Site Title and Tagline in Theme Options Page

The framework offers a filter for validating input values inside the optionsframework_validate function.
Just for reference, here’s the relevant part from the file wp-content/themes/your-theme/inc/options-framework.php:

/**
 * Validate Options.
 *
 * This runs after the submit/reset button has been clicked and
 * validates the inputs.
 */
function optionsframework_validate( $input ) {
/* code */
    $clean[$id] = apply_filters( 'of_sanitize_' . $option['type'], $input[$id], $option );
/* code */

So, considering that we have the following options in the file wp-content/themes/your-theme/options.php:

$options[] = array(
    'name' => __('Input Text Mini', 'options_framework_theme'),
    'desc' => __('A mini text input field.', 'options_framework_theme'),
    'id' => 'blogname',
    'std' => 'Default',
    'class' => 'mini',
    'type' => 'text');

$options[] = array(
    'name' => __('Input Text', 'options_framework_theme'),
    'desc' => __('A text input field.', 'options_framework_theme'),
    'id' => 'blogdescription',
    'std' => 'Default Value',
    'type' => 'text');

And in wp-content/themes/your-theme/functions.php, we filter the text input type (^{of_sanitize_ + text}) and if it matches our defined ids (blogname and blogdescription, just like in General Settings), it will update the site options that have the same id.

^{Please note, that this doesn’t work the other way around: changes made in Settings -> General won’t be reflected inside the theme options page…}

add_filter( 'of_sanitize_text', 'wpse_77233_framework_to_settings', 10, 2 );

function wpse_77233_framework_to_settings( $input, $option )
{
    if( 'blogname' == $option['id'] )
        update_option( 'blogname', sanitize_text_field( $input ) );

    if( 'blogdescription' == $option['id'] )
        update_option( 'blogdescription', sanitize_text_field( $input ) );

    return $input;
}