Source of Fremer's "1 arc second" claim?

The 1-arc-second likely originates from this turntable vendor whitepaper - Oswalds Mill Audio - K3 Whitepaper | OMA of which MF owns (or owned).  There are a number of errors in the white paper:

"...our device needs to actually physically trace modulations in a vinyl groove to the order of .005 microns."  The inherent surface roughness of the record reported by a couple sources is 0.01 to 0.005-microns (100 to 50 angstroms).  The RIAA curve is specifically intended to avoid the noise inherent to the record's inherent surface roughness, so the realistic smallest modulation is 0.1-microns, at least 10X the surface roughness.  And just to put the record's surface roughness into perspective, its surface finish (inherent to the material and pressing process) is finer than mirror polished stainless steel.  

As far as the arc-sec, read Minute and second of arc - Wikipedia, it's an angle measurement.  To apply that to a record of 12" diameter spinning at 33.333-rpm with outside groove tangential velocity of 51-cm/sec and inside groove velocity of as low as 20-cm/sec.  Converting 51-cm/s to radians/sec Angular Velocity Calculator = 3.3456 rads/sec which Angular Velocity Conversion Calculator - Radians, Degrees, Revolutions, and Grads = 191.74 deg/sec Degrees to Seconds Converter = 687,600 arc-secs.  Like the OP, the ability to detect 1-arc-sec is not possible.  However, angle encoders appear to have accuracies of 5-arc-sec and better accuracy_of_angle_encoders.pdf where "Angular measurement error (arc seconds) = bearing wander (μm) x 412.5/D" where D=mm.  If it's assumed a bearing radial wander of 5-microns and diameter of 13-inch, the angular measurement error in arc-sec is 1.2492.  But this does not take into account circuit noise, feedback error, etc. 

Like the 0.005 micron claim, the white paper claim of 1-arc-sec appears (being diplomatic) to be very 'optimistic'.  Otherwise, keep in mind that MF is not a scientist or mathematician.  He would help himself if he referenced the information source that is well out of his swim-lane, versus making claims that appear to be attributed to him.  

@antinn, for years I've read about Oswalds Mill Audio and Jonathan Weiss.  I've never seen MF associated with them in any capacity.  But that does not mean he was/is not.  So I'm curious, where you found that connection?

I don't think MF has anything whatever to do with OMA or even the K3, in a business sense.  Odds are he borrowed the K3 from OMA for an extended period of time, but I certainly do not claim to know that for a fact.  He may actually own it. And I don't think he is corrupt in any way, except subconsciously in the way we all are not to be trusted.  He says what he thinks. I think his main problem when discussing technical aspects of audio is that he has no scientific background to allow him to critique the BS he is fed.  (Someone else already said this, and I agree.) Very often he is just parroting what the manufacturer told him or what the manufacturer wrote in a brochure, uncritically.  On the other hand, we vinylphiles all owe him a debt of gratitude for his role in revitalizing this pursuit, and he is by no means a MFer. He could do with having a physicist or engineer available as a consultant to edit the tech aspects of his reviews.

@pryso

MF reviewed the Oswald K3 Analog Corner #314: OMA K3 turntable & Schröder tonearm Page 2 | Stereophile.com and per this article (last paragraph) confirms that he bought the unit - Oswalds Mill Audio K3 Turntable - The Absolute Sound.  

Gentlepeople

Michael's arc second comment probably came from a conversation I had with him about the speed sensing architecture in the OMA K3 turntable. The design sends a little over 1.3 million pulses, counts, to the motor controller every revolution. Slightly more than one count per arc second. This equates to a little more than 728,000 pulses per second at 33.33 RPM. The speed sensor assembly, like everything that exists, is not perfect. This means that  the time spaces between the pulses are not absolutely equal, even if the motor is running at a perfectly constant speed. The controller will sense these differences and signal the motor to correct a speed error that does not exist. The motor may or may not be able to accelerate or decellerate the platter in time to correct this non existent error but it will receive a current change none the less. 

The people who make the motor controller designed it to control systems that require much more speed precision than used in a TT. They also are well aware of speed sensor count errors. To mitigate this problem, the controller has a selectable function that activates a rolling average of the counts. With a few key strokes this can be set to 1, no averaging and 2 up to 8 count averaging. The controller also adds math to this function by giving more weight to the first count and little less for the second and so on. This function acts to smooth over the sense errors, resulting in more stable (smooth) and accurate rotation. It also acts to soften, smooth, the reaction, correction, of actual speed errors. When programming the controller, our listening panel trailed this function and found that it did indeed make an audible difference. The person making the program change did not tell the panel what change had been made, he only asked....better, worse, same?  Since it was software driven we could easily toggle it on/of or change the averaging number. In this way we could confirm in near real time what we were hearing. We also had a policy of revisiting the programming some weeks later to ensure that we hadn't make mistakes.

We settled on a rolling average count of 4.

When calibrating the speed to 33.33, 45 and 78 we simply adjusted the count command per second. Once close to the required speed we set about  incrementing or decrementing by 1 count per second. This meant that when targeting the required speed, we were changing the speed up or down by arc seconds per time. For a laugh, we listened to these changes, no one could detect a difference and no one was surprised.