520.lean`

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L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

2 declarations, 1 contain sorry, 0 declared as axioms

Erdős Problem 520

References:

erdosproblems.com/520
[Hø26] Høystad, S. W. R., A self-contained Lean 4 proof that Erdős Problem #520 has a negative answer (2026), https://github.com/saasom/Erdos520/blob/v1.1.0/paper/erdos520_note.pdf
[Ha13] Harper, A. J., Bounds on the suprema of Gaussian processes, and omega results for the sum of a random multiplicative function. Ann. Appl. Probab. 23 (2013), 584–616.

Imports (1)

FormalConjecturesUtil

structure Erdos520.IsRademacherMultiplicative A random function line 46 source
Source documentation
A random function $f$ is Rademacher multiplicative if $f(1) = 1$, for each prime $p$, we independently choose $f(p) \in \{-1, 1\}$ uniformly at random (so each $f(p)$ is a measurable function of the sample point), for each square-free integer $n = p_1 \cdots p_r$, $f(n) = f(p_1) \cdots f(p_r)$, and for each non-squarefree integer $n$, $f(n) = 0$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: MeasureTheory.MeasureSpace, Nat, Real
```
structure IsRademacherMultiplicative (f : ℕ → Ω → ℝ) : Prop where
…
```
theorem Erdos520.erdos_520 sorry line 74 source
depends on sorry what this means
Statement uses: Iff, False, Exists, Real, And, GT.gt, OfNat.ofNat, MeasureTheory.MeasureSpace, MeasureTheory.IsProbabilityMeasure, MeasureTheory.MeasureSpace.volume, Nat, Erdos520.IsRademacherMultiplicative, Filter.Eventually, Eq, Filter.limsup, Finset.sum, Finset.Iic, HDiv.hDiv, Real.sqrt, HMul.hMul and 4 more
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
41 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.