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Erdős·erdos:571

Erdős Problem 571

problem formal record: solved source: proved (Lean) F2 declared

No independent check recorded yet. A formal artifact, declaration or published object is attached, but no rebuild of it is recorded here.

Fidelity F2: The correspondence is declared through an alignment table and written divergences.

graph theory, turan number·Source

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Claimed on erdosproblems.com

1

Proof claims posted on erdosproblems.com, which says that listing a claim “is no guarantee of proof correctness”. The register records who claims what, with which systems, and links to each claim there. Nobody has examined them, and none counts in the register's totals.

Fidelity

How fidelity is graded

F2 declared. The correspondence is declared through an alignment table and written divergences.

declares divergences from its source

Declared by the projects

1

As each project's formalization.yaml states it.

Erdős problem #571 (rational exponents for Turán numbers of bipartite graphs): prooftadamcz/erdos571 · joined by names · no independent check

Read formalization.yaml

method
autonomous — GPT-6 Astra (pre-release version, OpenAI)
review
other — mechanically verified (comparator: lean kernel replay, standard axioms only) in the benchmark harness and again in this repository's ci; preliminary informal reading of the argument by thomas f. bloom; no independent refereeing (Thomas F. Bloom)
sorry
0 unproved goals declared
sources
Proof of Erdős problem #571: For every rational α ∈ [1,2) there is a bipartite graph G with ex(n; G) ≍ n^α. — other; Erdős problem #571 (erdosproblems.com) — background; Rational exponents in extremal graph theory — background; Cube-supersaturated graphs and related problems — background
related
epoch-research/LeanOpenProblems/blob/77882c437ca1dfefab3b27fa00f1d29788100311/apn/data/erdos_autoformalized/Isolated/Erdos571.erdos_571.lean — builds-on
divergences
The compared theorem is the benchmark's formalisation of the erdosproblems.com statement. `extremalNumber n G` is Mathlib's Turán number (maximum edge count of a `G`-free simple graph on `Fin n`); `G.IsBipartite` is Mathlib's bipartiteness; `Asymptotics.IsTheta atTop` encodes `≍` (two-sided `≪`) for `n → ∞`, with both sides cast to `ℝ` and `n^α` read as the real power `(n : ℝ) ^ (α : ℝ)`. The graph lives on `Fin q`, which loses no generality. No divergence from the informal statement is known. The relation between this proof and the substantial existing literature (Bukh–Conlon and later work) has not yet been worked out.
checked by
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Formal material

Formal statements · 1
Cited proofs · 1
Also known as · 3
  • https://www.erdosproblems.com/571
  • https://github.com/google-deepmind/formal-conjectures/blob/main/FormalConjectures/ErdosProblems/571.lean
  • FormalConjectures/ErdosProblems/571.lean

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qed.bot, “Erdős Problem 571”, https://qed.bot/s/erdos-571, as of 30 Sep 2026.

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