being an involution is not enough for harmony

theorem being_an_involution_is_not_enough_for_harmony :
  swap12 1 + 1 ≠ swap12 3 + 3

Accepted by the Lean 4 kernel. The proof rests on no axioms at all.

Proven means three things together: the kernel accepted the file, the proof contains no sorry, and #print axioms reports a dependency set within {propext, Quot.sound}. The dependency set above is the evidence, recorded per theorem rather than summarised.

source	lean/DigitSpace.lean:260
archive	doi:10.5281/zenodo.22178675 — the concept DOI, resolving to the newest release
corpus	every statement · the ledger
reproduce	git clone https://github.com/ceccec/zeropoint-node && npm run lean:check

Speaks of the same objects as

• non fixed points come in pairs
• swap12 is an involution
• the mirror is the involution with a constant orbit sum

What this does not establish

A theorem is a statement the kernel accepted. It says nothing about whether the surrounding package is useful, whether the idea is novel, or whether anything physical follows. Novelty is a universal negative no finite search decides; a dated deposit establishes priority, which is the defensible claim.