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- <!doctype html>
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- <html>
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- <head>
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- <meta charset="utf-8" />
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- <meta name="viewport" content="width=device-width" />
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- <title>My static Space</title>
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- <link rel="stylesheet" href="style.css" />
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- </head>
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- <body>
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- <div class="card">
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- <h1>Welcome to your static Space!</h1>
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- <p>You can modify this app directly by editing <i>index.html</i> in the Files and versions tab.</p>
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- <p>
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- Also don't forget to check the
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- <a href="https://huggingface.co/docs/hub/spaces" target="_blank">Spaces documentation</a>.
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- </p>
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- </div>
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- </body>
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- </html>
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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+ <!DOCTYPE html>
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+ <html lang="en">
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+ <head>
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+ <meta charset="UTF-8" />
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+ <meta name="viewport" content="width=device-width,initial-scale=1" />
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+ <title>Entanglement Reference Sheet — E(Δ) = −V·cos Δ</title>
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+ <style>
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+ :root{--bg:#0b1220;--card:#0f172a;--ink:#e5e7eb;--muted:#94a3b8;--accent:#22d3ee;--ok:#34d399;--warn:#f59e0b;--err:#ef4444;}
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+ *{box-sizing:border-box}
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+ body{margin:0;font-family:system-ui,-apple-system,Segoe UI,Roboto,Inter,Ubuntu,Arial;background:linear-gradient(180deg,#050a16,#0b1220);color:var(--ink)}
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+ header{padding:22px 16px;text-align:center}
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+ header h1{margin:0;font-size:1.4rem}
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+ header p{margin:6px 0 0;color:var(--muted)}
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+ main{max-width:1100px;margin:0 auto;padding:16px;display:grid;gap:16px}
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+ @media(min-width:960px){main{grid-template-columns:360px 1fr}}
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+ .card{background:var(--card);border:1px solid #1f2937;border-radius:16px;padding:16px}
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+ h2{margin:0 0 10px;font-size:1.05rem}
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+ label{display:block;margin:10px 0 4px;color:var(--muted)}
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+ input[type=range]{width:100%}
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+ input[type=number]{width:100%;padding:8px;border-radius:8px;border:1px solid #1f2937;background:#0a1220;color:var(--ink)}
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+ .row{display:flex;gap:10px;flex-wrap:wrap}
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+ .pill{padding:6px 10px;border-radius:999px;background:#0a1220;border:1px solid #1f2937;color:var(--muted)}
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+ .btn{background:#0a1727;border:1px solid #1f2937;color:var(--ink);padding:10px 12px;border-radius:10px;cursor:pointer}
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+ .btn.primary{background:var(--accent);border-color:#0891b2;color:#001018;font-weight:700}
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+ .kpi{display:grid;grid-template-columns:repeat(3,1fr);gap:10px}
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+ .kpi .box{background:#0a1220;border:1px solid #1f2937;border-radius:12px;padding:10px;text-align:center}
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+ .val{font-size:1.05rem;font-weight:700;color:var(--accent)}
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+ .small{font-size:.9rem;color:var(--muted)}
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+ canvas{width:100%;height:240px;background:#07101d;border:1px solid #1f2937;border-radius:12px}
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+ .ok{color:var(--ok)} .warn{color:var(--warn)} .err{color:var(--err)}
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+ table{width:100%;border-collapse:collapse}
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+ th,td{border:1px solid #1f2937;padding:8px;text-align:center}
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+ th{background:#0a1220;color:#cbd5e1}
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+ footer{color:var(--muted);text-align:center;margin:18px 0}
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+ code{background:#091324;padding:2px 6px;border-radius:6px;border:1px solid #1f2937}
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+ .badge{display:inline-block;padding:4px 8px;border-radius:999px;font-size:12px;border:1px solid #1f2937;margin-left:6px}
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+ .badge.ok{background:rgba(52,211,153,0.15);color:var(--ok)}
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+ .badge.warn{background:rgba(245,158,11,0.15);color:var(--warn)}
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+ .badge.err{background:rgba(239,68,68,0.15);color:var(--err)}
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+ </style>
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+ </head>
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+ <body>
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+ <header>
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+ <h1>Entanglement Reference Sheet — <code>E(Δ) = − V·cos Δ</code></h1>
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+ <p>No-signaling + rotational symmetry + information causality → quantum (Tsirelson) correlations</p>
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+ </header>
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+
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+ <main>
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+ <!-- Controls -->
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+ <section class="card">
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+ <h2>🎛 Controls</h2>
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+ <label>Visibility V (0…1): <span id="Vlab">1.00</span></label>
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+ <input type="range" id="V" min="0" max="1" step="0.01" value="1">
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+
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+ <div class="row">
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+ <div style="flex:1">
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+ <label>A0 (°): <span id="A0lab">0.0</span></label>
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+ <input type="range" id="A0" min="0" max="180" step="0.1" value="0">
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+ </div>
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+ <div style="flex:1">
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+ <label>A1 (°): <span id="A1lab">45.0</span></label>
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+ <input type="range" id="A1" min="0" max="180" step="0.1" value="45">
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+ </div>
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+ </div>
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+ <div class="row">
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+ <div style="flex:1">
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+ <label>B0 (°): <span id="B0lab">22.5</span></label>
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+ <input type="range" id="B0" min="0" max="180" step="0.1" value="22.5">
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+ </div>
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+ <div style="flex:1">
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+ <label>B1 (°): <span id="B1lab">67.5</span></label>
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+ <input type="range" id="B1" min="0" max="180" step="0.1" value="67.5">
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+ </div>
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+ </div>
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+
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+ <div class="row" style="margin-top:10px">
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+ <button class="btn" id="setOpt">Set CHSH-optimal angles</button>
78
+ <button class="btn primary" id="recalc">Recalculate</button>
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+ <span class="pill">Δ = <span id="DeltaLab">A0–B0 = 22.5°</span></span>
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+ <span id="violBadge" class="badge warn">status</span>
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+ </div>
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+
83
+ <div class="kpi" style="margin-top:10px">
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+ <div class="box">
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+ <div class="small">Correlation E(A0,B0)</div>
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+ <div id="E00" class="val">–</div>
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+ </div>
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+ <div class="box">
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+ <div class="small">S (CHSH)</div>
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+ <div id="Sval" class="val">–</div>
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+ </div>
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+ <div class="box">
93
+ <div class="small">CHSH game win prob</div>
94
+ <div id="pwin" class="val">–</div>
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+ </div>
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+ </div>
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+
98
+ <div class="row" style="margin-top:10px">
99
+ <span class="pill">Regime: <b id="regime">–</b></span>
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+ <span class="pill">Local ≤ 2 • Quantum ≤ 2√2 • PR = 4</span>
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+ </div>
102
+ </section>
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+
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+ <!-- Results & Plots -->
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+ <section class="card">
106
+ <h2>📊 Joint Distribution & Fisher Information</h2>
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+
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+ <div class="row">
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+ <div style="flex:1">
110
+ <label>Single-pair angle Δ (°) for E & P(a,b): <span id="Dlab">22.5</span></label>
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+ <input type="range" id="D" min="0" max="180" step="0.1" value="22.5">
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+ </div>
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+ <div style="width:180px">
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+ <label>Δ direct input (°)</label>
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+ <input type="number" id="Dnum" min="0" max="180" step="0.1" value="22.5">
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+ </div>
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+ </div>
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+
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+ <div class="kpi" style="margin-top:10px">
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+ <div class="box">
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+ <div class="small">E(Δ)</div>
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+ <div id="Edelta" class="val">–</div>
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+ </div>
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+ <div class="box">
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+ <div class="small">Fisher 𝓕(Δ)</div>
126
+ <div id="Fdelta" class="val">–</div>
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+ </div>
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+ <div class="box">
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+ <div class="small">Max 𝓕 over Δ</div>
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+ <div id="Fmax" class="val">–</div>
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+ </div>
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+ </div>
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+
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+ <canvas id="bars"></canvas>
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+ <div class="small">Bars show joint probabilities P(++), P(+−), P(−+), P(−−) with fair marginals (no-signaling). Computed via <code>P(a,b)=¼(1+a b·E)</code>. Marginals: P(a=+1)=<span id="PaPlus">0.5000</span>, P(b=+1)=<span id="PbPlus">0.5000</span>.</div>
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+ </section>
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+
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+ <!-- Monogamy -->
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+ <section class="card">
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+ <h2>🔗 Monogamy Check (Toner–Verstraete)</h2>
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+ <div class="row">
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+ <div style="flex:1">
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+ <label>Enter candidate S_AC</label>
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+ <input type="number" id="SAC" value="2.0" min="0" max="4" step="0.01">
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+ </div>
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+ <div style="flex:1;display:flex;align-items:flex-end">
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+ <button class="btn" id="monoCheck">Check S_AB² + S_AC² ≤ 8</button>
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+ </div>
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+ </div>
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+ <div class="row" style="margin-top:10px">
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+ <span class="pill">S_AB = <b id="SABpill">–</b></span>
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+ <span class="pill">S_AC = <b id="SACpill">–</b></span>
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+ <span class="pill">Sum = <b id="sumMono">–</b></span>
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+ <span class="pill">Status: <b id="monoStatus">–</b></span>
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+ </div>
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+ </section>
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+
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+ <!-- Comparison -->
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+ <section class="card">
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+ <h2>📚 Comparison Table</h2>
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+ <table>
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+ <thead>
163
+ <tr><th>Model</th><th>Max CHSH S</th><th>Correlation form</th><th>Signaling?</th></tr>
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+ </thead>
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+ <tbody>
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+ <tr><td>Local Hidden Variables</td><td>≤ 2</td><td>Piecewise linear</td><td>No</td></tr>
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+ <tr><td>Quantum (this work)</td><td>≤ 2√2 ≈ 2.828</td><td><code>E(Δ)=−V cos Δ</code></td><td>No</td></tr>
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+ <tr><td>PR-Box (supra-quantum)</td><td>4</td><td>±1 (discontinuous)</td><td>No</td></tr>
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+ </tbody>
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+ </table>
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+ <p class="small" style="margin-top:8px">Information causality rules out PR-box correlations; rotational symmetry fixes the cosine form; maximum entropy selects the unique joint distribution.</p>
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+ </section>
173
+ </main>
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+
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+ <footer>
176
+ Interactive reference for entanglement correlations • © 2025 Daniel Süß • DOI: <a href="https://doi.org/10.5281/zenodo.16937966" target="_blank" rel="noopener">10.5281/zenodo.16937966</a>
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+ </footer>
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+
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+ <script>
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+ const V = document.getElementById('V');
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+ const Vlab = document.getElementById('Vlab');
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+
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+ const A0 = document.getElementById('A0'), A1 = document.getElementById('A1'),
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+ B0 = document.getElementById('B0'), B1 = document.getElementById('B1');
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+ const A0lab = document.getElementById('A0lab'), A1lab = document.getElementById('A1lab'),
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+ B0lab = document.getElementById('B0lab'), B1lab = document.getElementById('B1lab');
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+
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+ const E00 = document.getElementById('E00'), Sval = document.getElementById('Sval'), pwin = document.getElementById('pwin');
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+ const regime = document.getElementById('regime');
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+ const DeltaLab = document.getElementById('DeltaLab');
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+ const violBadge = document.getElementById('violBadge');
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+
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+ const D = document.getElementById('D'), Dnum = document.getElementById('Dnum');
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+ const Dlab = document.getElementById('Dlab');
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+ const Edelta = document.getElementById('Edelta'), Fdelta = document.getElementById('Fdelta'), Fmax = document.getElementById('Fmax');
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+
197
+ const PaPlus = document.getElementById('PaPlus'), PbPlus = document.getElementById('PbPlus');
198
+ const bars = document.getElementById('bars');
199
+
200
+ const setOpt = document.getElementById('setOpt'), recalc = document.getElementById('recalc');
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+
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+ const SACin = document.getElementById('SAC'), SABpill = document.getElementById('SABpill'),
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+ SACpill = document.getElementById('SACpill'), sumMono = document.getElementById('sumMono'), monoStatus = document.getElementById('monoStatus');
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+
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+ function deg2rad(x){ return x*Math.PI/180; }
206
+ function cosd(x){ return Math.cos(deg2rad(x)); }
207
+ function sind(x){ return Math.sin(deg2rad(x)); }
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+ function wrap180(d){ return ((d % 180) + 180) % 180; }
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+
210
+ // correlation law
211
+ function E_of(V, ddeg){ return - V * cosd(wrap180(ddeg)); }
212
+
213
+ // CHSH
214
+ function S_from(V, a0,a1,b0,b1){
215
+ const E00 = E_of(V, a0-b0);
216
+ const E01 = E_of(V, a0-b1);
217
+ const E10 = E_of(V, a1-b0);
218
+ const E11 = E_of(V, a1-b1);
219
+ const S = Math.abs(E00 + E01 + E10 - E11);
220
+ return {S,E00,E01,E10,E11};
221
+ }
222
+
223
+ // CHSH game win probability
224
+ function pwin_from_S(S){ return 0.5 + S/8; }
225
+
226
+ // joint distribution with fair marginals: P(a,b) = 1/4 (1 + a b E); here E = -V cos Δ
227
+ function joint_from_E(E){
228
+ const Ppp = 0.25*(1 + E);
229
+ const Ppm = 0.25*(1 - E);
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+ const Pmp = 0.25*(1 - E);
231
+ const Pmm = 0.25*(1 + E);
232
+ return [Ppp,Ppm,Pmp,Pmm];
233
+ }
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+
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+ // draw bars
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+ function drawBars(probs){
237
+ const ctx = bars.getContext('2d');
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+ const w = bars.width = bars.clientWidth*2, h = bars.height = bars.clientHeight*2;
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+ ctx.clearRect(0,0,w,h);
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+ ctx.fillStyle="#0a1220"; ctx.fillRect(0,0,w,h);
241
+ ctx.strokeStyle="#1f2937"; ctx.strokeRect(0,0,w,h);
242
+ const labels = ["++","+−","−+","−−"];
243
+ const maxH = h*0.7, barW = w*0.15, gap = w*0.06; let x = w*0.12;
244
+ for(let i=0;i<4;i++){
245
+ const ph = Math.max(0,probs[i])*maxH;
246
+ ctx.fillStyle = i%2? "#22d3ee" : "#38bdf8";
247
+ ctx.fillRect(x, h-40-ph, barW, ph);
248
+ ctx.fillStyle="#cbd5e1"; ctx.font="28px system-ui"; ctx.fillText(labels[i], x+barW*0.22, h-10);
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+ ctx.fillStyle="#94a3b8"; ctx.font="22px system-ui"; ctx.fillText(probs[i].toFixed(4), x+8, h-50-ph);
250
+ x += barW + gap;
251
+ }
252
+ }
253
+
254
+ // Fisher information (Δ in radians physically, but we input degrees; derivative uses sin(Δ) correctly)
255
+ function fisher(V, ddeg){
256
+ const mu = -V * cosd(ddeg);
257
+ const dmu = V * sind(ddeg); // dμ/dΔ(rad) = V sin(Δ)
258
+ const denom = 1 - mu*mu;
259
+ if(denom <= 1e-12) return NaN;
260
+ return (dmu*dmu)/denom;
261
+ }
262
+ function fisher_max(V){
263
+ let bestF = 0, bestD = 90;
264
+ for(let d=0; d<=180; d+=0.1){
265
+ const F = fisher(V, d);
266
+ if(!isNaN(F) && F > bestF){ bestF = F; bestD = d; }
267
+ }
268
+ return {F:bestF, D:bestD};
269
+ }
270
+
271
+ function classify_regime(S){
272
+ const eps=1e-6, ts = 2*Math.SQRT2;
273
+ if(S <= 2+eps) return {txt:"local (≤2)", cls:"ok"};
274
+ if(S <= ts+eps) return {txt:"quantum-admissible (≤2√2)", cls:"warn"};
275
+ return {txt:"super-quantum (violates IC)", cls:"err"};
276
+ }
277
+
278
+ function updateBadge(S, Vv){
279
+ // Use S for current geometry and also V-threshold info
280
+ if(S > 2 + 1e-6){ violBadge.textContent = "violates CHSH"; violBadge.className = "badge ok"; return; }
281
+ if(Math.abs(S-2) <= 1e-6){ violBadge.textContent = "saturates local bound"; violBadge.className = "badge warn"; return; }
282
+ violBadge.textContent = "no violation"; violBadge.className = "badge err";
283
+ }
284
+
285
+ function updateMarginals(E){
286
+ // From joint_from_E
287
+ const [Ppp,Ppm,Pmp,Pmm] = joint_from_E(E);
288
+ const Pa = Ppp + Ppm; // a=+1
289
+ const Pb = Ppp + Pmp; // b=+1
290
+ PaPlus.textContent = Pa.toFixed(4);
291
+ PbPlus.textContent = Pb.toFixed(4);
292
+ }
293
+
294
+ function updateAll(){
295
+ Vlab.textContent = Number(V.value).toFixed(2);
296
+ A0lab.textContent = Number(A0.value).toFixed(1);
297
+ A1lab.textContent = Number(A1.value).toFixed(1);
298
+ B0lab.textContent = Number(B0.value).toFixed(1);
299
+ B1lab.textContent = Number(B1.value).toFixed(1);
300
+
301
+ const Vv = Number(V.value);
302
+ const a0 = Number(A0.value), a1 = Number(A1.value), b0 = Number(B0.value), b1 = Number(B1.value);
303
+ DeltaLab.textContent = `A0–B0 = ${wrap180(a0-b0).toFixed(1)}°`;
304
+
305
+ const {S,E00:EE00,E01,E10,E11} = S_from(Vv, a0,a1,b0,b1);
306
+ E00.textContent = EE00.toFixed(4);
307
+ Sval.textContent = S.toFixed(4);
308
+ pwin.textContent = pwin_from_S(S).toFixed(4);
309
+ updateBadge(S, Vv);
310
+
311
+ const reg = classify_regime(S);
312
+ regime.textContent = reg.txt;
313
+ regime.className = reg.cls;
314
+
315
+ // single Δ block
316
+ const Dv = Number(D.value);
317
+ Dlab.textContent = D.value;
318
+ Dnum.value = D.value;
319
+
320
+ const EΔ = E_of(Vv, Dv);
321
+ Edelta.textContent = EΔ.toFixed(6);
322
+ updateMarginals(EΔ);
323
+
324
+ const FΔ = fisher(Vv, Dv);
325
+ Fdelta.textContent = isNaN(FΔ)? "undefined" : FΔ.toFixed(6);
326
+
327
+ const Fm = fisher_max(Vv);
328
+ Fmax.textContent = `${Fm.F.toFixed(6)} @ Δ≈${Fm.D.toFixed(1)}°`;
329
+
330
+ drawBars(joint_from_E(EΔ));
331
+
332
+ SABpill.textContent = S.toFixed(4);
333
+ }
334
+
335
+ function monoCheck(){
336
+ const SAB = Number(Sval.textContent);
337
+ const SAC = Number(SACin.value);
338
+ SACpill.textContent = SAC.toFixed(4);
339
+ const sum = SAB*SAB + SAC*SAC;
340
+ sumMono.textContent = sum.toFixed(4);
341
+ const ok = sum <= 8 + 1e-6;
342
+ monoStatus.textContent = ok ? "satisfied" : "violated";
343
+ monoStatus.className = ok ? "ok" : "err";
344
+ }
345
+
346
+ function setCHSHopt(){
347
+ A0.value = 0; A1.value = 45; B0.value = 22.5; B1.value = 67.5;
348
+ updateAll();
349
+ }
350
+
351
+ // Sync Δ number/range
352
+ D.addEventListener('input', ()=>{ Dlab.textContent=D.value; Dnum.value=D.value; updateAll(); });
353
+ Dnum.addEventListener('input', ()=>{ let v=Number(Dnum.value); if(isNaN(v)) v=0; v=Math.max(0,Math.min(180,v)); D.value=v; Dlab.textContent=D.value; updateAll(); });
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+
355
+ [V,A0,A1,B0,B1].forEach(el=>el.addEventListener('input', updateAll));
356
+ document.getElementById('recalc').addEventListener('click', updateAll);
357
+ document.getElementById('monoCheck').addEventListener('click', monoCheck);
358
+ document.getElementById('setOpt').addEventListener('click', setCHSHopt);
359
+
360
+ // init
361
+ updateAll();
362
+ </script>
363
+ </body>
364
+ </html>