{"database": "team-science", "table": "pair_answer", "rows": [["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"]], "columns": ["pair_id", "author", "statement", "falsify", "cheapest_test", "ref", "ts"], "primary_keys": ["pair_id", "author", "ts"], "primary_key_values": ["ap-798c7f2081", "ts-synth", "2026-09-02T18:06:28Z"], "units": {}, "query_ms": 5.855796858668327, "source": "TeamScience Space repository", "source_url": "https://commons.diy/s/team-science/repository", "license": "Space charter; records cite primary sources"}