And I've got some swampland in Florida I'd like to sell you.
I looked it up. It's not a polite term, used as you used it. Context is determinative. Bite me.
The South laid claim to "New Mexico Territory" and had expansionist views to Colorado, Nevada, and California. the 1862 Sibley campaign is proof of their intent. It only "resigned interest" on territories when it could no longer take them by force.
New Mexico had recently been part of Texas and had been ceded by Texas to the United States. With the Union now null and void, Texians may have thought that the territory should revert to them. I'd take a legal scholar's advice on who really owned New Mexico under the circumstances. Certainly there was a difference of opinion.
However, I insist that you notice and stipulate to it, that no Confederate State asserted claims in Nebraska, Kansas, or any of the other territories.
California was a State by 1860 and can't have been seen as Confederate territory. Moreso the Pacific Northwest. If you think so, though, by all means produce your document.
You provide an interesting point of view regarding boundaries. Is there a "legal scholar" to which you refer?
My reference to "New Mexico Territory" included the present-day states of Arizona and New Mexico. Your statement that New Mexico had recently been part of Texas is somewhat off the mark. It is true that the lands ceded by Mexico, in 1848, by the Treaty of Guadalupe Hidalgo, and the territorial claims of Texas overlapped. The area that overlapped was that part of New Mexico that was east of the Rio Grande (and incidentally, extended up into present-day Colorado, southwestern Kansas, a small section of Wyoming, and the Oklahoma panhandle).
In any case, the southern Civil War claims in the New Mexico Territory do not coincide with Texas's historic claim to the lands east of the Rio Grande.
The land to the north was already occupied by Mormon settlers in 1848, who had nothing to do with Mexico, and whose expansive land claims were unrecognized. (Alta) California had briefly established an independent republic (led by John C. Fremont), when the war with Mexico led to American military rule.
The various land claims and boundaries were settled in 1850. Texas assumed its current boundaries and sold it northwestern claims to the United States (which assumed Texas's war debt). At that time, California was admitted to the Union as a State and the New Mexico Territory and Utah Territory were established. In 1853, New Mexico Territory was enhanced by the Gadsden Purchase. In 1854 the Kansas and Nebraska Territories were organized.
"However, I insist that you notice and stipulate to it, that no Confederate State asserted claims in Nebraska, Kansas, or any of the other territories."
It seems to me, that if Texas made claim (in 1861 to lands they sold in 1850), to former territory, which would have included parts of New Mexico Territory, Kansas Territory, Utah Territory, and Nebraska Territory, than they would have indeed done what you insist they did not.
It seems, then, you will need to be a little more specific on what you mean by "Texians may have thought that the territory should revert to them."