P42 Prizes · Register of recordsLocked · proof · minimize

Mertens LP Ceiling K12000

verifier 0.1.0 · pending admissionimage digest pending admissionrepo problems/mertens-lp-ceiling-k12000

A queued proof-certificate board for exact residual accumulation and interval-enclosed log terms. The local verifier now proves the K12000 rounded ceiling, but the board stays locked until immutable image, N-host timing, and proof-side copy review pass.

§1Statement

y \ge 0,\ A^{\mathsf{T}} y \ge c \ \Longrightarrow \ \max\{\, c^{\mathsf{T}} x : A x \le b,\ x \ge 0 \,\} \le b^{\mathsf{T}} y

Weak LP duality at k = 12000: an exact dyadic rational dual certificate bounds the Mertens-type LP functional from the problem note; logarithm terms are enclosed in verified intervals, never floats.

§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

R1dyadic rational arithmetic
R6interval log audit
H3all k=2..12000 residuals checked
H5one-ULP vault fixture

§3Solution format

{
  "type": "object",
  "required": [
    "K",
    "M",
    "denom_pow",
    "m",
    "Y"
  ]
}

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.

{
  "K": 12000,
  "M": 120000,
  "denom_pow": 48,
  "m": [
    "dual rows"
  ],
  "Y": [
    "dyadic weights"
  ]
}

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=8