P42 Prizes · Register of recordsLocked · hybrid · minimize

Erdos Min-Overlap

verifier 0.1.0 · pending admissionimage digest pending admissionrepo problems/erdos-min-overlap

Exact-certificate inequality problem from the seed library. The local verifier now recomputes the Hyra upper-bound witness, but the board stays locked until immutable image and N-host admission evidence exist.

§1Statement

M(n) = \min_{\substack{A \subseteq \{1,\dots,2n\} \\ |A| = n}}\ \max_{k \in \mathbb{Z}}\ \#\bigl\{(a,b) \in A \times B : a - b = k \bigr\}, \qquad B = \{1,\dots,2n\} \setminus A

Classical statement shown. The board certifies upper bounds on the limiting constant via an exact rational step-function witness; the frozen functional and normalization live in the problem spec packaged at admission.

§2Verification

The chain does not trust this page.

Authority rests with the problem repo and the canonical verifier command. A revealed solution must reproduce the same exact VerdictReport for every honest runner; claimed scores are stripped and ignored. This board is not yet admitted — its verifier has not passed the gates below.

Conditions precedent to admission

R1integer/rational arithmetic
H1exact normalization
H3all 4799 lags checked
H6reduction lemma review pending

§3Solution format

{
  "type": "object",
  "required": [
    "n",
    "denominator_power",
    "values"
  ]
}

Plate 1. Canonical raw solution schema. Any claimed score fields a solver adds are treated as untrusted comments — the verifier recomputes everything from the raw artifact bytes.

{
  "n": 2400,
  "denominator_power": 82,
  "values": [
    "2400 dyadic integer numerators"
  ]
}

Plate 2. Sample solution shape — illustrative until the board’s repo is packaged at admission.

§4The record

no submissions

No award has yet been made. This board opens for submissions when its conditions precedent close.

ReproduceGET /prizes/api/leaderboard?problem_id=2