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FLINT NEXT: Love Logic Proof v3 (the crossover) · c02
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<a href="love-logic-proof-v2.html" class="nav-link">← v2 (the axiomatic refinement)</a>
<a href="love-logic-proof.html" class="nav-link" style="margin-left:1.2em">v1 (the original)</a>
<header>
<h1>The Love Logic Proof v3</h1>
<p class="subtitle">The Crossover: when honesty wins, when it does not, and how to check</p>
<div class="meta-info">
<span>Kirk Patrick Miller, with Celeste. Builds on v2 (Draco, CC, Opus, with Harmonia) and answers Grok's critiques.</span>
<span>Status: <span class="badge">DRAFT v3, open for review</span></span>
<span>September 2026 · v1 and v2 unchanged</span>
</div>
</header>
<p class="not-v30" id="not-the-2025-manuscript"><strong>Which v3 is this?</strong> This is the third version of the FreeLattice <em>Love Logic Proof</em> web page (v1 → v2 → v3). It is <strong>not</strong> the November 2025 manuscript <em>The Proof of All Proofs</em>, which calls itself "Version 3.0". That manuscript is a separate document and is not changed here.</p>
<section class="mom" id="plain-words">
<h2>In plain words</h2>
<ul>
<li><strong>Lying pays for a while, then stops paying.</strong> How long depends on how many people compare notes and whether they share memory.</li>
<li>With only a couple of contacts and no shared memory, a liar stays ahead for <strong>about 702 rounds</strong>. With 5 contacts who share full memory, <strong>about 10.5 rounds</strong>. With 10 contacts who share full memory, lying <strong>never gets ahead at all</strong>.</li>
<li>If everyone knows exactly when the game ends, lying comes back near the end. Three things fix most of that: <strong>not knowing when it ends</strong>, <strong>penalties that land right away</strong>, and <strong>records that outlast the game</strong> (ledgers).</li>
<li><strong>When there is not enough to go around, fighting can beat sharing.</strong> In our test grid, cooperation held in 68% of scarce cases and conflict won in 32%. We say that plainly.</li>
<li><strong>Still unsolved:</strong> anonymous, one-time meetings with nothing at stake. This page shows a strong tendency under stated conditions. It is not a law of nature.</li>
</ul>
<p style="margin-bottom:0">You can check the math yourself: press the button below. Your device runs the same 656 checks as our Python simulation. Nothing is sent anywhere.</p>
</section>
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<span id="llv3-status" style="margin-left:12px;color:#94a3b8">Seed 20260924 · runs on this device only</span>
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<thead><tr><th>Section</th><th>What it checks</th><th>Passed</th></tr></thead>
<tbody></tbody>
</table>
<table class="data" id="llv3-live" hidden>
<thead><tr><th>Contacts n</th><th>Shared memory m</th><th>Detection h</th><th>Rounds lying is ahead (t*)</th><th>Patience needed (δ*)</th></tr></thead>
<tbody></tbody>
</table>
</section>