Chemistry Oxidation States Derived Iron Oxidation States Nodup

The iron list

Iron, element 26, is best known for two oxidation states in everyday chemistry: +2 in ferrous compounds and +3 in ferric ones. The element also appears in the zero-valent metallic form and, in rare high-valent complexes, at +6. Collecting these four values into the list [0, 2, 3, 6] is a standard summary of iron's accessible chemistry.

The declaration iron_oxidation_states_nodup establishes one precise fact about that list: it contains no duplicate entries. Each of the four oxidation states appears exactly once. The proof is a direct computation in the framework's machine-checked library of formal theorems, which verifies the claim by evaluating the definition of the list.

In Recognition Science, the list itself comes from a target table, not from a derived law. The framework models iron's accessible oxidation states as a definitional choice, a placeholder for a future derivation. The declaration proves the list has no repeats, but it does not prove that the list is correct, complete, or physically derived. Those remain open targets.

What the declaration does not claim matters as much as what it proves. It does not say iron has only these four oxidation states, nor that the list matches measured chemistry. It only certifies an internal consistency property: the chosen list has no duplicates. The count-law spine that could one day derive the list from valence occupation is available in the library, but this declaration does not invoke it.

/-- Iron's target list has no duplicate oxidation states. -/
theorem iron_oxidation_states_nodup :
    (accessibleOxidationStates 26).Nodup := by
  native_decide

/-- Target accessible oxidation states for selected elements. -/
def accessibleOxidationStates (Z : Nat) : List Int :=
  if Z = 26 then [0, 2, 3, 6]
  else if Z = 25 then [-1, 0, 2, 3, 4, 6, 7]
  else []

/-- The count-law oxidation certificate remains available. -/
theorem oxidation_count_law_available :
    Nonempty OxidationStateFromConfigDim.OxidationStateCert :=
  OxidationStateFromConfigDim.cert_inhabited

What this page does not claim

The list [0, 2, 3, 6] is not claimed to be complete or physically correct. No claim is made that iron cannot exhibit other oxidation states such as +1 or +4. The declaration does not derive the list from any deeper recognition principle.

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/OxidationStatesDerived.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

This page is generated by a question-recursion engine: the questions its answers raise become the next pages. The current agenda, with open targets marked red: