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Considering the quality of your rating comments I hope this one lives up to them:
Ill take this one apart criteria by criteria and hopefully help improve what is an already very good game!
Game Design:
Ive seen the idea of shoot to move before, but I dont think I've seen it in a endless (faller) runner type situation before. It gives a really nice touch of having to decide whether to shoot down to boost yourself up, shoot to the sides to dodge, or shoot (usually) up to kill enemies. All this also while breaking crates and grabbing coins. It's creating pseudo-mechanics through dynamics, which I really like.
You make items clear on their role even if you haven't played the game before: it's clear that the bad guys are bad (especially because you don't ever change their sprite so you wouldn't get confused on lower levels), that the crates are powerups, and that the coins are, well coins. Obstacles are clear too, even the laser which gives you a fair amount of time to dodge it with the warning laser if you've seen it for the first time.
The different guns give you a different way to play the game: they aren't especially better and so your experience as you go down the levels isnt especially harder and balanced because you get better guns: it forces you to get farther by just getting good: through experience. A good player will pick what gun to use at the right time. The shotgun for example is great to quickly take care of enemies or quickly dodge an object, but can be quite risky if you stay low because of it's longer shooting cooldown. The assault rifle is great to give you a breather from avoiding falling down to the bottom drill, but it also puts you at risk by placing you at the very top where enemies appear. The basic gun is just a nice all rounder that requires precision but also has a pretty nice cooldown.  I'm not too sure what the coins actually do: are they simply a score for you to appreciate at the end of a run or can you use them. Im guessing it's the first one because I didn't find a place to use them, so tell me if Im wrong. If that's the case, then maybe don't stack up coins between levels but simply let it factor into your "score", a value that you could show at the end of a run which depends on a function that takes the feet descended AND the coins a input. Otherwise, keep your coins and incorporate a shop to maybe buy player skins, a starting feet level, a starting gun, options for new guns, or a one run temporary boost.
For the enemies, maybe i would give a little warning at the top of the screen before they go down because it feels pretty unfair when you're up there at the top and they suddenly spawn on you and you lose health. Then again, that might make the assault rifle overpowered, but it's something to think about.

Fun:
Game is super fun and I can easily see it become a widely played mobile game if given some more content (especially a shop). Bullet time effects give really satisfying enemy kills, the dying sequence is clear as day and doesn't leave you unsatisfied... Even runs where you lose quickly were, for me, very fun to play.

Innovation:
Im not sure if it's innovative because I dont play this type of game often. To me it seems like the shoot to move mechanic incorporated into an endless (faller) runner is new, but I could be wrong and I can see it as an idea that someone might've already had. 

Theme:
As others have said, I don't really see it fitting the theme. I get what your point is (from your other answers) but I feel (and that's my opinion) like jam themes should be incorporated into gameplay, not just a background story that the game doesn't even tell you about.

Graphics:
One of the few jam games where the art is coherent in between individual elements! The style fits a mobile game perfectly and doesn't seem too hard to modify for individual sprites if you want to add content. So a great job on that: a simple, not too distracting art style that gives the game coherence but doesn't attempt to attract all the player's attention.

Audio:
The menu music is very nice and cute with simple phrases that come back later in the theme, which helps to cover up the loop. If the theme was a bit longer it would really succeed at that effect (I'm thinking an additional 8 bars to get a nice round 32, for a more bridge like section that isn't as pressing as the other part - when I say pressing I mean that the notes keep on coming and it could use pauses). Then again it's a menu so maybe a longer loop isn't really needed, it's just that I still have the game open while Im writing this so the loop is started getting a little frustrating haha.
For the levels, please make louder music. It's a real shame that we can't hear it better. It just sounds like some instruments are randomly playing in the background because they keep getting cut off by the relatively loud sound effects.
I would also add a different piece for the end of run screen. Maybe you might not need to though if you want quick reruns, then the fact that it links with the menu music will keep things smooth instead of jittery.
The sound effects are nice and crisp, but they could use some volume balancing compared to the music.

All around a really great game on it's own! Doesn't really fit the theme so I wouldn't say it's a great entry for this jam, but credit where credit is due: it's a very well designed game. I also want to say I really like how the menu works.
Great job on this!

Thanks for the informative writeup.

In response to your queries:

1. Coins, what for? A store is in the making. It will include accessories that alter gameplay as well as cosmetics. The game will also include an energy mechanic in the form of ammunition. There's too much to explain, but the long and short of it is that the jam version has no store as I wanted to nail the gameplay first.

2. Music too quiet: That's an issue of ducking. I've already addressed this post jam, but yeah, sfx are reducing the gain of the music mix excessively and abruptly as well.

3. Music too short: Agreed. Really a time constraint issue. For this jam I composed 2 songs, in essence, both with relatively few bars and instruments. As you descend down the mantles a different "style" of the same song plays, for a total of 9 individual arrangements. I thought this would be sufficient for a jam environment, however, I'm starting to think it may be enough for the final product as well. I think as long as the play loops are kept short, the repetition should not present itself as an issue, but that's hard to say. Adding more content to the compositions should not be an issue, in the end of the day.

4. Theme: I agree, but the more I think about it, the more I'm seeing a subtle yet stronger connection. I have yet to work out if this is delusion or not. :) Either way, it is my firm position that utilising a theme to the point of making a game deliberately less enjoyable, as many seem to have done during this event, is unacceptable. The most common other approach to the theme, when the game hasn't been damaged, is to make characters deceptive, or using some kind of extreme plot twist. In my estimation that's missing the theme, as it's about the game intrinsically lying. One more case is where some developer have opted for making the game itself into a character of sorts. While literal, I think this is a fairly good reading of the theme. Extremely rare are the cases in which the theme has in fact been embraced subtly and enjoyably, where the game truly is a lie in its mechanics. An example is https://charu12.itch.io/mindless-runner. So, in our case, our game's premise is a logical fallacy which our protagonist firmly believes in. Yet the game itself will never allow for anything to be proven one way or another due to its design. I suspect if we had added a piece of narrative (in the form of a cutscene, for instance), we may have scored higher on this metric. We opted against it due to it being a low priority. But, yes, despite my somewhat long reasoning here, I agree with your position on this to a large extent.

Thanks again for taking the time to play and review the game in a comprehensive way. I appreciate the effort that goes into doing such a thing.

Cheers.

Yeah from your reply it sounds like most of the problems were due to time constraints and I totally get that. For the music, yeah, 9 arrangements of the same track suffices for the descent, you just can't hear it because of volume, but it's definitely enough. I get what you're saying for the theme, it's just it's a shame that it doesn't say you're trying to prove flat earthers wrong in game. Thanks for taking the time to read the comment!