Stable Time Loop: The Chronological Consistency Protection Theorem (see: You Already Changed The Past) does appear to permit these kinds of predestination paradoxes (at least, the informational kind; the object paradox may also be possible, but testing it is dependent on finding an object that won’t age during the period of the loop, including in all the aspects that the universe will check that current technology may not be able to).
It is also somewhat limited by the main people who can make use of it for Retroactive Precognition/Retroactive Preparation being the transcendent/weakly godlike artificial intelligences. Experiments by lesser intellects… well, they don’t actually produce messages reading “YOU ARE NOT SMART ENOUGH TO BUGGER ABOUT WITH THE TEMPORAL CONTINUUM”, but the gist of the results appears to be fairly plain.
A duel begins and ends with one stroke. So it is said.
With tactical prolepsis, this is even more true than it once was.
I stared at my opponent without seeing him; in the view of proleptics, there are no objects, only clouds of probability and possibility. The quantum computer in my head purred to itself, whispering tactical analysis engrams into my undermind and running massively-parallel anticipatory simulations.
The target was a blob of probable solidity, fuzzy with microcausal jitter. Bifurcating arcs of destiny writhed in secondary visual fields, ignored to concentrate on the glittering blurs of near-term possibility, threatening to actualize at any moment.
One second passed. Two.
A third, and then a probability spike, one possible future hardening towards actualization. I took one step to the left, my cannon rising in my hand. Distantly, I felt the tremor as the flechette left the barrel; something whipped past my ear, ruffling my hair with the wind of its passage; and then he was falling, helmet shattered and venting rapidly-condensing gas into the void.