Hide play/pause once someone has run out

At a flag the game is over and togglePause is inert anyway — pauseNow
needs RUN, resumeNow needs PAUSE — so the button was there without being
able to do anything. It joins the other two visibility rules in render():
vacant at IDLE or FLAG. Reset stays, being the way out of a finished
game, and the bar comes down to Reset, score and sound.

Checked the whole state machine: shown while running and while paused,
vacant before a game's first tap and at a flag, and pausing and resuming
still work.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

README.md

@@ -69,8 +69,8 @@ everything works except installation and the service worker.
   included. Opening either sheet pauses automatically. The settings sheet leaves
   it paused — everything in there resets the clocks anyway — while the score
   sheet picks the turn back up when you close it, so glancing at the score
-  doesn't cost you a tap on play. It's absent before each game's first tap, with
-  no clock running to freeze.
+  doesn't cost you a tap on play. It's absent whenever there's no clock running
+  to freeze: before each game's first tap, and once someone has run out of time.
 
 Both buttons keep their space in the bar while they're away, so nothing shifts
 under your thumb — the same as the gear.

public_html/index.html

@@ -811,7 +811,9 @@
     var pristine = matchPristine();
     btnSettings.classList.toggle("btn--vacant", !pristine);
     btnReset.classList.toggle("btn--vacant", pristine);            // nothing played to reset
-    btnPlay.classList.toggle("btn--vacant", st.phase === IDLE);    // nothing running to pause
+    // nothing running to pause: before a game's first tap, and after a flag,
+    // where togglePause is inert anyway — the game is over, Reset is the way out
+    btnPlay.classList.toggle("btn--vacant", st.phase === IDLE || st.phase === FLAG);
   }
 
   function loop(){ render(); requestAnimationFrame(loop); }

public_html/sw.js

@@ -1,5 +1,5 @@
 /* Cache-first: once installed the clock never touches the network again. */
-const CACHE = "bgclock-v16";
+const CACHE = "bgclock-v17";
 const FILES = [
   "./",
   "./index.html",