Thank you for correcting your measurements report. The size you now report, 2.164" by 3.480" (55mm by 88mm), is at the upper edge of the correct size-ranges for a genuine US Army Model-1851 swordbelt's eagle-&-wreath plate. That type was manufactured from 1851 through 1873. (But see the time-dating for yours, later in this post.)
You asked:
> As to the plate I have no idea if stamped or cast. Please tell me what it should be?
Your US Model-1851 swordbelt plate is solid-cast brass, as it should be. A "stamped" beltplate's back shows a reverse-image of the front.
> What would the number mean?
The number is a manufacturer's "bench mark." It is a "batch-number" at the manufacturer's workshop, not a serial-number.
> Sorry for all the questions.
No need to apologize for asking the questions. That is how each of us learned much of what we now know. My two primary "Mentors" in relic-collecting were very patient with my endless newbie questions. What I do here in the What-Is-It forum is payback for all the valuable knowledge they gave me, for free.
> I can only assume that a C.W. veteran came to this area to mine gold or work in the mines
> in the 1870-80's, still wearing it, and at sometime in time lost it.
That is fairly likely to be how it got to the spot where you dug it. At that time, such belts were not used to hold up your pants. Miners don't carry a sword, so your plate's belt was probably used to carry a pistol holster.
> I've never even seen one of these and would like to know as much as possible about it.
> Any further info would be much appreciated.
Okay, since you asked for more info:
As I mentioned above, the US Army Model-1851 swordbelt plate was manufactured from 1851 through 1873, then the Army replaced it with the Model-1874. I should mention, a comparatively small number of STAMPED-BRASS with LEAD-FILLED-BACK Model-1851 plates were made for various State Militias up until about 1900. You found the solid-cast version, which is the US Army Regulation version.
As I also mentioned previously... your plate had a nickel-silver wreath, which was soldered onto the cast-brass plate's front. The "applied" wreath is typically missing from excavated plates. Having an "applied" wreath means your plate is the Enlisted-men's version. On the Officer version, the wreath was brass, being simply an "area" of the solid-cast brass plate's emblem. On that version, after it came out of the casting-mold, "silverplating" was applied onto its wreath.
Your specific plate (there are at least two dozen slight variations in the emblem) is shown as plate #665 (page 400) in the book "American Military Belt Plates" by O'Donnell & Campbell. The book says your specific variety was manufactured only during 1864-65.
I suspect some readers will want to know, so I'll mention that your plate's dollar-value on the civil war collectors' market is around $200 or slightly higher. As I said above, the majority of dug Enlisted-men's ones are missing the applied nickel-silver wreath, so a dug one which still has the wreath is worth about $50 more.