Analogous to yesterday's code snippet for the Guardian Open Platform, here's how to fetch articles (extracts, not the full text) from the New York Times Article Search API:

<?php
define('API_KEY', 'YOUR_API_KEY');
define('API_URL', 'http://api.nytimes.com/svc/search/v1');

$n = 10;
$i = 0;

do{
  $start = $i * $n;
  print "$start\n";
  
  $params = array(
    'api-key' => API_KEY,
    'query' => 'des_facet:[SCIENCE AND TECHNOLOGY]',
    'offset' => $i,
    'fields' => 'byline,body,date,title,url,des_facet',
    );
  
  $data = json_decode(file_get_contents(API_URL . '/article?' . http_build_query($params)));
  foreach ($data->results as $item)
    file_put_contents(sprintf('articles/%s.js', md5($item->url)), json_encode($item)); 
  
  sleep(1);
} while ($start < $data->total && ++$i < 5000);

Sadly it doesn't seem possible to get the categories assigned to an individual article - adding "facets=des_facet" only provides the sum of the categories across the 10 results. (see comment below).

The same Nature News story as before has these similar articles:

1. OBSERVATORY; Galaxies Made Simple, or at Least Less Complicated
2. THE YEAR IN IDEAS; Dark Energy
3. Q&A
4. Galaxies Twice as Bright as They Seem, Study Finds
5. Stars Suggest a Quark Twist And a New Kind of Matter
6. OBSERVATORY; Galactic Puzzle Solved? Threads Tie It Together
7. VAST 'HOLE' IN SPACE APPEARS TO DEFY THEORIES
8. ESSAY; Computing, 2016: What Won't Be Possible?
9. THE NOVEMBER REPORT; Scientists In Waiting
10. A Puzzle Finally Makes the 'Cosmic Figures' Fit

and the 50 most similar articles have these categories:

1. SPACE [17]
2. PHYSICS [14]
3. RESEARCH [6]
4. STARS AND GALAXIES [6]
5. UNIVERSE [6]
6. REVIEWS [5]
7. ASTRONOMY AND ASTROPHYSICS [5]
8. BOOKS AND LITERATURE [4]
9. HUBBLE SPACE TELESCOPE [4]
10. COMPUTERS AND THE INTERNET [4]
11. EDUCATION AND SCHOOLS [3]
12. SOCIAL CONDITIONS AND TRENDS [3]
13. TELESCOPES AND OBSERVATORIES [3]
14. UNITED STATES ECONOMY [2]
15. BIOGRAPHICAL INFORMATION [2]
16. GENETICS AND HEREDITY [2]
17. THIRD WORLD AND DEVELOPING COUNTRIES [2]
18. PHOTOGRAPHY [2]
19. ACCIDENTS AND SAFETY [2]