Chemistry Sublimation3 From Jcost Sublimation3 Cert

The certificate and its bounds

Sublimation is the phase change in which a solid passes directly to vapor, skipping the liquid state. For a familiar substance such as dry ice (solid carbon dioxide) at ordinary pressure, the enthalpy of sublimation is the energy needed to drive that change, typically reported in kilojoules per mole. Measured values for common materials fall in a wide band, roughly 1 to 100 kJ/mol, with many organic and molecular solids sitting between about 4 and 76 kJ/mol.

The Recognition Science declaration Sublimation3Cert is a formal certificate, a machine-checked bundle of three general facts about a cost function. The cost function here, written domainCost, takes two real numbers m and e and returns J(m/e), where J is the framework's forced cost function. The three bundled facts are: the cost is zero when the two inputs are equal; the cost is never negative when both inputs are positive; and a certain threshold value, phi minus 3/2, is positive, where phi is the golden ratio. Each of these is proved in the framework's machine-checked library of formal theorems.

What the certificate does not do is say anything about sublimation. The definition of domainCost uses the letter m for one input and e for the other, but nothing in the declaration ties m to a mass or e to an energy, and nothing connects the ratio m/e to a sublimation enthalpy. The docstring records a research note, a plan to place sublimation enthalpies on a phi-power ladder, with phi^3 about 4.24 and phi^9 about 76 kJ/mol, but that note is not a theorem. The certificate itself proves only the three general properties, which hold for any positive inputs whatsoever.

In plain terms, the certificate is a reusable scaffold. It establishes that the cost function behaves sensibly at equality and stays nonnegative, and that a particular threshold is positive. Those are true statements about J, and they are available for any future definition that actually connects m and e to a physical system. Until such a definition exists, the certificate is a statement about the cost function, not about chemistry.

structure Sublimation3Cert where
  cost_at_eq : ∀ r : ℝ, r ≠ 0 → domainCost r r = 0
  cost_nonneg : ∀ m e : ℝ, 0 < m → 0 < e → 0 ≤ domainCost m e
  threshold_pos : 0 < canonicalThreshold

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

theorem cert_inhabited : Nonempty Sublimation3Cert := ⟨cert⟩

What this page does not claim

The certificate does not prove any specific sublimation enthalpy value. The research note about phi^3 to phi^9 covering 4 to 76 kJ/mol is not a theorem. The certificate does not define what m or e mean physically.

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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