Shapefile without .prj read as lat/lon and lands 500 km east of Xi'an

• Coordinates with x between 350000 and 650000 and y near 3780000 are interpreted as longitude and latitude.
• QGIS reports an invalid layer extent or draws the layer near the Gulf of Guinea.
• ogrinfo -al -so prints Layer SRS WKT: (unknown).

1. Check the directory for a .prj whose filename matches the .shp exactly, including case.
2. Read the coordinate magnitude: x near 500000 with y in the millions means a Gauss-Kruger or UTM projection.
3. Derive the central meridian from x minus 500000 and the latitude from y, since 3780000 implies about 34.3 degrees north.
4. Look for accompanying metadata or result tables that state the original coordinate system.
5. Run ogrinfo -al -so to confirm the SRS is unknown before editing anything.

Write a WKT .prj with the matching name for CGCS2000 3-degree Gauss-Kruger CM 108E with false easting 500000, or rewrite in one step with ogr2ogr -f 'ESRI Shapefile' fixed districts.shp -a_srs EPSG:4546. No coordinate transformation is needed because the geometry values are intact.

# 查看是否有坐标系信息
ogrinfo -al -so districts.shp
# 输出中若为 Layer SRS WKT: (unknown) 即缺 .prj

# 用坐标反推：x=500000 -> 中央经线上；y=3800000 -> 北纬约 34.3

PROJCS["CGCS2000_3_Degree_GK_CM_108E",
  GEOGCS["China Geodetic Coordinate System 2000",
    DATUM["China_2000", SPHEROID["CGCS2000",6378137,298.257222101]],
    PRIMEM["Greenwich",0], UNIT["degree",0.0174532925199433]],
  PROJECTION["Transverse_Mercator"],
  PARAMETER["latitude_of_origin",0],
  PARAMETER["central_meridian",108],
  PARAMETER["scale_factor",1],
  PARAMETER["false_easting",500000],
  PARAMETER["false_northing",0],
  UNIT["metre",1]]

• Using -t_srs instead of -a_srs, which actually moves the numbers and destroys the original coordinates.
• Renaming another layer's .prj to fit: a WKT for a different zone shifts everything by whole degrees.