ESRI:53016

PROJCS["Sphere_Gall_Stereographic",
    GEOGCS["Unknown datum based upon the Authalic Sphere",
        DATUM["Not_specified_based_on_Authalic_Sphere",
            SPHEROID["Sphere",6371000,0],
            AUTHORITY["EPSG","6035"]],
        PRIMEM["Greenwich",0],
        UNIT["Degree",0.0174532925199433]],
    PROJECTION["Gall_Stereographic"],
    PARAMETER["central_meridian",0],
    PARAMETER["false_easting",0],
    PARAMETER["false_northing",0],
    UNIT["metre",1,
        AUTHORITY["EPSG","9001"]],
    AXIS["Easting",EAST],
    AXIS["Northing",NORTH],
    AUTHORITY["ESRI","53016"]]

PROJCRS["Sphere_Gall_Stereographic",
    BASEGEOGCRS["Unknown datum based upon the Authalic Sphere",
        DATUM["Not specified (based on Authalic Sphere)",
            ELLIPSOID["Sphere",6371000,0,
                LENGTHUNIT["metre",1]]],
        PRIMEM["Greenwich",0,
            ANGLEUNIT["Degree",0.0174532925199433]]],
    CONVERSION["Sphere_Gall_Stereographic",
        METHOD["Gall Stereographic"],
        PARAMETER["Longitude of natural origin",0,
            ANGLEUNIT["Degree",0.0174532925199433],
            ID["EPSG",8802]],
        PARAMETER["False easting",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8806]],
        PARAMETER["False northing",0,
            LENGTHUNIT["metre",1],
            ID["EPSG",8807]]],
    CS[Cartesian,2],
        AXIS["(E)",east,
            ORDER[1],
            LENGTHUNIT["metre",1]],
        AXIS["(N)",north,
            ORDER[2],
            LENGTHUNIT["metre",1]],
    USAGE[
        SCOPE["Not known."],
        AREA["World."],
        BBOX[-90,-180,90,180]],
    ID["ESRI",53016]]

PROJCS["Sphere_Gall_Stereographic",
    GEOGCS["GCS_Sphere",
        DATUM["D_Sphere",
            SPHEROID["Sphere",6371000.0,0.0]],
        PRIMEM["Greenwich",0.0],
        UNIT["Degree",0.0174532925199433]],
    PROJECTION["Gall_Stereographic"],
    PARAMETER["False_Easting",0.0],
    PARAMETER["False_Northing",0.0],
    PARAMETER["Central_Meridian",0.0],
    UNIT["Meter",1.0]]

proj4.defs("ESRI:53016","+proj=gall +lon_0=0 +x_0=0 +y_0=0 +R=6371000 +units=m +no_defs +type=crs");

{
    "$schema": "https://proj.org/schemas/v0.7/projjson.schema.json",
    "type": "ProjectedCRS",
    "name": "Sphere_Gall_Stereographic",
    "base_crs": {
        "name": "Unknown datum based upon the Authalic Sphere",
        "datum": {
            "type": "GeodeticReferenceFrame",
            "name": "Not specified (based on Authalic Sphere)",
            "ellipsoid": {
                "name": "Sphere",
                "radius": 6371000
            }
        },
        "coordinate_system": {
            "subtype": "ellipsoidal",
            "axis": [
                {
                    "name": "Longitude",
                    "abbreviation": "lon",
                    "direction": "east",
                    "unit": {
                        "type": "AngularUnit",
                        "name": "Degree",
                        "conversion_factor": 0.0174532925199433
                    }
                },
                {
                    "name": "Latitude",
                    "abbreviation": "lat",
                    "direction": "north",
                    "unit": {
                        "type": "AngularUnit",
                        "name": "Degree",
                        "conversion_factor": 0.0174532925199433
                    }
                }
            ]
        }
    },
    "conversion": {
        "name": "Sphere_Gall_Stereographic",
        "method": {
            "name": "Gall Stereographic"
        },
        "parameters": [
            {
                "name": "Longitude of natural origin",
                "value": 0,
                "unit": {
                    "type": "AngularUnit",
                    "name": "Degree",
                    "conversion_factor": 0.0174532925199433
                },
                "id": {
                    "authority": "EPSG",
                    "code": 8802
                }
            },
            {
                "name": "False easting",
                "value": 0,
                "unit": "metre",
                "id": {
                    "authority": "EPSG",
                    "code": 8806
                }
            },
            {
                "name": "False northing",
                "value": 0,
                "unit": "metre",
                "id": {
                    "authority": "EPSG",
                    "code": 8807
                }
            }
        ]
    },
    "coordinate_system": {
        "subtype": "Cartesian",
        "axis": [
            {
                "name": "Easting",
                "abbreviation": "E",
                "direction": "east",
                "unit": "metre"
            },
            {
                "name": "Northing",
                "abbreviation": "N",
                "direction": "north",
                "unit": "metre"
            }
        ]
    },
    "scope": "Not known.",
    "area": "World.",
    "bbox": {
        "south_latitude": -90,
        "west_longitude": -180,
        "north_latitude": 90,
        "east_longitude": 180
    },
    "id": {
        "authority": "ESRI",
        "code": 53016
    }
}

<?xml version="1.0" encoding="utf-8"?>
<Map srs="+proj=gall +lon_0=0 +x_0=0 +y_0=0 +R=6371000 +units=m +no_defs +type=crs">
	<Layer srs="+proj=gall +lon_0=0 +x_0=0 +y_0=0 +R=6371000 +units=m +no_defs +type=crs">
	</Layer>
</Map>

INSERT into spatial_ref_sys (srid, auth_name, auth_srid, proj4text, srtext) values ( 53016, 'ESRI', 53016, '+proj=gall +lon_0=0 +x_0=0 +y_0=0 +R=6371000 +units=m +no_defs +type=crs', 'PROJCS["Sphere_Gall_Stereographic",GEOGCS["Unknown datum based upon the Authalic Sphere",DATUM["Not_specified_based_on_Authalic_Sphere",SPHEROID["Sphere",6371000,0],AUTHORITY["EPSG","6035"]],PRIMEM["Greenwich",0],UNIT["Degree",0.0174532925199433]],PROJECTION["Gall_Stereographic"],PARAMETER["central_meridian",0],PARAMETER["false_easting",0],PARAMETER["false_northing",0],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Easting",EAST],AXIS["Northing",NORTH],AUTHORITY["ESRI","53016"]]');