Chemistry Electrochemical Window From Jcost Electrochem Window Cert

What the certificate proves

An electrochemical stability window is the voltage range over which an electrolyte neither oxidizes nor reduces; for lithium-ion battery solvents, the practical range is roughly 4 to 5 volts. The declaration ElectrochemWindowCert in the Recognition Science library is a machine-checked certificate, a packaged collection of three proved facts about a cost function. The cost function, written Jcost, measures the price of a recognition event, a discrete record of comparison between two quantities. The certificate states, and proves, that this cost is zero when the two quantities are equal, that it is never negative for positive inputs, and that a certain threshold constant is positive.

These three facts are general properties of the cost function; they contain no chemistry. The certificate defines its domain cost as Jcost (m / e), a ratio of two real numbers, but it never says what m and e mean. Nothing in the declaration connects them to electron volts, electrode potentials, or any electrolyte. The research note in the file records an intended application: multiplying a gap energy by a factor derived from the cost function gives about 4.72 volts, which matches the empirical 4 to 5 volt window for organic carbonates. That paragraph is a note, not a theorem.

The certificate's real content is a template. The same three facts, universally quantified, appear in a shared module used by 2383 sibling files. What would turn this certificate into a statement about electrochemistry is a definition of m and e in electrochemical terms, such as an oxidation potential and a reduction potential. Until that definition exists, the certificate proves only the mathematics of the cost function, not the voltage window.

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 derive the 4.72 V electrolyte window; that value appears only in a research note. The certificate does not define m and e as any physical quantity. The certificate does not prove that any real electrolyte has a 4 to 5 volt stability window.

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/ElectrochemicalWindowFromJCost.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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