Astrophysics Rs Astro Module 005 Rsastro005 Cert

The certificate's scope

In the Recognition Science framework, a ledger is a discrete record of events, and its cost is the forced price of recognizing one event from another. The declaration RSAstro005Cert is a machine-checked certificate, a bundled collection of three proved facts about a particular cost function called domainCost. That function takes two positive real numbers, divides the first by the second, and applies the framework's canonical cost function J to the result. The certificate proves that this cost is zero when the two inputs are equal, that it is never negative for positive inputs, and that a certain threshold constant, phi minus 1.5, is positive.

These three facts are general properties of the cost function, not results about any specific physical system. The certificate's own documentation is explicit on this point: the module in which it lives is shared verbatim with 2,383 sibling modules, and the content is stated once in a universal template. What would turn this certificate into a theorem about white dwarfs, or any other astrophysical object, is a definition of the two inputs in that subject's own terms. The module header records a research note suggesting that a white dwarf radius might be about 7,012 kilometers, but that note is a statement of intent, not a proved result.

In Recognition Science, this pattern is deliberate. The framework's library of formal theorems proves structural facts about cost and scaling, and individual modules attach those facts to particular subjects only when they define the relevant quantities. The certificate here establishes the structural facts cleanly and honestly; it does not establish that they apply to white dwarfs. A reader who wants the astrophysical application must look for a module that defines mass and radius in astrophysical terms, which this one does not.

theorem cert_inhabited : Nonempty RSAstro005Cert := ⟨cert⟩

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 certificate does not prove any fact about white dwarf radii. The certificate does not claim that the 7,012 kilometer value is derived or measured. The certificate does not establish that the cost function applies to any specific astrophysical system.

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/RS_Astro_Module_005.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.

Derived articles

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