Chemistry Carbon Ionization Rs Carbon Ionization Rs

Carbon ionization and the recognition ledger

Carbon's first ionization energy, the minimum energy needed to remove one electron from a neutral carbon atom, is 11.26 electronvolts (eV). Electronvolts measure energy at the atomic scale: one eV is the energy an electron gains moving across a one-volt potential difference. This value is measured spectroscopically and is a standard reference in chemistry and atomic physics. The number appears in tables of atomic properties and in models of chemical bonding and plasma behavior.

The Recognition Science framework defines a cost, a measure of discrepancy between two quantities, written J(x) = (x + 1/x)/2 - 1. The framework's library, a machine-checked collection of formal theorems, proves that this cost vanishes when its two inputs are equal, is never negative for positive inputs, and that the golden ratio phi minus 3/2 is positive. These are general facts about the cost function itself.

In Recognition Science, the framework models the carbon ionization energy as phi^5 eV, which equals 11.09 eV. The measured value is 11.26 eV, so the framework's expression lands about 1.5 percent below the measured value. This near agreement is a research note, not a proved result. The formal declaration CarbonIonizationRS packages the three general cost properties into a structure, but it defines its input as a ratio m/e without specifying what m and e mean for carbon. The theorem proves nothing about carbon specifically.

What the declaration does establish is a template: any subject that can supply its own definitions of m and e inherits the three guaranteed properties of the cost function. For carbon ionization, that subject-specific definition does not yet exist in the library. The near match between phi^5 eV and 11.26 eV is recorded as a research note, a target for future work, not a derivation.

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

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

structure CarbonIonizationRS 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

What this page does not claim

The declaration does not prove that carbon's ionization energy equals phi^5 eV. The 1.5 percent agreement is not a measured result and carries no uncertainty estimate. The template applies to any subject only after that subject supplies its own m and e definitions.

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/Carbon_Ionization_RS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

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