Diego Blas, Aurélien Hees, F. Javier Atapuerca, Giada Bargiacchi, Massimo Bassan, Joshua N. Benabou, Bruno Bertrand, Adrien Bourgoin, Clare Burrage, Nicolò Burzillà, Alfonso Caldiero, Roberto Campagnola, Andrea Caputo, Ana Caramete, Laurentiu Caramete, Joan Manel Casalta Escuer, Julien Chabé, Gabriel Chiritoi, Marco Cinelli, Florin-Ioan Constantin, Neil J. Cornish, Clément Courde, Simone Dell'Agnello, Alessandro Di Marco, Sebastian Ellis, Malcolm Fairbairn, Ariadna Farrés, Joshua W. Foster, Silvia Gasparotto, Marta Goli, Yann Gouttenoire, Michael Häfner, Antonio J. Iovino, Maria-Catalina Isfan, Justin Janquart, Alexander C. Jenkins, Jean-Paul Kneib, Sébastien Le Maistre, David Lucchesi, Marco Lucente, Angus Macdonald, Jorge Martín Camalich, Rosa Martínez Rubiella, Josep J. Masdemont, Ilia Musco, Toshimichi Otsubo, Cristóbal Padilla, Fco. Rogelio Palomo Pinto, Alice Paun, Alice Perego, Roberto Peron, Florentina-Crenguta Pislan, Florin Adrian Popescu, Luca Porcelli, Nanda Rea, Rafael Rebolo, Marco Reyes, Ignasi Ribas, José C. Rodríguez, Pascal Rosenblatt, Albert Roura, Soumen Roy, Mariano Sánchez Nogales, Francesco Santoli, Feliciana Sapio, Anja Schlicht, Ulrich Schreiber, Angela Serrano, Daniel Serrano Lombillo, Alberto Sesana, Carlos F. Sopuerta, Krzysztof Sośnica, Nicola Tamanini, Elisa Todarello, Sokratis Trifinopoulos, Miguel Vanvlasselaer, Dario Vetrano, Massimo Visco, Hanxi Wang, Xiao Xue, Miguel Zumalacárregui

GUEST is a space mission concept whose central objective is the detection of gravitational waves (GWs) in the microhertz band -- a physics-rich frequency window that no other present or planned detector can reach at a significant level. The concept is simple: two dense, passive spheres, covered with cube-corner retroreflectors, deployed in {highly eccentric} Earth orbits ($e \gtrsim 0.7$, period $P \gtrsim 33$ h), tracked continuously by the global network of satellite laser-ranging stations over a minimum observation time of 10 years, with an expected total duration of 30 years. The orbits themselves act as resonant detectors of the oscillating gravitational perturbations, with the microhertz sensitivity emerging from the selected orbital parameters. From the same data stream, GUEST delivers a programme of fundamental and applied science that cuts across particle physics, gravitational-wave astronomy, cosmology, astrophysics, and geodesy: the first coherent search for GWs from supermassive black-hole binaries in the $μ$Hz band, the exploration of primordial GW backgrounds in the unexplored energy-scale gap between pulsar-timing arrays and LISA, a dedicated probe of ultra-light dark matter in a parameter region untouched by any other experiment, a new way to search for ultra-light bosons, order-of-magnitude-improved tests of new gravitational interactions at astronomical ranges, and a step change in the absolute determination of $GM_\oplus$ that underpins the Global Geodetic Observing System and future navigation and Earth-observation missions. This white paper presents the motivation, scientific reach, and mission concept of GUEST.