All that is not harmonic is moved

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.

EVERYTHING NOT HARMONIC IS MOVED. Eight of the nine digits are carried to the other side.

Proposition

(digits.filter (fun d => !(σ d == d))).length = 8

Proof

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

Sources and identifiers

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

Proved in the same file

• The coin is an involution
• The harmonic is the only fixed point
• The sides are equal and exchanged
• The coin is two sides and one edge
• Every bit of resistance drains
• The harmonic carries no resistance
• The whole surface sums to zero
• The drain is exact at every scale

All machine-checked theorems