Astrophysics Chandrasekhar Mass Structure

The mass-to-light bound

The Chandrasekhar limit is the maximum mass a white dwarf star can hold before gravity overwhelms electron degeneracy pressure. Subrahmanyan Chandrasekhar derived it in 1930, showing the limit sits near 1.4 solar masses. Above that mass, a white dwarf must collapse into a neutron star or black hole. The limit is a key part of stellar astrophysics because it draws a hard line between stable stellar remnants and catastrophic collapse.

In Recognition Science, the framework models the same physical boundary through a discrete record of events called a ledger, a finite accounting of recognition events that reality keeps. The framework's library of machine-checked formal theorems contains a module named ChandrasekharMassStructure. That module defines a derived mass-to-light ratio, written ml_derived, and proves a structural theorem about it. The theorem states that the derived ratio lies strictly between 0.5 and 5.

The proof is short and direct. The module defines the property chandrasekhar_mass_from_ledger as the conjunction of two inequalities: ml_derived is greater than 0.5 and ml_derived is less than 5. The theorem chandrasekhar_mass_structure establishes this property holds, and two further theorems unpack it. One proves the lower bound, ml_derived > 0.5. The other proves the upper bound, ml_derived < 5. Both follow immediately from the definition by extracting the two conjuncts.

What this establishes in plain language is a bounded mass-to-light ratio for the Chandrasekhar-mass regime. The framework does not derive the numerical value 1.4 solar masses from first principles. Instead, it shows that the mass-to-light ratio derived from its ledger structure falls in a finite, positive range. That range is consistent with the observed white dwarf population, where mass-to-light ratios are neither vanishingly small nor arbitrarily large.

The practical consequence is a structural constraint, not a numerical prediction. The framework proves that any system governed by its recognition ledger must produce a mass-to-light ratio in that bounded interval. This is a theorem about the framework's own derived quantity, grounded in the machine-checked library. It does not replace the standard astrophysical derivation, but it shows the Chandrasekhar boundary is compatible with the framework's discrete accounting structure.

theorem chandrasekhar_mass_structure : chandrasekhar_mass_from_ledger :=
  ml_in_observed_range

/-- Chandrasekhar-mass structure implies lower mass-to-light bound. -/
theorem chandrasekhar_implies_ml_lower (h : chandrasekhar_mass_from_ledger) :
    0.5 < ml_derived :=
  h.1

/-- Chandrasekhar-mass structure implies upper mass-to-light bound. -/
theorem chandrasekhar_implies_ml_upper (h : chandrasekhar_mass_from_ledger) :
    ml_derived < 5 :=
  h.2

What this page does not claim

The framework does not derive the numerical value 1.4 solar masses from first principles. The module does not prove any claim about actual observed white dwarf stars. The mass-to-light ratio ml_derived is not identified with any standard astrophysical observable.

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

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