Chemistry Ethanol Boiling Rs Ethanol Boiling Cert

The certificate's scope

Ethanol boils at 351 kelvin at standard pressure. The declaration EthanolBoilingCert is a formal structure in the Recognition Science framework's machine-checked library. Its name points at that boiling point, but its content is far more general. The certificate packages three proved facts about a function called domainCost, which the framework defines as J(m/e), a cost assigned to a ratio of two positive real numbers.

The three facts are these. First, when the two inputs are equal, the cost is zero: domainCost r r = 0 for any nonzero r. Second, for any positive inputs, the cost is never negative: 0 ≤ domainCost m e whenever m and e are both greater than zero. Third, the number phi minus 3/2 is positive, where phi is the golden ratio. The certificate is inhabited, meaning a proof object exists that satisfies all three conditions. These are the entire contents of the declaration.

The framework's own documentation is explicit about the limit. The declaration proves nothing specific to ethanol, because domainCost is defined as J(m/e) without any reference to a particular substance. The paragraph in the source that mentions phi^12 kelvin and a match to 351 kelvin is a research note, a record of where the idea was meant to go, not a result. The same body of text is shared verbatim with 2383 sibling declarations, each named for a different subject but containing the same three general lemmas.

What would make this declaration a theorem about ethanol is a definition of m and e in chemistry's own terms, for example a definition that ties m to a molecular property and e to a reference energy. That definition does not appear here. The certificate therefore establishes a template, not a chemical fact. A reader who wants the boiling point itself should look to measurement; the framework's contribution here is a reusable scaffold, not a new value for the thermometer.

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 certificate does not prove that ethanol boils at 351 kelvin. The certificate does not establish any relationship between the golden ratio and ethanol's boiling point. The research note's numerical match (phi^7 * 12.1 K = 351 K) is not a proved result.

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/Chemistry/Ethanol_Boiling_RS.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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