Ayuda no encuentro el error en la cadena

en donde me equivoque alguien que me pueda ayudar plz no verifica el recaptcha envia igual verificado o no
----------------------------------------------------------------------------contact.php-------------------------------------------------------------------------------

<?php

// Only process POST reqeusts.
if ($_SERVER["REQUEST_METHOD"] == "POST") {
// Get the form fields and remove whitespace.
$name = strip_tags(trim($_POST["name"]));
$name = str_replace(array("\r","\n"),array(" "," "),$name);
$email = filter_var(trim($_POST["email"]), FILTER_SANITIZE_EMAIL);
$message = trim($_POST["message"]);

// Check that data was sent to the mailer.
if ( empty($name) OR empty($message) OR !filter_var($email, FILTER_VALIDATE_EMAIL)) {
// Set a 400 (bad request) response code and exit.
http_response_code(400);
echo "<script>alert('Oops! Hubo un problema con el envío. Por favor complete el formulario y vuelva a intentarlo.')</script>";
exit;
}

// Set the recipient email address.
// FIXME: Update this to your desired email address.
$recipient = "mail que recive";

// Set the email subject.
$subject = "$email";

// Build the email content.
$email_content = "Nombre: $name\n";
$email_content .= "Email: $email\n\n";
$email_content .= "Mensaje:\n$message\n";

$recaptcha = $_POST["g-recaptcha-response"];

$url = 'https://www.google.com/recaptcha/api/siteverify';
$data = array(
'secret' => 'key api',
'response' => $recaptcha
);
$options = array(
'http' => array (
'method' => 'POST',
'content' => http_build_query($data)
)
);
$context = stream_context_create($options);
$verify = file_get_contents($url, false, $context);
$captcha_success = json_decode($verify);
if ($captcha_success->success) {
// No eres un robot, continuamos con el envío del email
// ...
// ...
} else {
// Eres un robot!
}

// Build the email headers.
$email_headers = "From:$email";

// Send the email.
if (mail($recipient, $subject, $email_content, $email_headers)) {
// Set a 200 (okay) response code.
http_response_code(200);
echo "<script>alert('¡Gracias! Tu mensaje ha sido enviado.')</script>";
} else {
// Set a 500 (internal server error) response code.
http_response_code(500);
echo "<script>alert('Oops! Algo salió mal y no pudimos enviar su mensaje.')</script>";
}

} else {
// Not a POST request, set a 403 (forbidden) response code.
http_response_code(403);
echo "<script>alert('Hubo un problema con su envío, intente de nuevo.')</script>";
}

?>


---------------------------------------------------------------------------html index-----------------------------------------------------------------------------
.
<div id="fields">
<form id="ajax-contact-form" method="post" action="contact.php">
<div class="row">
<div class="col-sm-6">
<label for="">Nombre:</label>
<input type="text" id="name" name="name" required>
</div>
<div class="col-sm-6">
<label for="">Email:</label>
<input type="email" id="email" name="email" required>
</div>
</div>
<label for="">Mensaje:</label>
<textarea id="message" name="message" required></textarea>
<label for=""></label>
<div class="g-recaptcha" data-sitekey="api key"></div>
<input class="submit" type="submit" name="submit" value="ENVIAR" id="button_submit">
</form>
</div>
<div id="note"></div>