Can insulation specifications explain reported thermal transmittance? Interval feasibility and inverse resistance screening in an anonymised sports hall

A renovation schedule can specify an insulation thickness and a post-renovation thermal transmittance without exposing the construction layers connecting them. This paper develops a transparent screening test for such pairs using monotone interval propagation and inverse thermal-resistance calculations. Three opaque-element categories are extracted from a confidential sports-hall energy report. The existing element is represented by its reported baseline transmittance, and the stated insulation is provisionally treated as one added homogeneous layer with unchanged surrounding resistances. Author-defined bounds include thermal conductivity of 0.032–0.040 W/(m K), thickness variation of ±5 mm and transmittance rounding intervals of ±0.005 W/(m² K). The resulting forward intervals are 0.305–0.400 W/(m² K) for the floor, 0.139–0.177 for the wall and 0.147–0.190 for the roof. The reported floor and wall target intervals do not intersect these ranges, whereas the roof interval does. Inverse calculations require 0.217–0.295 m of added insulation for the floor target within the selected conductivity range, compared with a nominal 0.080 m specification. The wall's smaller incompatibility disappears in a lower-conductivity scenario, while the floor remains incompatible under a wider material range. These findings identify documentation priorities rather than proving construction defects or statutory non-compliance. Ground coupling, replaced layers and thermal bridges remain outside the simple model. The study shows how bounded, non-probabilistic calculations can separate a robust parameter mismatch from an assumption-sensitive one before a renovation report is reused as research evidence.