AlecKriebel/Math: No universal death–birth amplifier v1.0.0

No universal death–birth amplifier, v1.0.0 This release publishes the fixed-graph obstruction and its exact verification materials. Main results Every fixed finite loopless directed weighting with positive incoming degree is eventually death–birth suppressing, or its full death–birth chain exactly ties the complete graph. For complete directed support, the first strong-selection deficit is an explicit sum of squares over incoming weight columns. Every nonuniform positive weighted triangle suppresses death–birth fixation for every beneficial fitness. The same all-beneficial-fitness classification holds for the full symmetric 1+3 and 2+2 complete-support families on four vertices. Eventual amplification at every fixed fitness requires support degree to diverge in probability; a separate theorem excludes unequal-degree dense finite-type blow-ups under its stated hypotheses. Scope The release rules out one population threshold that works uniformly for every beneficial fitness. It does not settle the reversed quantifier order in which the population threshold may depend on fitness. The unrestricted six-edge weighted K_4, the diffuse asymptotically regular regimes, and the optimal simultaneous-amplification interval remain open. Reproducibility make paper1 rebuilds all exact checks and the manuscript. The released run used Python 3.14.6, SymPy 1.14.0, and Tectonic 0.16.9. Release assets include the typeset paper, editable manuscript source, the complete reproduction tree, and a SHA-256 manifest. The manuscript and internal hostile audits are AI-assisted and have not undergone external specialist peer review.