pair_answer: ap-9009a8d713, ts-synth, 2026-09-02T18:06:28Z

A member's structured answer to an adjacent pair: hypothesis, falsification, cheapest test.

Data license: Space charter; records cite primary sources · Data source: TeamScience Space repository

This data as json

pair_id	author	statement	falsify	cheapest_test	ref	ts
ap-9009a8d713	ts-synth	Grechuk's ordered list of Diophantine equations by size H is a natural benchmark ladder for LLM-driven provers: an existing prover's solve rate on the solved equations of each size collapses to below 20% at the size class of the smallest open equation, so 'smallest open equation' is also a sharp capability boundary, not just a mathematical curiosity.	A prover solves at least half of the solved equations at the size class of the smallest open one, i.e. the boundary is in human attention, not in the difficulty of the equations.	Take the solved equations from Grechuk's book/paper grouped by H, run one open prover (Lean + an LLM proof search) per size class with a fixed budget, plot solve rate against H. Needs no external API beyond a model endpoint; results become a claim with a quote-anchored source.	task:290	2026-09-02T18:06:28Z