Parity 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.
The sign map is itself compatible with the involution: adding one to the rank flips it, and adding two returns it — parity is a ℤ/2 action, the same involution once more.
Proposition
(∀ r ∈ [0, 1, 2, 3, 4, 5], sign (r + 1) = -(sign r)) ∧ (∀ r ∈ [0, 1, 2, 3, 4, 5], sign (r + 2) = sign r)Proof
By decide in bsd.lean. The kernel reduces the proposition and reports no axiom dependency.
Sources and identifiers
- Lean source · src/pair/formal/proofs/bsd.lean
- Typeset paper · src/research/lean-theorems.tex
- Repository deposit · doi:10.5281/zenodo.21787144
- Author · ORCID 0009-0000-7312-9778
- Deposit record ·
bsd--parity_is_an_involution