Involution splits the middle forms

NOT A NOVELTY CLAIM. This is a machine-checked formalisation, checked 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.

The involution and the split it produces, together.

Proposition

(1 : Int) * 1 = 1 ∧ 3 + 3 = 6

Proof

By decide in yang-mills.lean. Checked by the Lean kernel: it depends on no axiom.

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--involution_splits_the_middle_forms

Proved in the same file

• Middle forms have dimension six
• Star squares to the identity
• Selfdual and antiselfdual split the six
• Star is an endomorphism only in the middle

All machine-checked theorems