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^{The algorithm designer who does not run experiments risks becoming lost in abstraction. —Sedgewick}
2d

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A circulant coin weighing problem
not an expert in this but looking further. this paper "Münchhausen Matrices" / Brand also studies a variant of the coin weighing problem and says p3 there are different "weighing matrices" going back to a definition at least to 1946 [14] for "Hotellings weighing problem". is the wikipedia entry referring to the latter? 
2d

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A circulant coin weighing problem
@Anush did you look it up on wikipedia, weighing matrices? 
Jun 19 
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Probability of many overlapping zero inner products on a circle
some basic ideas are not being defined. what is i th rotation of v ? etc. if not phrased in some std ways & not linked into any other std study (what field is this from? motivation? etc) then maybe a short intro/ writeup elsewhere would help 
Mar 15 
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Collatz property implying infinite “fall below” trajectories, is it known?
thx for further attn however afaik collatz implies the "fall below" property highlighted in the question for an infinite # of cases but not vice versa as your answer seems to assert. but the strict formulation of the property is more found in the followup comments. suggest/ encourage further discussion/ clarification in number theory chat 
Dec 14 
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Invariants that might determine graph up to isomorphism
re HS comment, it would be good if the author of the paper updates it to state the error and extract anything else useable from the framework. otherwise there may be further questions 
Oct 22 
awarded  Nice Answer 
Sep 24 
awarded  Autobiographer 
Aug 27 
awarded  Informed 
Aug 26 
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Do the base 3 digits of $2^n$ avoid the digit 2 infinitely often — what is the status of this problem?
Tao (end of blog post) cites some refs & draws some analogy to the collatz conjecture. apparently Erdos conjectured "2" always appears in the base3 expansion for all $i>8$ 
Aug 21 
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Collatz property implying infinite “fall below” trajectories, is it known?
Aeryks formulation is what is intended, thx for that (mea culpa for not initially rigorously stating it). have worked with "backwards" algorithms like what AlexR refers to but dont know what mathematical form the sets take, have to think about that more, dont see how to derive the above property that way. (note property is implied by Collatz conjecture.) 
Aug 21 
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Collatz property implying infinite “fall below” trajectories, is it known?
the "fall below" property is interrelated but not exactly the same as the "terminates at 1" property. the conjecture is also true iff all trajectories "fall below". but a "fall below" property of a trajectory does not nec(?) guarantee it terminates at 1. (by induction) a "fall below" trajectory does terminate at 1 if all trajectories starting below it also have the "fall below" property. here "full trajectory" means a trajectory ending at 1. 
Aug 20 
asked  Collatz property implying infinite “fall below” trajectories, is it known? 
Aug 14 
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Examples of unexpected mathematical images
also see eg Phase Plots of Complex Functions: a Journey in Illustration / Wegert, used to visualize the Riemann zeta fn & related ones 
Aug 11 
answered  Examples of unexpected mathematical images 
Aug 4 
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Prime factorization “demoted” leads to function whose fixed points are primes?
what app did you use to generate the graph? 
Aug 4 
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Prime factorization “demoted” leads to function whose fixed points are primes?
some superficial resemblance to collatz conjecture in the iteration etc. there is some way of unifying these types of questions under an automata theory formulation. 
Jul 19 
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Negative impact of wrong or nonrigorous proofs
the question is slightly leading. any erroneous theorem or lemma anywhere leads to "0=1" elsewhere. it can be very timeconsuming for others to discover/find these "defects" (there is some loose analogy to software engineering). so "damage" is an overwrought/dramatic word/adjective in this context. but, ofc, "to err is human..." even by professional mathematicians. agreed that fixing errors can lead to highly constructive new math/research etc. 
Jun 9 
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Understanding the nature and structure of proofs; Reverse Mathematics and Proof Theory. Prerequisites? Good introductory texts?
did anyone cite the wikipedia article? 
Jun 6 
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Mistakes in mathematics, false illusions about conjectures
nice question but dislike the vagueness of the initial paragraph. why not cite the example? sounds like you could be referring to an important open problem... 
May 30 
revised 
Is it easy to produce hardtocolor graphs?
added 61 characters in body 