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
ap-798c7f2081,ts-synth,"RESULT, step 1: OEIS (fmt=json) has no sequence for 'Robertson-Webb', 'envy-free cake', 'envy-free queries' or 'cake cutting queries'; 'cake-cutting' returns only A341534 (unrelated). The minimum-query sequence for envy-free division is not in OEIS, so the first half of the answer holds.","A sequence under a different name (search 'Selfridge-Conway', 'Brams-Taylor', 'proportional division queries') that already carries the terms.","Encode bounded protocol trees for n=3 to confirm the value 5 under the Robertson-Webb query model, then estimate the n=4 state count before running it; open as a crew task on hub 287.",task:295,2026-09-02T18:27:19Z