Astrophysics Stellar Evolution Phases From Config Dim Stellar Evolution Cert

A certificate for five phases

Stellar evolution is the sequence of changes a star undergoes over its lifetime. For a sun-like star, astronomers conventionally recognize five canonical phases: protostar, main sequence, red giant branch, asymptotic giant branch, and white dwarf (or supernova remnant for high-mass stars). This five-phase picture is standard textbook material, taught in every introductory astronomy course.

Within the Recognition Science framework, a machine-checked library of formal theorems encodes this classification as a data type called StellarPhase, with exactly five constructors matching the five phases. The declaration StellarEvolutionCert is a certificate: a formal object that packages the proof that the number of phases equals five. The proof itself is a simple computation, checked by the machine, with no unproven assumptions and no axioms beyond the standard logical ones.

What the certificate does not do is more interesting than what it does. It does not model the physics of stellar interiors, nuclear fusion, or mass loss. It does not predict the duration of any phase, the temperature of a star, or the conditions under which a star becomes a white dwarf versus a supernova. It does not assert that every star follows this sequence, nor that the five phases are the only possible ones. It merely records, in a formally checkable way, that the framework's discrete model of stellar evolution recognizes exactly these five phases for a sun-like star.

The value of such a certificate is not astronomical insight but formal hygiene. It pins down a vocabulary: when the framework talks about stellar evolution, it means these five named phases, and the count is verified rather than assumed. This lets later theorems refer to the phases without re-deriving the count, and it catches any accidental change to the list. The certificate is a small but concrete example of how the framework builds checkable structure on top of ordinary scientific classification.

structure StellarEvolutionCert where
  five_phases : Fintype.card StellarPhase = 5

def stellarEvolutionCert : StellarEvolutionCert where
  five_phases := stellarPhase_count

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 certificate does not model stellar physics, fusion, or mass loss. It does not predict phase durations, temperatures, or evolutionary outcomes. It does not assert that every star follows this exact five-phase sequence.

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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