Nice paper, although the idea of using the sun as your sample source is really flawed unfortunately. The problem is the noise the sun emits is basically just thermal noise, so while you can try to make a good measurement of it to do cross-correlation you'll find out that your phase information is screwed up because there is no way to distinguish what is the sun and what isn't. You'd have better luck using an optical telescope, but then you'd run into the problem that there aren't any features on the sun that change sufficiently fast.
Not so— the optical flux coming off the sun has tremendous RF noise. I was mostly thinking of optical— simply because it's so much easier to get really strong spatial filtering— but I don't know if you've ever observed the RF output of the sun in 1-3cm, it's easily the hottest RF background source if you point a gain antenna anywhere near it and you can get reasonable gain at those frequencies. I was assuming that the sampling would be synced with the system stabilized oxco and so should be fairly low (And consistent) in phase noise.
Of course, I haven't actually tried it for this. But I've absolutely done correlations of pure noise signals for range-finding and gotten usable results. Not every fix would be successful.
What does work along these lines for time synchronization is to use radio telescopes to lock onto specific pulsars. Using multiple pulsars at once could give you enough information to resolve increasingly larger time intervals by comparing pulsars of different intervals and phase relationships. The requirement for a radio telescope though is a bit annoying...
Picking up pulsars requires costly enough equipment... enough that it would sort of moot the decentralization of it. (Well if equipment to observe the sun isn't too exclusive)
However... the electrical grid on the other hand would work just fine as it's a specific signal with fairly large variations distributed over a wide area. But as you say, you need the POW chain consensus to assign significance.
Yup, the other problem is that few parties can observe more than one grid, so it would be hard to extend it world wide. There is still the idea of securely timestamping the GPS signal though, which may still have value.
Still I figure a cheap wall-wart with AC output - rather than the usual DC - and a resistor divider could be connected directly to a soundcard line-in port with no issues. With a standard 48KHz sound card you'll be able to resolve phase differences down to 1/24KHz, or 41uS, with some effort. In reality jitter in your sound card -> computer chain would be the limiting factor. Even professional sound cards have hundreds of uS worth of jitter. That said if what you want to measure accurately is external to the computer, you can just build some hardware that puts a pulse associated with your measurement on another channel of the same sound card and you can ignore the computer's timing jitter again, at least for relative measurements.
FWIW I'm thinking of setting up a series of those monitoring stations with the data uploaded to a public server. It'd let people use that forensic technique themselves. Of course, that goes both ways...
You're not limited to phase differences of 1/24KHz, assuming the anti-aliasing filters are correct— your phase resolution is only limited by the noise floor (quite excellent on modern sound cards) and jitter (not excellent, as you note).
(Of course, to get better phase resolution than just a fixed basis transform like the FFT will give you you'll need a fast non-linear solver for sinusoid parameters— but no worries, I've got you covered there: [er. link to be provided once the server comes back up]).
