With a mass in the Neptune regime and a radius of Jupiter, WASP-107b presents a challenge to planet formation theories. Meanwhile, the planets low surface gravity and the stars brightness also make it one of the most favorable targets for atmospheric characterization. Here, we present the results of an extensive 4-year Keck/HIRES radial-velocity (RV) follow-up program of the WASP-107 system and provide a detailed study of the physics governing the accretion of its gas envelope. We reveal that WASP-107bs mass is only 1.8 Neptune masses ($M_b = 30.5 pm 1.7$ $M_oplus$). The resulting extraordinarily low density suggests that WASP-107b has a H/He envelope mass fraction of $> 85$% unless it is substantially inflated. The corresponding core mass of $<4.6$ $M_oplus$ at 3$sigma$ is significantly lower than what is traditionally assumed to be necessary to trigger massive gas envelope accretion. We demonstrate that this large gas-to-core mass ratio most plausibly results from the onset of accretion at $gtrsim 1$ AU onto a low-opacity, dust-free atmosphere and subsequent migration to the present-day $a_b = 0.0566 pm 0.0017$ AU. Beyond WASP-107b, we also detect a second more massive planet ($M_c sin i = 0.36 pm 0.04$ $M_{J}$) on a wide eccentric orbit ($e_c = 0.28 pm 0.07$) which may have influenced the orbital migration and spin-orbit misalignment of WASP-107b. Overall, our new RV observations and envelope accretion modeling provide crucial insights into the intriguing nature of WASP-107b and the systems formation history. Looking ahead, WASP-107b will be a keystone planet to understand the physics of gas envelope accretion.
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