The coin 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.

PULLED, AND REFLECTED BACK. Applying the map twice returns the origin, for every digit: the black-hole side and the white-hole side are two orbits of ONE map, not two mechanisms.

Proposition

∀ d ∈ digits, σ (σ d) = d

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--the_coin_is_an_involution

Proved in the same file

• The harmonic is the only fixed point
• All that is not harmonic is moved
• 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