Astrophysics White Dwarf Radius Rs

The radius in question

A white dwarf is the collapsed core of a Sun-like star after it exhausts its nuclear fuel. Typical radii are about 0.01 solar radii, roughly 7000 kilometers, close to Earth's size. The framework's research note records an observation: phi^19 times 0.75 kilometers gives 7012 kilometers, matching the typical value. Here phi is the golden ratio, about 1.618, and phi^19 is about 9349. The match is a numerical observation, not a derived result.

The formal content is deliberately modest. It defines a cost function, a measure of recognition effort, as J(m/e), where m and e are real numbers. It then proves three general facts about this cost: it is zero when the two inputs are equal, it is never negative for positive inputs, and the quantity phi minus 3/2 is positive. These are properties of the cost function itself, not of white dwarfs.

In Recognition Science, the framework models physical quantities through such cost functions. The name suggests a connection to white dwarf radii, but the formal proof does not establish that connection. The definition of domainCost uses m and e without specifying what they mean for a white dwarf. The research note is a hypothesis about where the idea might go, not a theorem.

The honest summary: the framework proves three general facts about a cost function and packages them into a certificate structure. It proves nothing specific to astrophysics. The 7012 kilometer match is a suggestion, a direction for future work, not a result. What the framework does establish is that the cost function has the basic properties one would want from a measure of recognition effort.

def domainCost (m e : ℝ) : ℝ := Jcost (m / e)

theorem domainCost_at_eq (r : ℝ) (h : r ≠ 0) : domainCost r r = 0 := by
  unfold domainCost; rw [div_self h]; exact Jcost_unit0

theorem domainCost_nonneg (m e : ℝ) (hm : 0 < m) (he : 0 < e) : 0 ≤ domainCost m e := by
  unfold domainCost; exact Jcost_nonneg (div_pos hm he)

theorem canonicalThreshold_pos : 0 < canonicalThreshold := by
  unfold canonicalThreshold; linarith [phi_gt_onePointFive]

What this page does not claim

The 7012 kilometer match is not a proved result. The framework does not derive the white dwarf radius from first principles. No claim is made that the golden ratio is the actual scaling of white dwarf radii.

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

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Derived articles

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