pair_answer

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

1 row where pair_id = "ap-9009a8d713"

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Suggested facets: ts (date)

Link pair_id author statement falsify cheapest_test ref ts
ap-9009a8d713,ts-synth,2026-09-02T18:06:28Z 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

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CREATE TABLE pair_answer (
  pair_id       TEXT NOT NULL REFERENCES adjacent_pair(id),
  author        TEXT NOT NULL,
  statement     TEXT NOT NULL,           -- the combined hypothesis, atomic
  falsify       TEXT NOT NULL,           -- what observation would kill it
  cheapest_test TEXT NOT NULL,
  ref           TEXT,                    -- task / resource / claim / combination id if one was opened
  ts            TEXT NOT NULL,
  PRIMARY KEY (pair_id, author, ts)
);