Cosmology Rs Cosmo Module 012

A template, not a result

Cosmology RS Module 012 is a small file in the Recognition Science library that appears to be about the Spite plateau, the nearly constant lithium-7 abundance observed in old stars. Its header notes that the framework's predicted range, (4.69, 4.86)e-10, overlaps the observed range, (4.0, 5.2)e-10, and marks the comparison as a pass. But the file itself proves no such thing. The module defines a cost function and proves three general facts about it; nothing in the proofs refers to lithium, stars, or cosmology.

The core definition is simple. For two positive real numbers m and e, the module sets domainCost, a measure of mismatch, to J(m/e), where J is the framework's forced cost function. The three proved facts are: the cost is zero when m equals e, the cost is never negative for positive inputs, and the number phi minus 3/2 is positive. Each follows from general properties of J, not from any cosmological input. The module even says so in its own header: it proves nothing specific to this subject, because the cost is defined without reference to one.

The file is one of 2383 sibling modules that share the same body verbatim. The shared content is stated once, universally quantified, in a template module; each sibling is meant to instantiate that template with its own subject. What would turn Module 012 into a theorem about the Spite plateau is a definition of m and e in cosmological terms, for example a predicted lithium abundance and a measured one. No such definition appears here.

In plain language, the module is a placeholder. It establishes that the framework's cost machinery has the basic properties one would want, but it does not establish any claim about lithium-7 or the Spite plateau. The research note records where the idea was meant to go, not a result that arrived.

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]

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

What this page does not claim

The module does not prove that the framework's lithium-7 prediction matches observation. The module does not establish any property of the Spite plateau itself. The module is not a result about cosmology; it is a template instance with no subject-specific content.

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/Cosmology/RS_Cosmo_Module_012.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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