Astrophysics Galaxy Morphology Types From Config Dim Galaxy Morphology

A formal census of galaxy shapes

Astronomers have long sorted galaxies by their visual appearance into a handful of broad classes. The Hubble sequence, introduced by Edwin Hubble in 1926, runs from round ellipticals through lens-shaped lenticulars to spirals with their arms, and ends with the catch-all irregulars. A barred spiral is a spiral whose arms emerge from a straight bar of stars across the nucleus. These five families, elliptical, lenticular, spiral, barred spiral, and irregular, are the standard vocabulary of galaxy morphology in textbooks and survey catalogs alike.

The Recognition Science framework's library, a machine-checked collection of formal theorems, contains a small declaration called GalaxyMorphology that encodes exactly this classical list. The declaration is an inductive type, a formal way of saying these are the five allowed cases and no others. A companion theorem, galaxyMorphology_count, proves that the number of these types is five. The proof is a direct computation, checked by the machine, with no unproved assumptions and no axioms beyond the standard logical ones. A separate certificate structure packages this count as a reusable fact.

What the declaration establishes is narrow and precise: within the framework's formal language, there exists a defined object with exactly five members, matching the five Hubble classes. It does not claim that real galaxies fall neatly into these bins, that the classes are physically fundamental, or that the framework derives the Hubble sequence from deeper principles. The declaration is a definitional choice, a formal mirror of a working astronomer's taxonomy, not a discovery about the cosmos. The count theorem is real, but it counts the members of a formally declared set, not the galaxies in the sky.

The value of such a declaration is bookkeeping. It gives the framework a fixed, unambiguous vocabulary for talking about galaxy shapes, so that other formal statements can refer to elliptical or spiral without drifting definitions. It also demonstrates that the framework can host ordinary scientific classifications alongside its more ambitious results. The practical consequence for a reader is simple: when the framework's library mentions a galaxy morphology type, it means one of these five, and the machine has verified that there are no others in the formal system.

theorem galaxyMorphology_count :
    Fintype.card GalaxyMorphology = 5 := by decide

inductive GalaxyMorphology where
  | elliptical
  | lenticular
  | spiral
  | barredSpiral
  | irregular
  deriving DecidableEq, Repr, BEq, Fintype

def galaxyMorphologyCert : GalaxyMorphologyCert where
  five_types := galaxyMorphology_count

What this page does not claim

The declaration does not claim that real galaxies are perfectly described by these five classes. It does not claim that the Hubble sequence is physically fundamental or derived from first principles. The count theorem counts formal members, not galaxies observed in the sky.

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/Astrophysics/GalaxyMorphologyTypesFromConfigDim.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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