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Edges vs Triangles

verifier 0.1.2 · pending admissionimage digest pending admissionrepo problems/edges-vs-triangles

A queued arena-derived board now packaged as a deterministic P42 verifier. It scores finite rational row distributions by exact edge/triangle moments, slope-3 area, and max-gap penalty; it stays locked until immutable image, N-host matrix, and external model review exist.

§1Statement

\max\ -\left(\operatorname{area}_{3}(P) + 10\max_i (x_{i+1}-x_i)\right), \qquad x=1-\sum_j p_j^2,\quad y=1-3\sum_j p_j^2+2\sum_j p_j^3

This is a rationalized P42 package for the documented slope-3 verifier model, not a recovered copy of the missing historical Arena incumbent artifact. The exact scope is frozen in the package spec before any funding gate can open.

§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

R1Fraction-only density and area arithmetic
H1fixed row-sum normalization
H3all canonical slope-3 segments checked
H5claimed-score trap
H6historical artifact scope review pending

§3Solution format

{
  "type": "object",
  "required": [
    "atoms",
    "row_sum",
    "rows"
  ]
}

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.

{
  "atoms": 20,
  "row_sum": 1000,
  "rows": [
    "up to 500 rows of 20 integers summing to 1000"
  ]
}

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=3

Edges vs Triangles

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Conditions precedent to admission

We have always made tools for thought.

Stone

Mark

Proof

Invitation

Protocol