Coherent End-to-End Search for Generic Extreme-Mass-Ratio Inspirals

Extreme-mass-ratio inspirals (EMRIs) encode more than $10^5$ strong-field orbital cycles and are key targets for space-borne gravitational-wave interferometers, yet coherent recovery of generic systems over astrophysically broad priors remains unresolved. Successive Mock LISA, LISA, and Taiji Data Challenges (MLDCs, LDCs, and TDCs) have not yet produced a complete, generally reliable solution for blind EMRI detection and parameter recovery across such priors. The central obstacle is a needle-in-a-haystack likelihood: six phase-evolution parameters span a vast domain, producing an exceptionally narrow global maximum amid numerous secondary maxima. We show that higher-likelihood secondary maxima concentrate progressively around the global maximum and can therefore guide an adaptive contraction of the search volume. We exploit this structure through a reduced-dimensional profile likelihood and a coherent hierarchical strategy to search for EMRI signals across the full 14-dimensional parameter space. This enables the first end-to-end coherent parameter estimation for generic EMRIs with astrophysically broad priors. In stationary Gaussian LISA noise, the search recovers two half-year analytical-kludge signals with signal-to-noise ratios near 50, yielding fitting factors of 0.989 and 0.971, fractional errors of $10^{-3}$--$10^{-2}$ in the phase-evolution parameters and near $3\%$ in the distance, and error of less than $0.1$ radian in the sky location. The method turns secondary maxima into guides for a coherent hierarchical search.