Astrophysics Stellar Evolution Phases From Config Dim Stellar Phase Count

A count of five phases

Astronomers divide a star's life into recognizable stages. For a star like the Sun, the standard sequence runs from protostar, through main sequence, to red giant branch, then asymptotic giant branch, and finally to a white dwarf. A machine-checked library of formal theorems, called the Recognition Science framework, encodes this familiar list as a finite set and verifies that the set has exactly five members. The declaration stellarPhase_count states that the number of phases is five, and the verification is a direct computation: the framework's software checks every case and confirms the count.

The five-phase list is not new astronomy. It is the textbook summary of stellar evolution for a solar-mass star, and the framework's contribution is to represent that summary as a formal object. The declaration StellarPhase (a named collection of the five stages) is defined, and the count is then verified for its size. A separate certificate structure wraps the count so that other formal results can rely on it without rechecking. The work is axiom-clean: the library reports zero unproved assumptions and zero axioms beyond the standard logical foundations.

In Recognition Science, this count connects to a broader claim about the number of spatial dimensions. The framework derives, from its cost-based foundations, that three spatial dimensions are forced, and it links that result to a recognition cycle with eight ticks. The stellar-phase count of five is presented in the same library as a separate, smaller structural fact: a five-stage list for one kind of star. The framework models the astrophysical sequence as a finite type, and the count establishes the cardinality of that model.

What the declaration does not claim is just as important. It does not establish that every star passes through exactly five phases, nor does it say anything about high-mass stars, which may end in a supernova and leave a neutron star or black hole. The five-phase list explicitly includes a white dwarf or remnant for the solar case, and the framework's own note mentions the supernova alternative for higher masses. The declaration also does not derive the phase count from first principles; it takes the five-stage list as a definitional choice and then verifies the count of that chosen list.

The practical upshot is a small, verified building block. Any later formal argument that needs the number of stellar phases can cite this declaration and know the count is machine-checked. The framework's larger claims about dimensions and cycles remain separate; this declaration is a modest, exact statement about a familiar astronomical sequence.

theorem stellarPhase_count : Fintype.card StellarPhase = 5 := by decide

inductive StellarPhase where
  | protostar
  | mainSequence
  | redGiantBranch
  | asymptoticGiantBranch
  | whiteDwarfOrRemnant
  deriving DecidableEq, Repr, BEq, Fintype

theorem stellarPhase_count : Fintype.card StellarPhase = 5 := by decide

What this page does not claim

The declaration does not establish that every star passes through exactly five phases. The declaration does not derive the five-phase count from first principles; it takes the list as a definitional choice. The declaration says nothing about high-mass stars, which may end in a supernova and leave a neutron star or black hole.

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/StellarEvolutionPhasesFromConfigDim.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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