How do I create a password reset link?

After much research, I finally turned to examining the WordPress core file wp_login.php hoping that WP would show how they do it in a non-obtuse manner. From the information around line 331 (WP 4.6.1), I put together the following code.

<?php

global $gw_activate_template;

extract( $gw_activate_template->result );

$url = is_multisite() ? get_blogaddress_by_id( (int) $blog_id ) : home_url('', 'http');
$user = new WP_User( (int) $user_id );

$adt_rp_key = get_password_reset_key( $user );
$user_login = $user->user_login;
$rp_link = '<a href="' . network_site_url("wp-login.php?action=rp&key=$adt_rp_key&login=" . rawurlencode($user_login), 'login') . '">' . network_site_url("wp-login.php?action=rp&key=$adt_rp_key&login=" . rawurlencode($user_login), 'login') . '</a>';

if ( is_wp_error( $key ) ) {
    return $key;
}

?>

<h2><?php _e('Your account is now active!'); ?></h2>

<div id="signup-welcome">
    <p><span class="h3"><?php _e('Username:'); ?></span> <?php echo $user->user_login ?></p>
    <p>To set your password, select the following link: <?php echo $rp_link; ?></p>
</div>

The important thing to constructing the link is the key that is put together by get_password_reset_key( $user ); This is a key that is stored in the database which allows the $user to have its password changed. I saw a website that refers to it as a cookie; however this is using a loose definition of “cookie” because nothing is stored on the users computer. The key is stored in the database and linked to the user account.