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Binary millisecond pulsar systems are superb probes of stellar, binary evolution and the physics of extreme environments. The location of millisecond pulsars relative to the `spin-up line' in the spin period and spin-down rate (P-Ṗ) diagram plays a critical role in understanding population studies of radio millisecond pulsars and accreting neutron stars in X-ray binaries. Here we report the discovery of the pulsar PSR J0435+3233, which exhibits an exceptionally high spin-down rate of 4.8775101(2) × 10<SUP>-17 </SUP>s s<SUP>-1</SUP>—two orders of magnitude higher than that of other known millisecond pulsars, thus occupying a distinctive position in the P-Ṗ diagram. This discovery implies a formation channel that differs from the classical evolutionary path, challenging the theoretical models of the recycling process and placing stringent constraints on spin-up theories. One plausible scenario is that its progenitor was a neutron star undergoing super-Eddington accretion, with the currently observed pulsar being a remnant of such a system. Another possible mechanism is its formation through the accretion-induced collapse of a magnetized ONeMg white dwarf, although this scenario requires specific theoretical assumptions. Hence, PSR J0435+3233 has an important impact on binary evolution theory.

Recent observations have revealed significant soft X-ray polarization from several quiescent magnetars, including the intriguing 90° polarization angle (PA) swing as a function of photon energy for some sources. We thus present a general semianalytical framework for calculating energy-dependent soft X-ray polarization signatures from magnetars, consistently incorporating both quantum electrodynamics (QED) vacuum resonance in the atmosphere and resonant Compton scattering (RCS) in the magnetosphere. Starting from the polarized radiative transfer equation for RCS and treating vacuum-resonance-induced mode conversion as an input, we employ a first-order approximation in RCS optical depth to evaluate the effects of magnetospheric plasma density (which depends on magnetic twist), drift velocity, temperature, and viewing geometry on the observed radiation. Our analysis reveals that magnetic twist and plasma drift velocity are the critical parameters controlling the impact of RCS on both the absolute polarization degree and its variation across the soft X-ray spectrum. We find that sufficiently strong RCS can wash out the PA swing caused by vacuum resonance. Furthermore, in addition to the QED vacuum resonance effect, significant relativistic signatures arising from plasma drift velocity (β<SUB>0</SUB> ≳ 0.5) may introduce an extra 90° PA swing in the spectrum. Our calculation framework, based on the single-scattering approximation, bypasses the need for complex, multidimensional Monte Carlo simulations, providing an analytical pathway for modeling full-surface emission and rotational-phase-resolved radiation from magnetic neutron stars in support of current and future X-ray polarization missions.