I do respect Advantest for doing the meter in first place, but in my book high-end instrument is not just a piece of hardware, but also documentation (anyone see any document about 6581T?), service procedures and reliability of the internal and external calibration procedures. Yes, long service hours affect instrument aging, stability and bring wear and tear issues. Actually that what is making high-end instrument so, ability to sustain it's tight specifications over the time and use abuse. One can calibrate "cheap" 6.5d DMM and 8.5d DMM to same initial accuracy, but over 1 year, you will see why 8.5d is priced 10 times more.
Single 7V/-7V point does not tell us much, sorry. You need linear source or a reference meter with proven linearity (hello, 3458A/5440/720A-732 etc), to verify issues that multiple people see.
Don't get me wrong, R6581T is nice meter to have, but saying it's on par with other industry proven 8.5d ones is bit over-excitement (unless we find out exact root cause of performance issues).
Or maybe all of the R6581T that multiple people have here are simply broken in various ways, yet pass external and internal calibrations and self-tests, giving a false pass and out-of-spec results.
Running external calibration on Ohms, with 10000.0011 Ohm standard and getting 9999.8791 ohm as result is bit unsettling
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Given simple statistics we should have at least one person here with R6581T which actually does meet R6581 specs? Maybe it's you?