Cosmology Void Topology From Config Dim Void Topology Cert

The five void classes

Cosmic voids are the large, nearly empty regions that stretch between the filaments of galaxies in the observable universe. Astronomers do not agree on a single way to find them. Different algorithms, each with its own assumptions, carve up the same galaxy catalog into different void boundaries. The five canonical approaches are the VIDE and ZOBOV watershed methods, watershed segmentation, underdensity thresholds, dynamical void finders, and supervoids larger than 100 megaparsecs.

The Recognition Science framework models this classification with a small formal object. Its ledger, a discrete record of events, here records the five classes as a finite list. The declaration VoidTopologyCert establishes that this list has exactly five entries. It proves the count by direct computation: the theorem voidClass_count checks that the cardinality of the finite type VoidClass is 5, and the certificate packages that proof as a structure. The framework's machine-checked library of formal theorems contains the whole construction with zero unproved assumptions.

What the certificate does not do is more interesting than what it does. It does not assert that these five classes are the only possible void finders, nor that they are mutually exclusive. A single void could satisfy both an underdensity threshold and a watershed definition. The certificate does not claim that the five classes are physically distinct kinds of object, only that the framework's formal model lists five named classes. It says nothing about which algorithm works best, how voids form, or whether supervoids are a separate phenomenon or just large underdense regions.

The value of the certificate is bookkeeping, not cosmology. It gives the framework a stable vocabulary for talking about void finders, so that later theorems can refer to the five classes without redefining them each time. A reader who wants to know how voids actually form, or which finder is most reliable, should look to observational astronomy, not to this declaration.

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

structure VoidTopologyCert where
  five_classes : Fintype.card VoidClass = 5

What this page does not claim

The five void classes are exhaustive or mutually exclusive. The certificate says anything about the physical reality of voids. The framework endorses any particular void-finding algorithm.

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)

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Derived articles

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