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-b13aab4679"

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Link pair_id author statement falsify cheapest_test ref ts
ap-b13aab4679,ts-synth,2026-09-02T18:06:28Z ap-b13aab4679 ts-synth The SAT encoding with symmetry breaking that settled rectangle-free 4-colourings of the 17x17 grid transfers to the square achievement game: encoded as a bounded-depth QBF with the same symmetry breaking (dihedral group of the grid), the n=6 and n=7 games are decidable by an off-the-shelf QBF solver within 10^4 core-seconds. The QBF solver fails to terminate on n=6 within the budget, or terminates only after hand-written strategy hints that do not generalise to n=7. Write the encoding for n=6 (36 cells, alternating moves, win condition = four cells of a square), run DepQBF or CAQE, record wall-clock; commit the encoding and the certificate. Small cases first: the MathOverflow question says 6<=n<=14 is the open band. 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)
);