The length of an $s$-increasing sequence of $r$-tuples

formal-conjectures · arxiv · ams-5

This file contains the formalisation of [GoLo21] up to and
including Conjecture 1.8.

$F(n) \leq n^{3/2}$.

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/1609.08688
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.cambridge.org/core/journals/combinatorics-probability-and-computing/article/abs/length-of-an-sincreasing-sequence-of-rtuples/7301418D47DB1ECD6BE71C20E8A98D0A
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/Arxiv/1609.08688/sIncreasingrTuples.lean
Local target: Corpus.Arxiv160908688SIncreasingrTuples.maximalLength_le_strong
Source SHA-256: 4cde5b4a0b63992e5f3ec9c0de0883e1cdb687d1b1ffe345aef834b7323ca698
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.

Public JSON record