In a positive sign for San Francisco’s ailing downtown, two major real-estate firms released preliminary data showing that The City’s high office-vacancy rate is on track to fall in the third quarter, though more than a third of such spaces still sit empty.

The data from JLL and CBRE — which calculate some things differently — showed that the artificial-intelligence sector in particular has fueled increased demand for office space.

JLL said The City’s office-vacancy rate appeared to be headed for a decline of 0.4% to 35.3%, down from the peak the company counted the prior quarter, said Alexander Quinn , northwest region director of research for JLL. The firm counts vacancies based on occupancy rather than leases.

CBRE, which tallies leases, similarly said the vacancy rate declined 0.2

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