I pick up street litter, and having picked up thousands of pounds, I have never felt that loose caps are a problem, let alone one that requires such a solution. The number of littered bottles, with or without a cap, is greater than the number of loose caps, and the amount of plastic in every bottle dwarfs the plastic in a cap. Fixing the cap to the bottle will do nothing to improve the recycling rate of plastic if entire bottles are already tossed anyway.
I consider the idea of cap tethers as adversarial memetic warfare thrust upon us for some unknown ulterior purpose, possibly to make us hate the very idea of environmental consciousness. Same as paper straws. I like plastic bag bans though.
As far as picking litter is concerned, I personally prefer finding bottles without a cap. At least those are empty, all liquid having evaporated after the bottle has spent several months in the bushes. The capped bottles are often half-full and are just nasty. (Who even pays for a bottle of drink and not drinks half of it anyway?)
For an object heavier than the Earth, 1g radius will be greater than the radius of Earth. For 56 Earth masses that’s sqrt(56) times bigger = 48000km.
A 56 Earth mass black hole will take 5.5e55 years to evaporate according to this calculator. A 100kg black hole (more close to what Richard used to be) is much smaller than the nucleus of an atom and will evaporate in 0.05 nanoseconds.
Curiously there was a paper recently that calculated that even if there was a small black hole in the center of the Sun, it would take millions of years for it to grow, because the aperture is so small not much can fit through, and the infalling gas heats up so much as to repel the rest, creating an internal hot bubble.