Cosmology Void Topology From Config Dim Void Class

The five void classes

Cosmic voids are the large, nearly empty regions that sit between the filaments and walls of the galaxy distribution. Astronomers who study them have developed several ways to find and classify these regions, depending on what they are looking for. A census of these methods, as used in the literature, yields five canonical types: VIDE and ZOBOV voids, watershed voids, underdensity voids, dynamical voids, and supervoids, the last being voids larger than about 100 megaparsecs.

The Recognition Science framework's machine-checked library of formal theorems captures this census in a declaration called VoidClass, a finite list of exactly those five kinds. The framework proves, by direct computation, that the list has five members. This is a small but useful result: it turns a working taxonomy into a certified fact, so that any later argument about void topology can rely on the count being exactly five, not approximately five or five for now.

What the declaration does not do is more interesting than what it does. It does not claim that these five classes are the only possible ways to define a void, nor that they are physically fundamental. It does not assert that every void in the universe falls cleanly into one of the five bins. It does not even claim that the five classes are mutually exclusive or jointly exhaustive in an observational sense. The declaration is a formal container for a community's current working vocabulary, not a theory of what voids really are.

The practical payoff is precision. When a researcher says "watershed void" in a paper, the framework's declaration pins down that they mean one of exactly five enumerated types, and that the total count is five. This lets subsequent formal work about void statistics, shapes, or evolution proceed against a fixed, checkable backdrop. The cost of that precision is scope: the declaration certifies a list, and nothing more.

theorem voidClass_count : Fintype.card VoidClass = 5 := by decide

What this page does not claim

The five classes are not claimed to be the only possible void definitions. The declaration does not assert that the classes are physically fundamental or mutually exclusive in observation. It does not claim that every real void fits one of the five bins.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Cosmology/VoidTopologyFromConfigDim.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

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