What Stacking Limits on Catalogued Blazars Do and Do Not Say About the Diffuse Neutrino Flux

Stacking analyses of catalogued blazars limit their combined contribution to at most 27 per cent of the diffuse neutrino flux. That statement is often shortened, incorrectly, to 'blazars contribute at most 27 per cent'. This paper computes the gap between the two statements. In a schematic luminosity function, sources bright enough to be catalogued — taken as those above 10^45 erg per second — carry only 16.3 per cent of the class's total luminosity density, and sources above 10^46 erg per second carry just 1.42 per cent. Dividing the stacking limit by the catalogued share gives a formal ceiling on the whole class of 1.66, which exceeds unity: the stacking result, propagated honestly, does not bound the total blazar contribution below the full diffuse flux at all. What it does bound is the catalogued population's own flux, at most 1.620e-08 in E-squared units against a total of 6.000e-08, leaving at least 4.380e-08 to be supplied by everything else if the catalogued objects saturate their limit. The study is computed from stated assumptions, not measured.