I really enjoyed the world and the writing. If you enjoyed this, then I recommend both "Swordspoint," by Ellen Kushner, which avoids the anticlimactic nature of final duels by having a plot that just sort of meanders around pointing at interesting tourist attractions in the worldbuilding and then stops at a semi-arbitrary point, and the King's Blades series by Dave Duncan, which is more swashbuckly but has some interesting and amusing takes on the idea of (in this case magically) sworn weapon-wielders. (The idea tangentially appears in one of my favorite series, "The Silent Tower" and "The Silicon Mage" by Barbara Hambly, but I can't recommend those to fans of swordfights. I do enjoy the sworn-weapon character in that series, though, and his eventual resolution.)
I was as confused as most other people when it came to who was arguing what side of which argument in the duel in question. The explanation of challenging a scientific principle as heretical in a religion where scientific principles are God-ordained truth makes sense and clarifies why she went for the tie answer (or at least why she wanted to lose the fight in the first place, with the tie being her way around her pride.) I have a creeping fridge-logic feeling that there's no way to make this a coherent religion, though, not with the way science is always overturning and/or refining theories as our understanding refines itself.
I was pleasantly surprised at the female pronoun applied to God, but then I went, "Wait, why would a female Deity be hung up on the purity and chastity of women?" That's strictly a male concern, just from an evolutionary perspective, even without the accreted cultural baggage. Not sure if that was just a whoopsie-let's-not-change-society-TOO-too-much-lest-the-reader-collapse-from-novelty-fatigue thing or something that the author just didn't notice.