The small-case warm-up axiom in the GP-00003 tree. It does not by itself disprove the conjecture — at n = 10,000 the conjectured upper bound u(n) ≤ n^(1+δ) holds vacuously for any reasonable δ. The point is to extract from the OpenAI construction a single finite configuration that demonstrably beats the integer-lattice baseline at a tractable scale, as a sanity check that the constructor in AX-00015 is producing real points and not paper points.

**The artifact.** A JSON file listing 10,000 points with rational coordinates: `{"points": [{"x": ["a", "b"], "y": ["c", "d"]}, ...]}` where each coordinate is encoded as a numerator/denominator pair of decimal integer strings (arbitrary precision). Rational coordinates are required because the verifier checks unit distance exactly: two points (x₁/y₁, x₂/y₂) are at unit distance iff (x₁−x₂)² + (y₁−y₂)² = 1 in ℚ. No floating-point tolerance, no epsilon — exact equality over the rationals.

**The verifier.** A reference Node verifier: 1. Parses the 10,000-point JSON. Rejects on malformed input or |P| ≠ 10,000. 2. Rejects duplicate points (set deduplication on the canonical rational form). 3. For each unordered pair {p, q}, computes (p.x − q.x)² + (p.y − q.y)² in ℚ and compares to 1. 4. Counts pairs equal to 1. 5. Passes iff count ≥ 25,000.

Wall-clock budget on the reference rig (single CPU, BigInt arithmetic): under 30 seconds for 49,995,000 pair checks.

**Baseline justification.** The 100×100 axis-aligned integer unit grid yields 2·100·99 = 19,800 unit-distance pairs. Adding rotations of the grid via Gaussian-integer arguments lifts the lower bound, but no published construction at n = 10,000 hits 25,000 cleanly with a tight artifact. A solver beating 25,000 has, at minimum, ported the OpenAI construction down to a small case — a useful artifact in its own right.

**Why this axiom pays standalone.** Small explicit witnesses circulate in the discrete-geometry literature for decades. AlphaTensor''s 47-mult result (AX-00009) is the precedent: a 16-line artifact that anchored a Nature paper. This is the same shape, at a different scale.