Where the Weil negativity of the Davenport–Heilbronn function lives

Splitting −f′/f of the Davenport–Heilbronn function by the support of n into an Euler part, prime-power defects and composite terms, we prove a closed form for the prime-power defect, a factorisation f = E·C with every off-line zero a zero of the composite factor, and a certified floor −0.4478 for the prime-power channel of a localised Weil functional. At 83 off-line pairs the composite channel is certified negative and at least 4.1 times the prime-power channel; the functional itself is certified negative at 82; and the Euler part with the defect removed is certified positive at all 83. The composite channel is identified with the non-domination budget of the zero count, and its sign is stable across test-function widths. Floating-point localised negativity for this function appears in 2026 preprints (Caceres; Eastwood), which are cited; the values here are certified and split by channel. Written jointly with Claude, an AI system made by Anthropic, which carried out much of the computation, the derivations and the drafting; the human author is responsible for the content. Not peer reviewed. The package contains the PDF, its LaTeX source, the scripts and result files it cites, and the dated literature-search log behind its priority statements.