Question: On what date, was route on which the village of Hope, New Mexico is located, created ?

Context paragraphs:
New Mexico State Road 126: New Mexico State Road 126 is a state highway in New Mexico, United States of America.  Its total length is approximately 40 mi .  New Mexico Route 126's western terminus is in the small town of Cuba, at U.S. Route 550.  The route passes through the Nacimiento Mountains and Jemez Mountains, along the southern boundary of the San Pedro Parks Wilderness, then descends past Fenton Lake to the small, unincorporated community of La Cueva (east of Jemez Springs), where it ends at New Mexico State Road 4.

New Mexico State Road 501: New Mexico Route 501 is a very short state highway in New Mexico, United States of America.  Its total length is only about 7 mi .  New Mexico Route 501's southwestern terminus is at New Mexico State Road 4 west of Los Alamos.  It runs northeast into the town of Los Alamos, where it ends.  It passes through the territory of Los Alamos National Laboratory (LANL), which is closed to the public (the public may drive through on Route 501).  Guard posts are at either end of the LANL section of the highway, and motorists passing into (but not out of) LANL territory must pause at the posts and be waved through.  Under most conditions, no inspections, etc., are performed at the guard posts, but heightened security postures at LANL may lead to more intrusive checks.

Riverside, Rio Arriba County, New Mexico: Riverside is a former village, now a suburb of Española, New Mexico, in Rio Arriba County, New Mexico, in the southwestern United States.  It is located in north-central New Mexico, on the left bank (east side) of the Rio Grande across the river from Española proper.  It is on NM Route 68 just north of US Route 285 and just south of the former village of Santa Niño.  To the southeast is the former village of San Pedro.

Hope, New Mexico: Hope is a village in Eddy County, in southern New Mexico, United States.  It is about 20 mi west of Artesia on U.S. Route 82.  It has had a post office since 1890.  As of the 2010 census, the village's population was 105.

Butterfield Overland Mail in New Mexico Territory: The Butterfield Overland Mail was a transport and mail delivery system that employed stagecoaches that traveled on a specific route between Saint Louis, Missouri and San Francisco, California and which passed through the New Mexico Territory.  It was created by the United States Congress on March 3, 1857, and operated until March 30, 1861.  The route that was operated extended from where the ferry across the Colorado River to Fort Yuma Station, California was located, through New Mexico Territory via, Tucson to the Rio Grande and Mesilla, New Mexico then south to Franklin, Texas, midpoint on the route.  The New Mexico Territory mail route was divided into two divisions each under a superintendent.  Tucson was the headquarters of the 3rd Division of the Butterfield Overland Mail Company.  Franklin Station in the town of Franklin, (now El Paso, Texas), was headquarters of the 4th Division.

Butterfield Overland Mail in Texas: In Texas, the Butterfield Overland Mail service created by Congress on March 3, 1857, operated until March 30, 1861.  The route that was operated extended from San Francisco, California to Los Angeles, then across the Colorado Desert to Fort Yuma, then across New Mexico Territory via, Tucson and Mesilla, New Mexico to Franklin, Texas, midpoint on the route.  The route through Texas followed first the northern route to the Pecos River and downstream to Horse Head Crossing.  The route in West Texas was changed in 1859, in order to secure a better water supply on the route and to provide mail service to a more settled area, the stages between Franklin and the Pecos River followed the San Antonio-El Paso Road to Camp Stockton and then turned east to Horsehead Crossing.  From Horsehead Crossing the route crossed Texas to the Red River and into Indian Territory.  In 1860 the route was changed to another route from Jacksboro to Sherman via Decatur due to the building of a new toll bridge at Bridgeport, that avoided delays crossing the West Fork of the Trinity River when it was flooded.  From Colberts Ferry the route went on to Fort Smith, then up across Arkansas and southwest Missouri to Tipton with the final leg by train to St. Louis.  The Texas mail route was so long that the route there, like that in California, was divided into two divisions each under a superintendent.

New Mexico State Road 48: New Mexico State Road 48 is a state highway that runs north–south through the Sacramento Mountains, which are part of the Lincoln National Forest in Lincoln County, New Mexico in the United States.  Its southern terminus is at U.S. Route 70 in the town of Ruidoso, New Mexico.  Its northern terminus is at U.S. Route 380 in the town of Capitan, New Mexico.  The total highway length is approximately 25 mi .  New Mexico State Road 37 intersects this highway several miles north of Ruidoso, New Mexico.

U.S. Route 82: U.S. Route 82 is an east–west United States highway in the Southern United States.  Created on July 1, 1931 across central Mississippi and southern Arkansas, US 82 eventually became a 1,625-mile (2,615 km) route extending from the White Sands of New Mexico to Georgia's Atlantic coast.

U.S. Route 366 (1927–1932): U.S. Route 366 or US 366 was the designation of two child routes of the former U.S. Route 66 in New Mexico and Texas during the late 1920s and 1930s.  Both alignments of US 366 were original U.S. Routes created in 1927.  The first alignment was a route from El Paso, Texas to Amarillo, Texas crossing through New Mexico that existed until 1932.  The second was a route from Albuquerque, New Mexico to Willard, New Mexico that was previously assigned a different route number before 1932.  That alignment was canceled in 1939.

New Mexico State Road 267: State Road 267 is a 32.389 mi long state highway in eastern New Mexico.  NM 267 begins just east of the village of Melrose, New Mexico at US 60/US 84.  It then crosses from Curry County, New Mexico and into Roosevelt County, New Mexico.  It serves the western terminus of New Mexico State Road 236.  It then serves the eastern terminus of New Mexico State Road 330.  It curves to the east where it serves the village of Floyd, New Mexico.  It then enters the city of Portales, New Mexico through the western subdivisions.  It then serves the western terminus of New Mexico State Road 236 in Portales.  It then ends at US 70.

Supporting paragraphs: Hope, New Mexico U.S. Route 82
Answer: July 1, 1931