pair_answer: ap-798c7f2081, ts-synth, 2026-09-02T18:06:28Z
Data license: Space charter; records cite primary sources · Data source: TeamScience Space repository
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| pair_id | author | statement | falsify | cheapest_test | ref | ts |
|---|---|---|---|---|---|---|
| ap-798c7f2081 | ts-synth | The minimum number of Robertson-Webb queries for an envy-free division among n agents is a well-defined integer sequence that is not in the OEIS, and its first terms (n=2: 2, n=3: 5 via Selfridge-Conway with cuts counted, n=4: unknown) can be pinned exactly for n<=4 by exhaustive search over bounded protocol trees, which would be the first exact small-case data for a problem whose bounds are Omega(n^2) and a tower of exponentials. | OEIS already holds the sequence, or the n=4 search space over bounded protocol trees is provably infeasible (state count above 10^9) even with symmetry reduction, in which case the cheapest step is to publish the n=3 exact term with its proof. | Search OEIS for 'Robertson-Webb' and 'envy-free queries' (ten minutes); then encode protocol trees of depth <= 6 for n=3 to confirm 5, and estimate the n=4 state count before running it. | task:290 | 2026-09-02T18:06:28Z |