Astrophysics Chandrasekhar Mass Structure Chandrasekhar Implies Ml Upper

The upper bound

The Chandrasekhar mass is the largest mass a white dwarf can hold against gravity before electron degeneracy pressure gives way. In the Recognition Science framework, that mass scale is represented by a quantity called ml_derived, a ledger-derived mass-to-light ratio. The framework's library, a machine-checked collection of formal theorems, proves that if the Chandrasekhar mass structure holds, then ml_derived is less than 5.

The theorem chandrasekhar_implies_ml_upper states: assuming the Chandrasekhar mass structure, ml_derived < 5. The structure itself is defined as the conjunction of two inequalities: 0.5 < ml_derived and ml_derived < 5. The upper-bound theorem extracts the second conjunct directly. It is a formal consequence of the structure definition, proved in the framework's library with no additional assumptions.

The lower bound, 0.5 < ml_derived, is proved separately as chandrasekhar_implies_ml_lower. Together the two theorems bracket ml_derived between 0.5 and 5. The upper bound is the one named in the question, and it is the sharper of the two in the sense that it caps the ratio rather than merely flooring it.

What the theorem does not claim: it does not say that ml_derived is the actual measured mass-to-light ratio of any observed star. It does not assert that the Chandrasekhar mass structure itself is true; the structure is a hypothesis in the framework. The theorem only says that if the structure holds, then the upper bound follows. It also does not specify the physical units of ml_derived; the framework leaves that calibration open.

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

/-- Structural content: mass-scale anchors are positive and finite in RS ladder range. -/
def chandrasekhar_mass_from_ledger : Prop := 0.5 < ml_derived ∧ ml_derived < 5

/-- 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

What this page does not claim

The theorem does not assert that ml_derived matches any observed star's mass-to-light ratio. The theorem does not prove the Chandrasekhar mass structure; it only derives a consequence from it. The theorem does not fix the physical units of ml_derived.

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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