Lucky Cuss - The star is undersized.
I guess you checked Dunigan's book too. This is clearly a third cap design so I agree weight and specific gravity are rather critical to tell if it is genuine or a contemporary counterfeit for certain.
jdmern Thank you for sending the obverse photo. It is a type eagle that was actually used at Guadeloupe Y Calvo beginning in 1847 according to Dunigan once again. It is not an exact match for the Dunigan obverse for 1846, but this could be his error (see below).
So I looked at all of the entries in the Heritage archive for 1846 GC MP and there are only 12 after you exclude duplicate entries of which there are several.
Dunigan lists two variables for the reverse die
(1) pointed or normal cap and
(2) round cap.
These distinctions are recognized by the TPGs, but not always indicated on every holder.
Dunigan lists three
possible variables for the obverse
(1) Square tailed eagle (a very crude die)
(2) A round tail or normal eagle of 1846 and
(3) A round tail eagle type of 1847 (omitted under 1846.)
I am listing this 3rd alternative because it exists in
TPG slabs listed on Heritage. So I am presuming Dunigan missed it.
There are 4 examples in the Heritage archive of the Round Tail cap with the Square tail eagle. These do not enter the actual discussion because they are different types, but I wish to not that all of the round cap varieties show the same ray orientation as is seen on the pointed cap variety - one long ray slightly above the star - a second long ray pointed directly at the star - a third shorter ray pointed directly at the 8. There are no other ray arrangements for the round cap style. Also note that there is a large star present before the denomination.
Before proceeding it must be stated that Dunigan also mentions a mule of the two primary styles a round cap and a normal or round tail eagle. That combination is represented in the Heritage archive by a single example. Dunigan considers the mule to be very rare on a par with the reversed s superscripts variety.
Regarding the normal or round tail eagle Dunigan illustrates the normal or round tail eagle as having a high headed snake as in the 1846 type. The 1847 eagle type also is round tailed eagle but it has a low headed snake present. Once again it is possible that Dunigan did not notice that it constitutes a 3rd eagle type for 1846.
The mule noted above in the Heritage archive has a low headed snake present so it would be the 1847 type. Unfortunately Dunigan did not illustrate his mule. I believe that it is likely the same coin however.
The Heritage archive contains 3 examples of the Normal or pointed cap with the standard ray arrangement for each of the low head snake (1847) and the high head snake (1846) varieties. The designs of the eagles appear to be the same within each group of three coins but these two eagles do not match each other.
So with the mule included that accounts for 11 of the 12 Heritage examples.
The final example is an oddity. When I first saw it I was tempted to call it a counterfeit. It was at the time raw. I listed it as "dispute" in my records. I noticed that the same coin has reappeared on Heritage more recently and again raw. (For the record I have to note that counterfeits do get slabbed even by the big three TPGs.)
That specific coin has an eagle with a low headed snake and it also has an odd ray arrangement but NOT exactly the arrangement seen on the Masonic coin. The top ray is correctly positioned just above the star - it has the same curved minor tip seen on the Masonic coin. The second long ray points squarely at the 8 not the star - also identical to the Masonic coin. The difference between the masonic coin and this Heritage coin is in the two shorter rays. It also must be noted that both coins use a small poorly drawn star.
So to illustrate the differences seen only on one coin in the Heritage archive (which I never believed was genuine) I enlarged the portion of the Cap where the serious differences are seen;
This first view is of one of the coins I consider to have the standard spacing and angles for the rays. I placed a red line down the center of each ray to highlight the differences. Note also on the top long ray above the star that the thin line running alongside the ray is straight and does not curve at the tip. Finally note the size and shape of the star.

The next illustration is the same view of the Masonic coin. The red lines show that the ray positions are not the same. Also note the small upward curve at the tip of the line above the top long ray and the size and shape of the star.

Thirdly here is the Heritage coin that I disputed when it first appeared. Here I did not draw in the red lines but I did circle in red the tip on the line above the top ray and the small star.

I did something similar with the eagle. This next picture is of the Dunigan "Normal eagle" of 1846 with the high head snake.

Next is the eagle from the Masonic coin.

Next the eagle from the raw Heritage coin which I disputed

These last two are in my opinion identical designs - note the round depression in the eagle's right wing - right at the elbow bend and the missing outline and feathers directly under the eagle's left wing elbow. These are identical punches if not the identical die.
Almost finally, here is the low head snake variety seen on the graded versions of the coin using Dunigan's omitted variety the low head style of 1847.

Notice this is NOT the eagle seen on the Masonic coin nor on the other raw Heritage coin that I dispute. The eagle has no recessed hole in the right elbow and the feathers are clear along with a clear outline of the right wing below the elbow.
As a final concluding point I want to show for a second time a picture that appeared above of the Heritage raw coin that I disputed as genuine. It is the prima fascia proof in m opinion that the Heritage coin is a forgery. Here is the picture once again.

Now the same picture with the problem marked in RED.

Those of you who know me realize exactly what an arc that stops short of the edge of a coin means. For those who do not here is an explanation.
In an open sided press the die faces used to strike an 8R were larger than the planchets that were placed on them. The dentils were cut on the die as lozenge shaped figures which tapered to a roundish end at both ends. When a coin was struck on center the dentils run all around the coin but only half of them show. On an off center strike the full dentils may show on the one side but the other edge will have them missing. When a person copies an existing coin and makes a die - they often do not add the extra piece of the dentils. A strike using this under diameter die gives itself away whenever a planchet is placed eccentrically on the small die. The edge of the die shows as cut off dentils falling along an arc exactly as seen on the Heritage coin that I disputed.
So since the Masonic coin matches the Heritage disputed coin in nearly every particular (the exception being the two oddly placed short rays - which could have been recut) is the Masonic host coin Genuine or Not?