pair_answer: ap-b13aab4679, 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-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