OK, so you were 66 in 2008, and 63 in 2005 and 58 when your spouse passed away in 2000, and 60 in 2002.
IN 2000 - At age 58 at the time of his passing, and not disabled, not eligible for any kind of benefit (unless you had a minor child).
Next date, at age 60, in 2002, you became eligible for a surviving widow benefit at 71.5% of his rate. You did opt for this reduced widow amount (the 71.5%). But not eligible for your own benefit, because you were not of regular "early" retirement age, nor disabled.
Then, in 2004, at age 62, you became eligible for your own reduced retirement benefit, but likely didn't take it because you were taking survivor benefit.
In 2005, at 63, you become disabled and apply for SSDIB, you now become eligible for that one more option - your own disability benefits (at FULL amount). You state, ".SSA put me on my own work record. Not on a disabled widows." This is correct because disabled widows is ONLY when you are between 50 and 60. At 60, it is JUST widows benefits if on his record, which you took until you decided to file for your own disability benefit. You OWN disability benefit is equal to your OWN full retirement rate retirement amount.
In 2008, at the age of 66, your FRA, your SSDIB you took changes in name to SS retirement - in full.
I think you are saying that you sought to change from your Full retirement back to a survivor benefit. They denied you, you appealed for Recon, and you won in 2011, getting a lump sum benefit of some amount. Then SSA appealed that Recon decision and it was found that you shouldn't get the increase. So you appealed that. Apparently you lost after ALJ hearing.
Now you also say, I THINK:
At 60, you got your survivor benefit of 1102. I think you are saying that, yes? Doing the math, 1102 is 71.5% of 1541 (which may have been his PIA at that time because the 2016 amount would be after adding years of COLA (cost of living adjustment).
I am NOT sure what you are saying 770 is - at your FRA. You mention 50%, which implies you are speaking of a spousal benefit, but you weren't eligible for spousal because you were a widow. The 50% spousal is replaced by the higher widow amount. SO what is the point you are making about the $770?
You then seem to be adding the 770 to the 1102 to get your 1872. But we don't add these two because we are not permitted a spousal PLUS a survivor benefit - but anyway, please clarify. And why to you believe that sum, 1872 is your spouse's PIA in 2016?
OK, moving on, you indicate your own PIA is 1643. So, that is what you are collecting as a retired person who did NOT collect retirement earlier than FRA, correct?
So is your end question, why am I not getting 1872 instead of 1643? Let me know.
Now, I am going to try to find the 2 references you suggest. The ALJ's RS and (if I can find it, the OIG's letter). While I am doing that, please confirm my various questions above, OK?
You then say, I think, that you are adding the 1102 you got at age 60, plus a his PIA was 1872 in 2016 - I would imagine COLA would have increased it, yes, although I can not say how much in those 8 years, as I am not the accountant.