Uniform count-scale changes had small mean effects on a bird thermal trend in 1997-2025

We tested whether common count changes can alter a community temperature index with log(count + 1) weights. An exact derivative shows that the index can change even when all species have the same proportional count change. We audited 76,692 BBS runs on 4,785 routes in 1997-2025, with fixed thermal scores for 444 species. A gradual halving of counts changed the route fixed-effect trend by +0.000258 C per decade, against an unscaled trend of 0.04384. Simulated independent loss of detections, from full retention in 1997 to half retention in 2025, changed the mean log-weight trend by +0.000489 C per decade across 40 replicates (Monte Carlo SE 0.000046). A fixed-total log index changed the observed trend by -0.000136 C per decade. Local scale effects had opposite signs and were much larger than the pooled mean. These tests show small mean effects for the stated common-scale changes. They do not estimate historical detection loss or bound species-specific bias. Code, proofs, aggregate results and exact external input hashes are included.