A fitness-independent family of simultaneous amplifiers beyond relative fitness 3/2

We study fixation from a uniformly random single mutant on finite connected loopless undirected weighted graphs under both Birth–death (Bd) and death–Birth (dB) Moran updating. Let R_sim be the supremum of R for which one fitness-independent graph family eventually amplifies fixation under both rules for every fixed r in (1,R). Let R_hyb be the unique root in (3/2,151/100) of

R^6 − 8R^5 + 22R^4 − 30R^3 + 21R^2 − 6R + 1.

We construct one fitness-independent family that simultaneously amplifies every fixed 1 < r < R_hyb for all sufficiently large members of the sequence. Therefore R_sim ≥ R_hyb = 1.5028569127905696… > 3/2.

The construction combines a large clique with dilute hub pendants and dilute, internally heavy two-vertex satellites. An exact finite-state derivation of the weak-cut limiting trace, together with uniform establishment, cleanup, and reciprocal-invasion estimates at the scale of the eventual gain, reduces the two normalized fixation corrections to explicit response functions. Optimizing their common positivity interval yields the displayed sextic. The same analysis proves that R_hyb is optimal among fixed positive (sigma, lambda) in the displayed first-order dilute pair–pendant response model; a specialization with entirely rational edge weights already crosses 3/2. Thus 3/2 is not the exact simultaneous-amplification threshold. The unrestricted value of R_sim, and even a finite universal upper bound, remain open.

Version note

Version 2.0.4, August 2026. This is an unrefereed preprint. It supersedes the earlier v1 source/software archive at https://doi.org/10.5281/zenodo.21852072.

This record contains the preprint and its complete source-and-certificate archive. The supplied exact verifiers replay the finite symbolic, rational, and finite-state calculations. The weak-cut and population asymptotics are analytic proofs in the manuscript and are not claimed as computer-assisted consequences of the replay.