Cannot use `p` with browserify: `Error: Cannot find module 'its'`

[cvan]

% cat test.js
require('plink');
% ./node_modules/.bin/browserify test.js
Error: Cannot find module 'its' from '/opt/galaxy.js-mobile-gamepad/node_modules/internet/lib'
    at /opt/galaxy.js-mobile-gamepad/node_modules/browserify/node_modules/resolve/lib/async.js:50:17
    at process (/opt/galaxy.js-mobile-gamepad/node_modules/browserify/node_modules/resolve/lib/async.js:119:43)
    at /opt/galaxy.js-mobile-gamepad/node_modules/browserify/node_modules/resolve/lib/async.js:128:21
    at load (/opt/galaxy.js-mobile-gamepad/node_modules/browserify/node_modules/resolve/lib/async.js:60:43)
    at /opt/galaxy.js-mobile-gamepad/node_modules/browserify/node_modules/resolve/lib/async.js:66:22
    at /opt/galaxy.js-mobile-gamepad/node_modules/browserify/node_modules/resolve/lib/async.js:21:47
    at Object.oncomplete (fs.js:97:15)

If I make its a dev dependency, things work:

diff --git a/package.json b/package.json
index 344e995..79dd14d 100644
--- a/package.json
+++ b/package.json
@@ -2,7 +2,9 @@
   "name": "internet",
   "description": "Framework for creating peer-to-peer browser networks",
   "version": "0.3.1",
-  "dependencies": {},
+  "dependencies": {
+    "its": "~1.0.2"
+  },
   "devDependencies": {
     "grunt": "~0.4.0",
     "grunt-hug": "~0.5.0",
@@ -17,7 +19,6 @@
     "grunt-contrib-jasmine": "~0.5.0",
     "browserify": "~2.35.4",
     "grunt-browserify": "~1.2.11",
-    "its": "~1.0.2",
     "sinon": "~1.7.3"
   },
   "main": "./index.js",