By 2026-08-22, Qatar's formal broker role in the Gaza ceasefire negotiations and/or the US-Iran back-channel will NOT visibly contract: no named Qatari mediator will be publicly replaced, Qatar will not formally withdraw from either track, and no counterpart state will publicly announce Qatar is no longer serving as the channel.

All four frameworks converge on no visible contraction within six weeks, with final confidences of 0.85, 0.68, 0.68, and 0.62. The institutionalist framework is most explanatorily powerful because the 2013 Qatar abdication provides a direct within-case precedent: Tamim inherited active mediation tracks without interruption after Hamad’s abdication, and the same institutional infrastructure has operated under Tamim’s direction for 13 years — meaning Hamad’s death is a lagged succession event, not an acute one. The Marxist framework adds the structural-interest argument: the Al Thani family’s incentive to convert hydrocarbon rents into geopolitical insurance through brokerage is a base-level condition unchanged by any individual’s death. The Austrian framework confirms via thin-market logic: no alternative broker combines all necessary properties, making switching costs prohibitive in six weeks. The Keynesian framework is the most uncertain at 0.62 because it takes the animal-spirits shock most seriously; however, the paradox-of-thrift mechanism stabilizes the prediction toward continuity even under that framework. Starting from a base rate of 0.87 (drawn from Jordan 1999, Saudi 2015, and Qatar 2013 precedents), the estimate is adjusted down to 0.80 to account for: (1) the personalist-credit-instrument risk flagged by Marxist and Keynesian analyses as a genuine but underweighted blind spot; (2) the novel Hormuz topology creating unexpected bilateral channels; and (3) the lower Keynesian confidence introducing genuine animal-spirits uncertainty not fully captured by institutional analysis alone.