formal-conjectures · arxiv · ams-51 · ams-70
Atiyah and Sutcliffe associate a homogeneous binary polynomial to each point
in a configuration of distinct points in Euclidean three-space. Their first
conjecture says that these polynomials are always linearly independent.
Atiyah–Sutcliffe Conjecture 1, stated as
Conjecture 1.1 in Mazur–Petrenko: the configuration
polynomials are linearly independent.
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://doi.org/10.1098/rspa.2001.0913
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://arxiv.org/abs/1102.4662
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Arxiv/1102.4662/AtiyahSutcliffe.lean
Local target: Corpus.Arxiv11024662AtiyahSutcliffe.conjecture_one
Source SHA-256: 34ed31a91d32f45282f87c1c83471d7f2703e97d67a9670b404c06f5761216d4
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.
[Atiyah–Sutcliffe Conjecture 1](https://doi.org/10.1098/rspa.2001.0913), stated as Conjecture 1.1 in [Mazur–Petrenko](https://arxiv.org/abs/1102.4662): the configuration polynomials are linearly independent.
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