Date moments allow both signs of temperature slopes for summer count shares of Meadow Brown in England and Wales in 1985-2024

We tested whether selected flight-date summaries determine the spring-temperature slope for the share of observed Meadow Brown counts in a fixed July 15 to August 7 window. Linear programs used date support, mean and variance. Four weighted site models used England and Wales in 1985-2004 and 2005-2024. The exact-moment sample has 19,147 site-years after feasibility and site filters. All four slope ranges include negative and positive values. An independent vertex calculation agrees with four row bounds. We report a rounding relaxation and a higher-count check. These are possibility bounds for real-valued date distributions, not confidence intervals. Missing visits, count constraints, uncertain SD convention, selected sites and coarse country weather limit interpretation. The result does not establish a causal climate effect or a pollution effect. External source records and derived row tables stay outside the bundle. Code, hashes, aggregate results and a figure support regeneration.

phenology · butterfly · observation bias · moment bounds · temperature · survey window · partial identification