Or, Foot Artillery did not always refer only to those manning static fortifications [underlines mine - B.E.]:
from Artillerists Manual / Gibbons / Second Edition / 1859:
"...342 Field Artillery
[that's right, this is from the Field Artillery section of the book, not from a separate chapter covering static heavy artillery - B.E.]
...In the mounted batteries, formerly called foot-artillery, the cannoneers are on foot, and remain so during the manoeuvres of the battery, except when it is desired to move at a very rapid rate, when they are mounted on the ammunition -boxes."
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from Hand-Book of Artillery / Roberts / Fifth Edition Revised /1863:
"...On Field Guns and Batteries
[once again, not from a separate chapter covering static heavy artillery - B.E.]
...5. Are all field batteries alike?
No; field-batteries accompanying infantry are composed of the heavier, and those accompanying cavalry of the lighter pieces, the first manned by foot-artillery, and the latter by horse-artillery.
8. In what respect does a battery of horse artillery differ from one of foot artillery?
The main difference consists in the cannoneers in a battery of horse-artillery being mounted; in rapid evolutions of foot-artillery they are conveyed on the carriages.
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The big picture is that it cannot be denied that the sword was issued and used at some level to some kinds of artillerists and that surviving examples are definitely of CW provenance, regardless of how much or how little they were used. Let's leave it to the reenactors to advocate.
Further research would imply that you are either being disingenuous or just incomplete, our purpose should be to get it right:
Gibbons compiled a series of manuals, more for instruction for cadets at West Point than anything else and states as such, but he also states:
"Divided. - The following is the most recent division of the United States Artillery into two kinds according to its duties. Heavy or foot-artillery is that portion which takes charge of and manoeuvres the siege, sea coast and mountain artillery. Light or field-artillery, is that portion which manoeuvres field pieces with troops in the field. It is divided into horse-artillery and mounted batteries." Page 342, Field-Artillery section; Artillerist Manual printed August 14, 1859
Directly copied from the source:
342 FIELD-ARTILLERY. Divided.- The following is the most recent division of the United States artillery into kinds according to its duties. Heavy or foot-artillery is that portion which takes charge of and manoeuvres the siege, sea -coast, and mountain -artillery. Light or field-artillery, is that portion which manoeuvres field -pieces with troops in the field. It is divided into horse-artillery and mounted batteries. In horse-artillery, the cannoneers, of which there are eleven to each piece, are mounted on horses, from which they have to dismount before attending on the piece, the two extra men holding the horses of the rest. In the mounted batteries, formerly called foot -artillery, the cannoneers are on foot, and. remain so during the manoeuvres of the battery, except when it is desired to move at a very rapid rate, when they are mounted on the ammunition -boxes. The horse-artillery was originally and is still designed for service with cavalry, receiving the lightest guns, which enables it to move at the same rate as the cavalry, and to keep it up for a considerable time. In time of peace, or in the state of preparation for war, a
Further:
The official artillerist manual is the "Instruction for Field Artillery", completed in 1860 though begun in 1856 and "prepared by a board of artillery officers: Maj William H French, Capt. William F Barry and Maj Henry J Hunt and approved by Secretary of War, John B Floyd on March 6, 1860, revised 1864. Looking at the first page, below, foot-artillery is described, delineating it from the field-artillery: