doubling stays in orbit

theorem doubling_stays_in_orbit :
  ∀ d ∈ orbit, dbl d ∈ orbit

Accepted by the Lean 4 kernel. The proof rests on propext, Quot.sound.

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:66
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

• doubling stays in orbit axiom free
• every axis digit mirrors an orbit digit
• every axis digit mirrors an orbit digit axiom free
• orbit and axis and void exhaust the digits
• orbit and axis are disjoint
• orbit and axis are disjoint axiom free
• orbit axis void exhaust the digits axiom free
• orbit closes after six

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.