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A player in our group has an Arc-50 Light Rail Gun but can't remember what book it comes from so the GM can't verify it. Does anyone know what book it comes from?

I've never heard of it. The closest I know of is this:

Q5-50 Light Rail Gun. This is a light, anti-personnel weapon used by human troops wearing power armor, cyborgs, and characters with a strength of 24 or greater. The Q5-50 rail gun can use what is called a short clip with 200 rounds (10 bursts), light drum with 600 rounds (30 bursts), or a heavy belt feed drum containing 2000 rounds (100 bursts). The latter is typically reserved for cyborgs and is carried as a backpack or by a partner in a two-man team.
Weight: Gun: 45 pounds (20.25 kg), short clip: 10 pounds (4.5 kg), light ammo-drum: 30 pounds (13 kg), or a heavy ammo-drum: 100 pounds (45 kg). Ammo-drums are hooked to the back of body armor or housing on the back of a 'Borg or power armor.
Range: 4,000 feet (1,219 m).
Mega-Damage: A full damage burst fires 20 rounds and inflicts 4D6 M.D.; a single round does 1D4 M.D.
Rate of Fire: Equal to the character's hand to hand attacks per melee round.
Payload: The short clip holds 200 rounds and is capable of firing ten full damage bursts (20 rounds). The light drum holds 600 rounds and can fire 30 bursts. The 2,000 round drum is capable of firing 100 full damage bursts (20 rounds each). Reloading a drum will take about two minutes for those not trained, but only 20-30 seconds by a capable field mechanic or Reload Team. A strength of 24 or higher is required to handle the drum.
Cost: 32,000 credits. Good availability. Not yet available on the Black Market. When it is, it should sell for 60,000-70,000 credits.

Do you think he might've named an Archon weapon wrong or something like that?

The Q5-50 is from Free Quebec if that helps.