paths.

This is also meant to be pursued computationally, with code present at every step. The least complex natural computable geometric notions are defined and implemented, and it is studied whether they can branch out and reproduce structures known from continuous models in the limit of many rewriting steps. This is tested empirically by setting up computational experiments involving the detection of emergent persistent features with respect to defined observables, and the clustering of behaviors across different rewriting paths. In the future, the aim is also to formulate what the limit is and to prove limit theorems about the resulting structures.

The central question is whether the seemingly continuous, unbounded, and unique macroworld might emerge from a discrete substrate characterized by indivisibility, boundedness, and ambiguity. Given physics’ advances in uncovering homogeneous microstructure by probing ever smaller scales, the approach presented here appears to be the most natural way from the point of view of fundamental theories of nature. The aim is not to model macroscopic effects efficiently by starting from idealized notions, but to build a coherent framework in which emergence can be demonstrated.

See the talks in Srní and Madrid for some very early work; see also the Austin conference post (to be published), and stay tuned for more mature work later in 2026.