It's always hard to analyze things spread across multiple documents, but I'll see what I can do.

This will take me a while to process. I will edit this post as I go.

Spoiler: CLASS
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Chassis:
The class has poor (very low) skills, but it's Intelligence focused.Skills known are knowledge and Int based, even more restricted than the wizard. Notably missing Acrobatics (although you can grab it with a Calculation).
It has only light armor access and a d8 hit die; highly reminiscent of the rogue defensively, relying on escape to survive. Not a frontliner! However, lacks Acrobatics, making it somewhat more difficult to withdraw from melee.

Power points/day and powers known: Missing from the table- I had to reread the text to spot that it's as the psychic warrior. Int based manifesting, which helps out with the lack of skills.

Paradox: Basic power source. Notably, it's described here as a way to suppress the downsides of time manipulation. This holds up well with Rifts, but less well elsewhere. You only have 13 points per day at the height of your career, unless you take the feat for 2 more points- usually, if you have the option, you'll want to avoid spending them, and take the penalties associated with Rifts.

Temporal Reflexes: + to Reflex saves, buffing up an otherwise poor save. Looks fine.

Rifts: Your basic attacking option. Deals sub-sneak attack damage. By default, you must attack as a standard action to use one, gaining a benefit on one round, but then reversing the benefit on the next one. Full analysis of rifts to come, but for now, note that the standard action + tempo system heavily incentivizes skirmishing by swinging with a rift one round, then retreating the next, or using ranged attacks.

2nd level:
Disjointed Perspective: A neat bonus to a skill you'll be boosting a bunch. Skill check will hit at least +33 by level 20, probably more (Int bonus, skill focus), which is important, because you'll be using it on several class features. In general, assume that the skill check will win. By, like, a lot. You could be hitting +40 with this easily. Buut, it's not actually great at the level you get it. This class feature synergizes with:

Practiced Aversion: Long story short, pick another skill to always succeed on. Perception is a good option here. Oddly, you can use it on Knowledge skills, which conflicts with the description.

Calculations: A mix of passive abilities and active ones representing "specialist" options. Equivalent of Rogue talents. The real winner of this level.

3rd level:
Precognitive Dodge: 1/day (increasing with level), Knowledge(History) replaces your AC for one attack. Can be life-saving, but takes up your immediate action- you may need your swift action later. Unclear if you make the choice before or after the roll is made- looks like before. More important on a rogue chassis than otherwise.

Extended Rift: Expend your psionic focus (which, recall, takes at least a move action or more to gain), and a paradox point (4 at this point) to add the effects of a rift to each attack you make this round, ignoring the backlash. It seems that the effect of the rift (but not the damage) stacks with whatever you already had. No action to use, though. You can combine this with Accelerated Rift to combine three effects on one hit! However, it's pretty lackluster at this point, since your full attack is useless at this level. Its presence at this level pushes the class's early game towards archery builds which can make use of multiple attacks at this level with Rapid Shot and the like. The psionic focus requirement makes it a bit more difficult to get out, but you can deal serious burst damage with this.

4th level: One more Calculation! More Rift damage! 2nd level powers! Good fun.

5th level: Personal Velocity: You get this spell two levels before you would otherwise select it, and it's on when you need it. Extended Rift is now relevant. Archery is still good.

6th level: Calculation, new Rift. It's OK. Pick your last 2nd level power.

7th level: Twin Paradox. Spend a point of paradox as a swift action, get a standard action out. It's a bit confusing- can your copy use rifts? If so, if they use a self-affecting rift like Accuracy, what happens after they disappear? What if you also use Accuracy in the same round? What if you Extended Rift it- does it affect the copy's attacks? Can it... regain your psionic focus for you?
Also, extra dodge/day.
Also this level: 3rd level powers! You can toss out your own Physical Acceleration at this point.

8th level: Calculation, + to Rift damage, NEW ATTACK ON FULL ATTACKS. It's pretty good! Extended Rift -> Accuracy + Physical Acceleration for free + Rapid Shot means you deal a heckuvalotta damage if you need to. Melee attackers can do all of that except for Rapid Shot for almost as much damage.

9th level: Impending Destiny, new Rift. Impending Destiny is nice, but what's even more nice is that you're getting some of the good Rifts now- Expulsion, Latency, etc.

10th level: Calculation, and 4th level spells. There are some nice spells to choose from.

11th level: Very meh. New dodge/day.

12th level: Pick up another one of the good rifts, deal more damage with them, and new Calculation. Nothing fancy, but a good level. Most of your numbers go up by 1 here.

13th level: New spell level. Twin Paradox now does 2 at once- more attacks are good, but the cost is pretty high...

14th level: New calculation, not much else.

15th level: Precog dodge again. New Rift known! Extra attack on full attack!!!

16th level: Final spell level. Calculation. Rifts damage goes up again.

17th level: 1HKO! When it works, anyway.

18th level: Calculation, Rift. At this point, unless I'm going for the Age Resistance chain, there's not much to offer here, I don't think? Need to look over Calculations again.

19th level: 3rd twin paradox, another precog dodge. The first won't see much use, the second one might- twin paradox eats through your paradox points like crazy.

20th level: More calculations. You do get time regression, which is one of my favorite powers.


Todo:
Calculations
Rifts

Verdict so far:
It is, almost without meaning to do so, almost perfect for an archery build, both for the opportunity to deal precision damage consistently with attacks (which rogues have trouble with), the ability to gain extra attacks per round from "teammates", easy and automatic access to haste, the ability to dodge attacks when needed with Precognitive dodge, and so on. Calculations might change my mind about this, though.

Rift mechanics are interesting and unique! Like them a lot.
Class features are not as great. Time theme is present, but doesn't feel central to the class.

I will continue editing this post as I go.

Spoiler: Obligitory bookmark dig for time-related stuff
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Leaving off notes due to lateness
Time-travel RPG- maybe crib their notes on recording the future and frag-as-paradox
Time-related combatant. Loads of time-focused powers. Notable features involve stopping time- not as unbalanced as you might think.
Literal time travel. Paradoxes built into the class. Maybe too punishing...
There was one class which I have lost the location of. Notable features involved synching yourself with an ally, shifting your intiative towards each other each turn. Then... something? Messing with initiative feels appropriate, though.