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    $\begingroup$ As stated, this would be unsuitable, as it is unclear how to "parallelize" in a fashion desirable for Polymath. If you were to provide, say, an additional predicate P(n) such that P(n) and the Collatz dynamic terminates upon input n, that might be suitable. Many of the other examples provided are sufficiently restricted that the leap to parallelize is not so great. Please edit this to find a restriction that suits the conditions of the post. Gerhard "Polymath Is Not Group Mathematics" Paseman, 2017.01.07. $\endgroup$ Commented Jan 7, 2017 at 21:13
  • $\begingroup$ +1, nice paper. We're making progress. Still don't know how to parallelize. $\endgroup$ Commented Aug 16, 2017 at 3:00
  • $\begingroup$ Regarding the question of parallelising the efforts, here are the three most important theorems that the paper demonstrates: 1) for any odd number a, whoever can prove that 4a+1 and 8a+3 have a common number in their orbit (anywhere, backward or forward) solves Syracuse 2) for any odd number a, either the orbits of 8a+1 and 16a+1 will merge, or 8a+1 will merge with 64a+17 and 16a+1 will merge with 2a-1. 3) theorem 2) will occur at least once in any odd number's forward orbit, because any odd number will have either a number 8a+1 or 16a+1 where a is odd, at least once in its forward orbit. $\endgroup$ Commented Aug 19, 2017 at 9:20
  • $\begingroup$ Calling the pairs (4a+1, 8a+3) where a is odd "buds", and having established that their solving solves Syracuse, it is important to observe that some of them "solve themselves", and I can demonstrate why. As some buds point one to another (are redundant), it is relevant to ask which proportion of the set of all buds must be solved to solve Syracuse, typically the sort of question one might ask in Ramsey theory. In any case, the systematic attacking of buds can be parallelised, and is one way to parallelise the solving of Syracuse. $\endgroup$ Commented Aug 19, 2017 at 9:20
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    $\begingroup$ Oh, and don't worry about ego injuring. Most mathematicians (of my acquaintance, and probably outside of it too) are more concerned with time misspent on studying worthless claims than on priority claims. Gerhard "And This Is My Claim" Paseman, 2017.10.05. $\endgroup$ Commented Oct 5, 2017 at 15:06