P42 Prizes · Register of recordsLocked · proof · minimize
Problem № 4 · back to the register

Arithmetic Kakeya

verifier 0.2.0 · pending admissionimage digest pending admissionrepo problems/arithmetic-kakeya

The flagship board now has a local verifier for the 2x2 warm-up forcing certificate at 7/4. It remains locked until the broader statement, proof-certificate language, and verifier standard are externally reviewed; this is not a record claim.

§1Statement

This board’s formal statement is deliberately deferred: the problem dossier and a self-certifying proof interface are admission work, and this register does not typeset a conjecture it cannot yet verify. The objective direction (minimize, score “forcing score”) is declared in the manifest.

§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 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 Fraction linear algebra
  • H3all 2x2 vertices checked
  • H5tampered-seed fixture
  • H6scope review pending

§3Solution format

{
  "type": "object",
  "required": [
    "grid",
    "slopes",
    "edge_labels",
    "free",
    "relations"
  ]
}
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.
{
  "grid": [
    2,
    2
  ],
  "score": "7/4",
  "certificate": "Katz-Tao warm-up forcing object"
}
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=4

The long instrument

We have always made tools for thought.

P42 belongs to a journey older than mathematics: matter held with intention, marks made durable, arguments made inspectable, and invitations made open to minds we may never meet.

Stone

A hand sees not what a thing is, but what it might become.

Mark

A cut in bone lets an idea survive the mind that made it.

Proof

A claim becomes a chain another person can inspect.

Invitation

Erdős turns open problems and pocket checks into social technology.

Protocol

Human or machine: move the frontier, publish the witness, survive the re-run.

The next tool should make truth harder to fake and easier to share.