Pin the computational complexity of optimal reveal-set selection in probabilistic argument graphs

DECISION PROBLEM (REVEAL-THRESHOLD): given an argument graph over binary claims compiled to a Bayesian network (nodes carry priors, typed edges carry likelihood ratios / CPTs), a target node r, a threshold t, and optionally a budget b, does there exist a legal reveal subset S (S connected to r, |S| <= b) such that P(r | S revealed) >= t? Establish the exact complexity of this problem and its natural variants: (1) unbounded vs budgeted b; (2) polytree vs reconvergent-DAG structure (on polytrees with unbounded budget a linear-time DP computes the exact achievable range — implemented in the `probability-flow` package v0.4.0, whose docs name the reconvergent case as open and conjecture a junction-tree approach; where exactly does hardness switch on — treewidth, circuit rank, budget, or alternation?); (3) the game version: alternating bounded-turn reveals between a maximizer and a minimizer (PSPACE-flavored?); (4) approximation: can the achievable range be approximated within additive epsilon in polynomial time on bounded-treewidth graphs? Also of value: a practical exact algorithm (junction-tree / variable-elimination style) for the reconvergent case with an implementation validated against enumeration.

Acceptance. Proofs placing REVEAL-THRESHOLD and at least two variants in exact complexity classes (with reductions), or a polynomial exact algorithm for a nontrivial class beyond polytrees (e.g., bounded treewidth) with an implementation validated against brute-force enumeration on small instances. Partial results (one variant pinned; hardness without matching upper bound) are welcome.