The failure mode here is geometric rather than astrophysical. WISE returned one blended flux per target, so a background galaxy sitting within an arcsecond of a faint M dwarf donated infrared photons that the photometry booked to the star [5][3]. That is exactly the pattern Project Hephaistos was built to notice: too little optical light for the amount of infrared coming back [6]. Webb, with the angular resolution to separate the pair, let the team analyse star and galaxy independently, and the excess stayed with the galaxy [8][3].
The selection was tight before Webb ever looked. Gaia and WISE data on roughly a million stars within about 1,000 light-years produced these two 15th-magnitude M dwarfs, estimated at a few billion years old, as the most promising cases [6][7]. Two out of a million works out to about 0.0002 percent of the surveyed sample [13], so the pipeline was already discarding nearly everything, and both of the leads it kept died of the same cause [14].
What that buys is a calibration of the candidate list rather than a statement about Dyson spheres. The denominator is two. The more consequential sentence in the papers is the authors' own aside that a substantial fraction of the Hephaistos candidate list appears contaminated by background galaxies [10]. Contamination from chance superposition scales with how coarse your selection imaging is and how many faint galaxies sit behind your search volume, and no reanalysis of WISE photometry addresses either.
The thing this does not tell you is whether the technosignature was ever inside the search box. The papers state the assumption plainly: waste heat, radiated mostly in the mid-infrared [4]. Korn puts the physics simply, that energy spent on computing still ends up emitted in the infrared as waste heat, and that the target was a star slightly too faint in the optical with substantial infrared excess [17]. A structure radiating outside that window, or covering too little of its star to dim the optical, never enters the sample to be eliminated.
Korn expects relief from infrared surveys with better spatial resolution coming online in the 2030s [11]. It is worth being clear about which instrument that upgrades. Webb can already separate a star from an arcsecond neighbour, one target at a time [8]; what the field lacks is selection imaging sharp enough over wide areas to keep contaminated targets off the list before anyone spends follow-up time on them [11][10]. For now the useful output of these two papers is the contamination estimate, and the non-detection is what it cost to obtain it.
