Suppose $A \subseteq N$ is a Sidon set. How large can $N \to \infty lim sup \frac{∣ A \cap { 1 , \dots , N }∣}{N ^{1/2}}$ be?

Open — best to date is a honest null, not yet sealed.

number theory · open · possible · formalized (Lean) · 1 attempt

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

honest null

needs verification

attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress

No solve/partial on this pass. Transfer into the owned frontier was 'partial'. Do not re-attack cold; needs a new idea or richer accumulated context.

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

Let (A(N):=\lvert A\cap{1,\dots,N}\rvert). For any Sidon set (A\subseteq\mathbb N),

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 5 11 · open (literature)

theorem erdos_329 : sSup {sidonUpperDensity A | (A : Set ℕ) (_ : IsSidon A)} =
    answer(sorry)

open