The Alliance for I-69 Texas, in an article on its website, I-69 Scores Victory in Passage of MAP-21 Highway Bill, indicates that the Texarkana I-69 Spur will eventually be a 3di:
A 5-mile section of US 59 connecting to I-30 in Texarkana is being processed for designation as part of an I-69 system element. Because the primary national I-69 route extends into Louisiana south of Texarkana in Shelby County, section 118-mile section from I-30 south to Tenaha will be on the I-69 system but its specific numbering will be determined under the guidelines for interstate spur routes which carry a three-digit number using the number of the main route with an odd-number prefix such as 369 or 569.
A good place to start is FHWA's Statutory Listing of High Priority Corridors. I-69 is described in Subsections 18 and 20:
18. ...
20. United States Route 59 Corridor from Laredo, Texas, through Houston, Texas, to the vicinity of Texarkana, Texas. [I-69]
Next, page 23/599 of the MAP-21 pdf has the following provision:
(1) IN GENERAL.—Section 1105(e)(5)(A) of the Intermodal Surface Transportation Efficiency Act of 1991 (105 Stat. 2031;109 Stat. 597; 115 Stat. 872) is amended—
(A) in the first sentence, by striking ‘‘and in subsections(c)(18) and (c)(20)’’ and inserting ‘‘, in subsections (c)(18) and (c)(20), and in subparagraphs (A)(iii) and (B) of subsection(c)(26)’’; and
(B) in the second sentence, by striking ‘‘that the segment’’ and all that follows through the period and inserting ‘‘that the segment meets the Interstate System design standards approved by the Secretary under section 109(b) of title 23, United States Code, and is planned to connect to an existing Interstate System segment by the date that is 25 years after the date of enactment of the MAP–21.’’.
(above quote from
Across-the-Board Changes for Interstate Designations in New Highway Bill? thread)
in Texarkana, I would not mind driving the US 59/ Future I-x69 segment. In about 18 months, it may hold the record for the signed disconnected "child" that is the greatest distance from its signed "parent". 
(above quote from
Louisiana/Mississippi Road Meet thread)
After making the joking comment about US 59/ Future I-x69 in the road meet thread, I started thinking about how absurd (illogical?) it would be to have a signed disconnected child an extremely long way from its signed parent. In addition to the 113 mile length of the Texarkana Future I-x69's connection to mainline I-69 in Tenaha, it is approximately another 135 miles to what will definitely be a signed I-69 in Cleveland, Texas connected to the interstate system. In the other direction from Tenaha, it is approximately 42 miles to Stonewall, La., which is the southern (southwestern) terminus of I-69 SIU 15 connected to the interstate system (
LaDOTD has indicated in email correspondence that they are planning on completing I-69 SIU 15 approximately 25 years from now).
To make a long story short, there is NO WAY that TxDOT can assert with a straight face in its application to FHWA/ AASHTO that the Texarkana I-x69 segment will be connected to a mainline I-69 segment that is itself connected to the interstate system within 25 years. However, TxDOT will not have to make that assertion because the Texarkana I-x69 segment is already connected to I-30, an existing route on the interstate system.
I think that, since subparagraph (c)(20) statutorily defines the US 59 Laredo to Texarkana corridor as "I-69" (and the I-69 for Texas Alliance is concluding that it will be an I-x69 designation because, from Tenaha to Texarkana, it is both an I-69 spur and an I-69 "system element" off of mainline I-69), then FHWA/ AASHTO would be powerless to require the Texarkana I-x69 segment to be signed as an "I-x30".
[as an aside, the Alliance's description of the I-69 Spur as a "system element" echoes the
I-69/I-269 "system" for the I-69 Corridor in Memphis; I-x69 would sort of be a "spur cousin" to I-269]
This situation provides a good example of how the MAP-21 provisions for I-69 and I-11 differ from the provisions for other interstates. If the Texarkana I-x69 segment had been statutorily required to be analyzed as a "logical addition or connection" (the new MAP-21 requirement for the other interstates), then I believe the easy conclusion would have been that the segment connects to I-30 and should therefore be an I-x30, particularly considering the current distance from mainline I-69. It's definitely a quirky situation that leads to a seemingly "abandoned child".
