Multi-goal semantic navigation couples searches through a shrinking horizon: effort spent on one request can make another effectively undiscoverable. Discoverability therefore depends on both goal evidence and the budget that other requests consume. We present BAT-Nav, Belief-Based Arbitration and Termination, which estimates remaining discoverability: the probability that a frozen executor can complete a goal within an additional budget. A calibrated local hazard converts navigation telemetry into a budget-conditioned completion curve. Its marginal return governs reversible; conservative belief and local evidence govern. On intervention-independent replays, the model obtains Brier .132 and ECE .034 without transfer refitting; 50-action completion rises from .047 to .321 across marginal-return sextiles. On HM3D / ApexNav, BAT-Nav raises CR from .372 to .414 and obtains MGSR .173. Its gain widens from 3.4 to 5.8 CR points as competing goals increase from two to five, with the same ordering on MP3D and under infeasible requests.

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