Chemistry Sublimation3 From Jcost

Sublimation enthalpies

Sublimation is the phase change in which a solid passes directly into a gas, skipping the liquid state. Dry ice turning into carbon dioxide vapor at room temperature is the familiar example. The energy required to make that change happen, per mole of substance, is the sublimation enthalpy, measured in kilojoules per mole. For ordinary solids the values run from about 1 to 100 kJ/mol, with molecular crystals like naphthalene at the low end and metals like zinc at the high end.

In Recognition Science, the framework models this energy scale with a discrete record of recognition events, called the ledger. The central object is the cost function, which assigns a nonnegative price to any mismatch between two quantities. The framework's cost function J(x) = (x + 1/x)/2 - 1 measures the price of a ratio x being different from 1. It is zero exactly when the two quantities are equal, and it grows as the ratio moves away from 1 in either direction.

The module chemistry-sublimation3-from-jcost defines the domain cost as J(m/e), where m is a molar mass and e is a reference value. It establishes three general facts about this cost: it vanishes when m equals e, it is never negative for positive inputs, and the golden ratio minus 3/2 is positive. These are facts about the cost function itself, not about any particular substance. The module does not define m or e in chemical terms, and it establishes nothing specific to sublimation.

The research note in the module records where the idea was meant to go. The framework's phi-ladder suggests that sublimation enthalpies should fall on powers of the golden ratio phi, about 1.618. The note lists phi^3 = 4.24, phi^6 = 17.9, and phi^9 = 76 kJ/mol, and observes that this range covers 4 to 76 kJ/mol, consistent with the observed 1 to 100 kJ/mol band. That is a hypothesis, not a theorem. The module itself contains no definition tying m and e to actual substances, so the chemical claim is not yet established.

What the module does establish is the mathematical skeleton: a cost function that is zero at equality, nonnegative everywhere, and a positive threshold constant. The chemical content, the identification of m and e with real molar masses, remains a target for future work.

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 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 establish that any real sublimation enthalpy equals phi^k kJ/mol. The module does not identify m or e with any specific substance's molar mass or reference energy. The module does not establish the phi-ladder as a measured law of chemistry.

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/Sublimation3_FromJCost.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.

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