The whole surface sums to zero

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.

AND THE WHOLE SURFACE DRAINS AT ONCE. Summed over every digit, resistance is zero — the two sides cancel exactly, which is the sentence's "measured to drain" as an arithmetic identity.

Proposition

(digits.map resistance).sum = 0

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_whole_surface_sums_to_zero

Proved in the same file

• The coin is an involution
• 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 drain is exact at every scale

All machine-checked theorems