the triangles are the residues mod three

theorem the_triangles_are_the_residues_mod_three :
  nonzero.filter (fun d => d % 3 == 1) = triangleOne ∧ nonzero.filter (fun d => d % 3 == 2) = triangleTwo ∧ nonzero.filter (fun d => d % 3 == 0) = axis

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:507
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

• every axis digit mirrors an orbit digit
• every axis digit mirrors an orbit digit axiom free
• every mirror orbit sums to ten
• every mirror orbit sums to ten axiom free
• mirror table is through void
• mirror table is through void axiom free
• orbit and axis and void exhaust the digits
• orbit and axis are disjoint

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.