formal-conjectures · arxiv · ams-11 · ams-26
If $n = ab$ is a crystal, then there are no other pairs of
positive integers $c, d > 1$, different from the couple $a, b$, such that $n = cd$ and
$B(c, d) ∈ ℕ$, i.e., the components of the crystals are unique.
Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).
Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.
Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/1601.03081
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Arxiv/1601.03081/UniqueCrystalComponents.lean
Local target: Corpus.Arxiv160103081UniqueCrystalComponents.crystals_components_unique
Source SHA-256: 06c09f24018f5f79d02038f75313cdf79544c13479feafdf638ffbc4b1ad3936
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.
Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.
If $n = ab$ is a crystal, then there are no other pairs of positive integers $c, d > 1$, different from the couple $a, b$, such that $n = cd$ and $B(c, d) ∈ ℕ$, i.e., the components of the crystals are unique.
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