Chemistry Carbon Ionization Rs

Carbon's first ionization energy

Carbon's first ionization energy is the energy needed to remove one electron from a neutral carbon atom, leaving a positive ion. The measured value is about 11.26 electronvolts (eV). In the Recognition Science (RS) framework, the number 11.09 eV appears as phi^5, where phi is the golden ratio, about 1.618. That is 1.5% below the measured value. The framework's own notes call this "CLOSE," but the status is explicit: it is a research note recording where an idea was meant to go, not a result.

The ledger (a discrete record of events) in the framework's machine-checked library of formal theorems proves three general facts about a cost function applied to a ratio of two masses. First, the cost is zero when the two masses are equal. Second, the cost is never negative when both masses are positive. Third, a certain threshold value involving the golden ratio is positive. These are true for any positive numbers, not for carbon specifically, because the cost is defined as a function of a ratio without linking that ratio to any physical quantity.

In Recognition Science, the framework models the cost of recognition as J(x) = (x + 1/x)/2 - 1, which is forced by five plain conditions. The cost function is just this J applied to the ratio m/e. The general theorems follow from properties of J, not from any chemistry. The structure named CarbonIonizationRS bundles these three facts together, and the library proves such a structure exists.

What this means in plain language: the module does not establish anything about carbon. It establishes that the framework's cost function behaves sensibly on positive ratios, which is a prerequisite for any future use, but the connection to ionization energy is a hypothesis awaiting a definition of m and e in chemical terms. The 1.5% gap between phi^5 and the measured value is the distance between a suggestive coincidence and a physical derivation.

noncomputable def cert : CarbonIonizationRS where
  cost_at_eq := domainCost_at_eq
  cost_nonneg := domainCost_nonneg
  threshold_pos := canonicalThreshold_pos

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)

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

What this page does not claim

The module proves no fact specific to carbon or ionization. The 11.09 eV value is not a derived prediction, only a noted coincidence. The framework does not yet provide a physical definition of m and e for this system.

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)

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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