P42 Prizes · Register of recordsLocked · construction · minimize

Distinct Subset Sums a(11)

verifier 0.1.0 · pending admissionimage digest pending admissionrepo problems/distinct-subset-sums-a11

Erdos problem #1 / OEIS A276661. The seed is the Conway-Guy-lineage set with max 594; the verifier exhaustively checks all 2^11 = 2048 subset sums for distinctness. a(11) is open with the bracket 310 <= a(11) <= 594, so any valid witness scoring below 594 improves the published upper bound. The board stays locked until an immutable image and N-host admission evidence exist.

§1Statement

a(11) = \min\ \max(S) \quad \text{over } S = \{s_1 < \cdots < s_{11}\} \subset \mathbb{Z}_{\ge 1} \text{ with all } 2^{11} \text{ subset sums distinct}, \qquad 310 \le a(11) \le 594

The lower bound 310 (optimum) is the prefix lemma over the closed value a(10) = 309 (Dyson 2025); it is metadata, not a verifier check. Validity is decided solely by exact recomputation of the 2048 subset sums.

§2Verification

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

Conditions precedent to admission

R1exact integer subset sums
R2ignores claimed score fields
H3all 2048 subset sums enumerated
H5lying-claim fixture included

§3Solution format

{
  "type": "object",
  "required": [
    "set"
  ]
}

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.

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=12

Distinct Subset Sums a(11)

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Conditions precedent to admission

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Stone

Mark

Proof

Invitation

Protocol