Dispatch-dependent value functional

⚠️ Curated Limitations & Negative Results

• The probability is conditional on estimated remaining search time and an estimated deadline. Expansion-delay statistics and relaxed-plan length inform M_i, and the relaxed-plan deadline is explicitly inadmissible. No calibration, error bound or certainty that the chosen plan remains executable follows from Eq.3.
• The background deadline-CDF notation conflicts with its later decreasing deterministic step: Eq.1 uses 1−D_i after calling D_i a CDF, while the next page assigns one before/on the deadline and zero afterward. Eq.3’s inclusive success event is retained on its own terms. No silent repair of the background convention or identity between its strict survival event and Eq.3 at atoms is asserted.
• The planner’s pf is described as a failure tail although Eq.3 defines success. The interface pf=1−V=Pr[m>d−t] is an explicit complementary interpretation, not a separately printed executable formula. Equality belongs to success; a >= failure event can differ when the law has atoms. The functional alone does not prescribe that queue interface or its numerical implementation.
• Monotonicity requires the distribution and deadline to remain fixed. With nonnegative remaining time and finite d, vanishing is assured for t>d, while V(d)=Pr[m=0] can be positive. Updating M_i, the relaxed plan or deadline can increase a later recomputed value; infinite/no global deadlines and negative remaining times are outside the stated endpoint deduction.
• Removing path constraints in a frozen hypothetical comparison is not the same as performing an irreversible action. Actual dispatch restricts accessible subtrees and can invalidate alternatives or make a goal unreachable. The source’s background abstract action exclusivity also must not be transferred unqualified to the concurrent multi-robot planner.
• The none/all argument assumes matching ancestor/successor relaxed-plan structure. It does not prove equality of M_i laws, equal probabilities, retention of the requisite ancestors in OPEN, or sufficiency for arbitrary prefix policies and changed temporal constraints. It is a heuristic reduction argument rather than a general optimal metareasoning theorem.
• This rule does not specify an estimator-training procedure, full search algorithm, scheduler, dispatch threshold, stopping test or duplicate-state policy. The source’s dual planner adds alternating queues, tie-breaking and periodic refresh, and uses an earlier dispatch integration. Those control rules and their reported performance are not properties of the mathematical functional alone.
• The simulated RCLL coverage and queue-agreement results assess complete configured planners rather than isolated correctness or calibration of this functional. Their repeated scenario/rate combinations, chosen weights and thresholds, and absent table uncertainty measures do not establish a universal benefit of the rule in other domains.
• Evidence comes from the byte-distinct author and official PDFs of one 2025 work, not independent replications. Name-form, institutional-date and OPTIC/COLIN citation differences remain in research context. No referenced original algorithm or implementation is newly certified here, and all 38 bibliography occurrences and original follow-up objects remain unchanged in the retained ledger.