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The multicycle JWST Treasury program NEXUS will obtain cadenced imaging and spectroscopic observations around the north ecliptic pole over 2024─2028. Here, we report a systematic search for nuclear variability among ∼25,000 sources covered by NIRCam (F200W+F444W) imaging using the first two NEXUS epochs separated by 9 months in the observed frame. Difference imaging techniques reach a 1σ variability sensitivity of 0.18 mag (F200W) and 0.15 mag (F444W) at 28th magnitude (within 0<inline-formula> <mml:math><mml:mover><mml:mrow><mml:mi>.</mml:mi></mml:mrow><mml:mrow><mml:mi>″</mml:mi></mml:mrow></mml:mover></mml:math> </inline-formula>2 diameter aperture), improved to 0.01 mag and 0.02 mag at &lt;25th magnitude, demonstrating the superb performance of NIRCam photometry. The difference imaging results represent a significant improvement over aperture photometry on individual epochs (by &gt;30%). We identify 465 high-confidence variable sources among the parent sample, with a two-epoch flux difference at &gt;3σ from the fiducial variability sensitivity. Essentially, all these variable sources are of extragalactic origin, based on preliminary photometric classifications, and follow a similar photometric redshift distribution as the parent sample up to z<SUB>phot</SUB> &gt; 10. While the majority of these variability candidates are likely normal unobscured active galactic nuclei, some of them may be rare nuclear stellar transients and tidal disruption events that await confirmation with spectroscopy and continued photometric monitoring. We also constrain the photometric variability of 10 spectroscopically confirmed broadline Little Red Dots (LRDs) at 3 ≲ z ≲ 7, and find none of them show detectable variability in either band. We derive stringent 3σ upper limits on the F444W variability of ∼3%−10% for these LRDs, with a median value of ∼5%. These constraints imply weak variability in the rest-frame optical continuum of LRDs.

The Galactic center exhibits a persistent 0.511 MeV emission characteristic of electron─positron annihilation. Various astrophysical sources may be responsible for supplying the positrons, yet their contributions with respect to the total annihilation rate is uncertain. X-ray binaries have historically been a primary candidate, possibly contributing a significant fraction of the Galactic positrons. X-ray binaries can produce positrons through the Blandford─Znajek mechanism, two-photon pair production in the corona, and/or one-photon pair production for strongly magnetized compact objects. These positrons may then be channeled into the interstellar medium through jets or winds. In this work, we argue that X-ray binaries cannot contribute to the electron─positron annihilation flux alone. We present 0.511 MeV line fluxes and all-sky maps produced by X-ray binaries and stellar flares from the Galactic stellar population, along with the gamma-ray continuum from positrons produced by X-ray binaries. To do so, we solve the particle transfer equation using Green's functions. The total morphology is slightly asymmetric toward negative longitudes and positive latitudes. We find five 0.511 MeV flux hot spots in the generated all sky maps and scrutinize the contribution of individual sources to these hot spots. Observations of these hot spots can reveal the contribution of X-ray binaries to the Galactic positrons. The upcoming Compton Spectrometer and Imager mission could image a hot spot near Cygnus X-1. The detection of the other hot spots requires a telescope with improved arcminute angular resolution.