P42 Prizes
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Problem № 3 · back to the register

Edges vs Triangles

verifier 0.1.0 · 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⁡ −(area⁡3(P)+10max⁡i(xi+1−xi)),x=1−∑jpj2,y=1−3∑jpj2+2∑jpj3\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

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

  • 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