Provision density is doctors ÷ pop_total × 1,000 for each district and specialisation. “Doctors” is the count of practice entries in the source register, not a headcount of unique physicians. A physician at several addresses or under several specialisations is counted once per entry. Population is registered residents on 1 January 2023.

PTAI sums exp(−d / 400) over all 1,807 Wiener Linien stops for every practice, averages the values within each district–specialisation group, and rescales them so the Vienna mean equals 100. The 400 m decay represents a typical walking catchment: a stop 400 m away contributes about one third as much as one at the practice.

An index is used because 98% of practices are already within 300 m of a stop and the citywide mean distance is 137 m. Unlike nearest-stop distance, PTAI does not saturate: it distinguishes locations served by one stop from locations served by many and spans 61.8 to 153.4 for all specialisations.

Provision uses five quantile classes because Innere Stadt's resident denominator creates a 14× outlier relative to Leopoldstadt. Access uses five equal-width intervals. Missing district–specialisation rows are grey and are not treated as zero.

Both maps describe supply-side geography. PTAI is not service quality: the stop data contains no line, frequency or operating-hours information. Provision does not distinguish contracted insurance practices from private practices.

District polygons are the official City of Vienna BEZIRKSGRENZEOGD WFS layer. The CSV district integer is joined to the verified polygon field BEZNR.