I have looked around noth in StackOverflow and WP.SE.

Like many before me, I just want this structure

mysite.com/custom-post-type/custom-taxonomy-term/post-name

Or, in other words,

mysite.com/publication/book/post-name (single post)
mysite.com/publication/book/          (all posts in the term 'book')
mysite.com/publication/               (all posts in this publication CPT)

I followed this instruction by TheDeadMedic for making custom post type with custom taxonomy permalink, and another one by Matthew Boynes to fix the pagination issue.

All works well, except... everytime I open the single post, it returns the 404 page.

I have tried opening the Permalink page and setting flush_rewrite_rules() to no avail. I still can't open the single page.

The only fix that works is if I change the slug in my custom taxonomy to its original form.

So instead of publication (the rewrite slug for this tax, in accordance to my custom post type name), I would have the default type (the default slug for this tax). Which would defeat the purpose.

Here is my code:

    function cptui_register_my_taxes_type() {

/**
 * Taxonomy: Types.
 */

$labels = array(
    "name" => __( 'Types', 'mysite' ),
    "singular_name" => __( 'Type', 'mysite' ),
    "menu_name" => __( 'Types', 'mysite' ),
    "all_items" => __( 'All Types', 'mysite' ),
    "edit_item" => __( 'Edit Types', 'mysite' ),
    "view_item" => __( 'View Type', 'mysite' ),
    "update_item" => __( 'Update Type Name', 'mysite' ),
    "add_new_item" => __( 'Add New Type', 'mysite' ),
    "new_item_name" => __( 'New Type Name', 'mysite' ),
    "parent_item" => __( 'Parent Type', 'mysite' ),
    "parent_item_colon" => __( 'Parent Type:', 'mysite' ),
    "search_items" => __( 'Search Types', 'mysite' ),
    "popular_items" => __( 'Popular Types', 'mysite' ),
    "separate_items_with_commas" => __( 'Separate Types with commas', 'mysite' ),
    "add_or_remove_items" => __( 'Add or remove Types', 'mysite' ),
    "choose_from_most_used" => __( 'Choose from the most used Types', 'mysite' ),
    "not_found" => __( 'No Types found', 'mysite' ),
    "no_terms" => __( 'No types', 'mysite' ),
    "items_list_navigation" => __( 'Types list navigation', 'mysite' ),
    "items_list" => __( 'Types list', 'mysite' ),
);

$args = array(
    "label" => __( 'Types', 'mysite' ),
    "labels" => $labels,
    "public" => true,
    "hierarchical" => true,
    "label" => "Types",
    "show_ui" => true,
    "show_in_menu" => true,
    "show_in_nav_menus" => true,
    "query_var" => true,
    "rewrite" => array( 'slug' => 'publication', 'with_front' => true,  'hierarchical' => true, ),
    "show_admin_column" => true,
    "show_in_rest" => false,
    "rest_base" => "",
    "show_in_quick_edit" => true,
);
register_taxonomy( "tyoe", array( "publication" ), $args );
}

add_action( 'init', 'cptui_register_my_taxes_type' );

Is there a way to fix this?