Middle forms have dimension six

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, decided by the Lean 4 kernel and depending on no axiom. It is dated and citable. Prior art, where it exists, is cited below. No discovery is claimed.

dim Λ²(ℝ⁴) = 6 — the middle degree in four dimensions, where ★ maps 2-forms to 2-forms.

Proposition

choose 4 2 = 6

Proof

By decide in yang-mills.lean. The kernel reduces the proposition and reports no axiom dependency.

Sources and identifiers

• Lean source · src/pair/formal/proofs/yang-mills.lean
• Typeset paper · src/research/lean-theorems.tex
• Repository deposit · doi:10.5281/zenodo.21787144
• Author · ORCID 0009-0000-7312-9778
• Deposit record · yang-mills--middle_forms_have_dimension_six

Proved in the same file

• Star squares to the identity
• Selfdual and antiselfdual split the six
• Star is an endomorphism only in the middle
• Involution splits the middle forms

All machine-checked theorems