The instance is an involution

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.

Proposition

∀ d ∈ carrier, σ (σ d) = d

Proof

By decide in involution.lean. The kernel reduces the proposition and reports no axiom dependency.

Sources and identifiers

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

Proved in the same file

• Orbit sums to zero
• Odd vanishes at a fixed point
• EvenPart is symmetric
• The split loses nothing
• The instance cancels over every orbit
• The instance has one harmonic point
• The instance splits without loss

All machine-checked theorems