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Patersbier is not, strictly speaking, a style. Meaning, it doesn't really have a framework of color, ingredients or flavors that can be used to group them together. It's a Monastic reference to being "Father's Bier" or beer brewed for the Monks, themselves. As such, they are widely different and extraordinarily rare. I've been told that they are usually pared down versions of Trappist commercial styles, but having had a couple, I'd say that is overly simplistic.
I'm prefacing my response this way because you might very well have a perfectly reasonable beer, depending on your ingredients and techniques.
Your hydrometer is calibrated for 60 F. warmer and the reading will be lower.
Candi sugar and other highly fermentable adjuncts increase alcohol, which lowers the hydrometer reading (the term is "apparent attenuation"). BeerSmith has an adjustment tool for that. I punched in your two numbers (1.045 and 1.000) and it shows a likely 1.004 final gravity when adjusted for alcohol.
The yeast you chose is a high gravity strain, capable of 12% abv and more. You may have given it merely a snack! If you saw a healthy fermentation, then I will lean in that direction over a contamination. How long did it sit in the fermenter?
How does it taste? Is it fragrant, lightly fruity and spicy like black and green peppercorns? That is a typical clean Belgian profile. Does it taste like stale cinnamon, old cloves, over ripe bananas and a hint of Grandpa's closet? That is often a wild yeast contaminaton.
Sounds familiar. I did a Patersbier based on the Northern Brewer recipe: 100% German Pils, mashed long and low, pitched with Belle Saison yeast starting at 65 F, ramping up to 75 F. After 18 days it's down to 1.002. It has a great Belgian flavor: a little hop bitterness, a light sweetness, some clove, and just the least bit of a hint of sour on the finish.
Your yeast is described as more aggressive than Belle Saison, so 1.000 is not surprising, especially if you fermented a bit warmer. How's it taste?
My wife and I like my belgien ales but they aren't the best session beers... so I thought that the patersbier might be a compromise. I suspected that the HG yeast was the reason for the low reading. I had inquired to another help-line about adding a mini-wort to boost flavor and gravity since I had hungry yeast... and when they suspected wild yeast contamination I was rattled and needed a 2nd opinion!
Taste is OK (like a slightly watered down belgian golden ale), but I think that the complex flavors should emerge with some time.
My one experience with wild yeast infection (ruined a perfectly good Oktoberfest) was obvious. It fermented EVERYTHING. My FG was much lower than I expected, the color was way off, and it tasted a lot like sour green apples. Being the trooper that I am I tried to save it with cider spices and cinnamon sticks. LOL Horrible! One and only batch in years of brewing that went down the drain.