Chemistry Acetone Boiling Rs

Acetone's boiling point

Acetone, the simplest ketone, boils at 329 kelvin at standard pressure. That is the temperature at which its vapor pressure equals the surrounding atmospheric pressure, so bubbles of vapor can form throughout the liquid. The value is a measured property of the molecule, determined by the strength of the intermolecular forces between acetone molecules, mainly dipole-dipole interactions and London dispersion forces.

The module named chemistry-acetone-boiling-rs does not establish that value. Its own documentation states this plainly: the Lean code proves three general facts about a cost function (a measure of the price of recognition, a discrete record of events), and it proves nothing specific to acetone. The definition domainCost m e := Jcost (m / e) takes two real numbers and applies the framework's universal cost function to their ratio. It never defines what m and e mean for acetone, so the module cannot connect the mathematics to the chemistry.

What the module does prove, with machine-checked certainty, are three properties of that cost function. First, when the two inputs are equal, the cost is zero. Second, for positive inputs, the cost is never negative. Third, the golden-ratio-derived constant phi - 3/2 is positive. These are general theorems about the cost function, not about acetone. The module bundles them into a certificate structure, which is a way of packaging the three proofs together.

The research note at the top of the file records an idea: that phi^12 kelvin, about 321.9 K, is close to acetone's boiling point, off by about 2.2 percent. The note also mentions a second expression, phi^7 * 11.34, which gives exactly 329 K. But the note is explicitly labeled as a research direction, not a result. No theorem in the module connects either expression to the boiling point, and no definition of m and e in acetone's own terms exists.

In Recognition Science, the framework models physical quantities through a forced cost function. A genuine theorem about acetone's boiling point would require defining m and e from molecular properties, such as molar mass or intermolecular potential well depth. That definition does not exist here. The module therefore is a template, shared verbatim with 2383 sibling modules, showing the general shape a subject-specific proof would take.

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)

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 module does not derive or prove acetone's boiling point. The phi^12 expression is a research note, not a theorem. No definition of m and e in acetone's own terms exists in this module.

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/Acetone_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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