SQL to grab posts by coauthor user ID

<?php

    /**
     * Create an SQL statement for searching posts by coauthor name.
     *
     * @todo I'm having trouble getting $wpdb -> prepare to work, although I don't think it's necessary since I am sanitizing the data very strictly.
     * @todo I really have no idea if this is actually how you do a JOIN.
     *
     * @param string $s The search term.
     * @param string $matching_users A comma-sep list of user ID's.
     * @param int $limit The maximum number of results.
     * @param int $offset The number of results to skip, as per pagination.
     * @return string SQL for searching posts by coauthor name.
     */
    private function sql( $s, $matching_users, $limit, $offset ) {

        // Sanitize the search term and matching users, although replacing illegal chars with a wildcard.
        $s              = $this -> sanitize( $s, '_' );
        $matching_users = $this -> sanitize( $matching_users, '_' );

        // And then hit them with esc_sql because I'm paranoid.
        $s              = esc_sql( $s );
        $matching_users = esc_sql( $matching_users );

        // Sanitize the LIMIT making sure it's an int, defaulting to 10.
        $limit = absint( $limit );
        if( empty ( $limit ) ) { $limit = 10; }

        // Sanitize the the OFFSET, making sure it's an int, defaulting to 0.
        $offset = absint( $offset );
        if( empty ( $offset ) ) { $offset = 0; }

        // We're gonna need this to build our table names.
        global $wpdb;

        // Shorten the name of the psots table for easier reading.
        $p  = $wpdb -> posts;
        $tt = $wpdb -> term_taxonomy;
        $tr = $wpdb -> term_relationships;
        $t  = $wpdb -> terms;

        $sql = <<<SQL

            /* We're selecting posts in order to fulfill the search query. */
            SELECT

            /* This will prevent multiple copies of the same post, though I don't totally understand why we'd otherwise be getting them. */
            DISTINCT

            /* Populates a value so you can determine how many rows you would have gotten without the LIMIT clause. */
            SQL_CALC_FOUND_ROWS

            /* We want every column from the posts table. */
            $p.*

            /* I want results from the posts table, but I have to invoke these other tables for when I am sort of using them later in WHERE clause.  */
            FROM $p, $tr, $t, $tt

            WHERE (

                /* See if the search term matches the post title. */
                (
                    $p.post_title LIKE '%$s%'

                /* See if the search term matches the post content. */
                ) OR (
                    $p.post_content LIKE '%$s%'

                /* See if the post author is in the array of author ID's that I have from my script. */
                ) OR (
                    $p.post_author IN ( $matching_users )

                /* This is the part where I'm hazy. */
                ) OR (

                    /* Search the TT table for terms from the 'author' taxonomy ...  */
                    (
                        $tt.taxonomy = 'author'

                    /* ... and whose term description matches the search term ...  */
                    ) AND (
                        $tt.description LIKE '%$s%'

                    /* ... and whose ID matches the ID in the terms table where ...  */
                    ) AND (
                        $tt.term_id = $t.term_id

                    /* ... the term_id matches the TR table where ...  */
                    ) AND (
                        $tr.term_taxonomy_id = $t.term_id

                    /* ... the object_id in the TR table matches the post ID ... */
                    ) AND (
                        $tr.object_id = $p.ID
                    )

                /* End the part where I'm hazy. */
                )

            /* Limit results to the normal post types. */
            ) AND $p.post_type IN (
                'post', 'page'

            /* Limit results to the normal post status. */
            ) AND (
                $p.post_status = 'publish'

            /* WP Core does this and I have no idea why. */
            ) AND (
                1 = 1
            )

            /* Get results in reverse cron, like usual. */
            ORDER BY $p.post_date DESC

            /* Of course we only want our normal posts per page. */
            LIMIT $limit

            /* And we need to account for pagination. */
            OFFSET $offset

SQL;

        return $sql;
    }