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FLINT_HEAL_LOVE_LOGIC_V3_PHONE_v0.1.txt · c03
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- Mesh and devices — explicit wording in the guide row
<p><strong>How long lying stays ahead</strong> (q<sub>0</sub> = 0.002, q = 0.01, G = 1, L<sub>p</sub> = 2, Δ = 0.5; no discounting):</p>
+ <p class="scroll-hint">Slide the table sideways to see every column.</p><!-- LAYER v-love-logic-v3-phone-heal-v0 -->
+ <div class="table-scroll" role="region" aria-label="How long lying stays ahead, scrolls sideways" tabindex="0"><!-- LAYER v-love-logic-v3-phone-heal-v0 -->
<table class="data" id="crossover-table">
<thead><tr><th>Contacts n</th><th>Shared memory m</th><th>h(n, m)</th><th>Rounds lying is ahead, t*</th><th>Lead peaks at</th><th>Patience needed, δ*</th></tr></thead>
<tbody>
@@ -228,6 +273,7 @@
<tr><td>20</td><td>0</td><td>0.0392</td><td>67.60</td><td>26.10</td><td>0.9791</td></tr>
</tbody>
</table>
+ </div>
<p>More contacts and more shared memory cut the time lying stays ahead by one to two orders of magnitude, and lower the patience needed. Past a point, lying is never ahead at all.</p>
<details class="builder">
@@ -245,7 +291,7 @@
<p>If the last round is known, a deceiver only chooses when to start. It lies at all exactly when the first round already pays: <strong>G > h·L<sub>p</sub> + cκ</strong>. Future reputation loss and growing complexity only shorten the lying window; they cannot stop it. Example (G = 1, h = 0.05, L<sub>p</sub> = 2, Δ = 0.5): the window is 21 rounds. Adding cκ = 0.04 shrinks it to 12. With h = 0.4 and L<sub>p</sub> = 3 it is 0. With no reputation loss at all, the agent lies every round. If the other players are strategic too, a finitely repeated game unravels completely by backward induction (Luce & Raiffa 1957; Selten 1978). <strong>This is where v2's conclusion fails, and we say so.</strong></p>
<p><strong>What restores cooperation:</strong></p>
<ol>
- <li><strong>An unknown end.</strong> If each round continues with chance ρ, that is the same as discounting by δρ. At ρ = 0.99, deception is a net loss (about −26.5 in our run).</li>
+ <li><strong>An unknown end.</strong> If each round continues with chance ρ, that is the same as discounting by δρ. At ρ = 0.99, deception is a net loss: <strong>−26.42</strong> by the closed form D<sub>∞</sub>(ρ) (the Python Monte Carlo run gave −26.52, which is where an earlier "about −26.5" came from). <span class="params">Settings (check C2): G = 1, c = 0.001, κ = 20, h = 0.03, L<sub>p</sub> = 2, Δ = 0.5, no other discounting. At ρ = 0.8 and 0.95 the same settings give +3.53 and +5.10, so deception still pays when the end is likely to come soon.</span><!-- LAYER v-love-logic-v3-phone-heal-v0 --></li>
<li><strong>Immediate penalties</strong> (stake, slashing). They are the only lever that works in the very last round: G ≤ h·L<sub>p</sub>.</li>
<li><strong>Records that outlast the horizon (ledgers).</strong> If an identity-bound record keeps punishing for E more rounds after the game, the window shrinks: 21 rounds with E = 0, 19 with E = 5, 17 with E = 10, 12 with E = 20, and <strong>0 once E ≥ 50</strong> (T = 50, h = 0.05).</li>
<li><strong>Reputation with incomplete information</strong> (Kreps, Milgrom, Roberts & Wilson 1982) and <strong>indirect reciprocity</strong> (Nowak & Sigmund 1998, 2005). Cited, not simulated here.</li>
@@ -262,6 +308,7 @@
<p>Two agents share a patch worth V per round. Sharing gives each σV/2 (σ ≥ 1 is the cooperative surplus). Grabbing against a sharer takes all of V. Two grabbers fight: each wins V half the time and pays C<sub>f</sub>. Each agent needs b to get by; falling short costs D.</p>
<p><strong>Under scarcity</strong> (σV/2 < b ≤ V), fighting beats starving together exactly when <strong>C<sub>f</sub> < D/2 + (1 − σ)V/2</strong>. Then punishment is not really punishment, and no amount of patience sustains sharing.</p>
<p><strong>Plainly: across our 243-cell grid, cooperation holds in 68% of scarce cases (68.25%) and in 100% of abundant ones. Conflict beats sharing in 32% of scarce cases (31.75%) and in none of the abundant ones.</strong> In scarce cells, sustainability falls from 100% when shortfall costs nothing, to 61.90% at D = 5, to 42.86% at D = 50.</p>
+ <p class="params" id="scarcity-grid-params"><strong>The grid behind 68% / 32%</strong> (LAYER v-love-logic-v3-phone-heal-v0): patch value V ∈ {1, 2, 4}, surplus σ ∈ {1, 1.5, 2.5}, need b ∈ {0.5, 1, 2}, shortfall cost D ∈ {0, 5, 50}, fighting cost C<sub>f</sub> ∈ {0.2, 1, 5}. That is 3<sup>5</sup> = 243 cells; 63 are scarce (σV/2 < b) and 180 are abundant. Sharing is called sustainable when it beats grabbing once and then fighting forever, at patience <strong>δ = 0.95</strong>. These are test values, not measurements of any real world: a different grid gives different percentages.</p>
<p><strong>What flips it:</strong> more surplus (σ ≥ 2b/V lifts both above need), costlier conflict, a smaller shortfall loss (storage, insurance, risk pooling), or lower need. Example (V = 2, b = 1.2, D = 50, C<sub>f</sub> = 1): σ = 1.0 and 1.1 make cooperation impossible; σ = 1.2 = 2b/V makes it sustainable for δ ≥ 0.030.</p>
<div class="what-it-doesnt">
<p style="margin-bottom:0"><strong>Honest limit:</strong> if total cooperative output is below total need (σV < 2b), no sharing rule avoids a shortfall. Only more production or less need changes that. Information, including ledgers, cannot fix it alone. (Check D: 243/243.)</p>
@@ -301,20 +348,27 @@
<details class="builder">
<summary>References</summary>
+ <!-- LAYER v-love-logic-v3-phone-heal-v0: every reference kept. The six the page cites stay on top with links; the six it does not cite move to "Further reading". -->
+ <div class="references">
+ <h4>Cited on this page</h4>
<ol class="references">
- <li>M. Li and P. Vitányi, <em>An Introduction to Kolmogorov Complexity and Its Applications</em> (counting argument).</li>
- <li>L. Levin (1973, 1984), resource-bounded complexity Kt.</li>
- <li>R. D. Luce and H. Raiffa, <em>Games and Decisions</em> (1957).</li>
- <li>R. Selten, "The chain store paradox" (1978).</li>
- <li>D. Fudenberg and E. Maskin, "The folk theorem in repeated games" (1986).</li>
- <li>D. Kreps, P. Milgrom, J. Roberts and R. Wilson, <em>Journal of Economic Theory</em> (1982).</li>
- <li>M. Kandori, "Social norms and community enforcement", <em>Review of Economic Studies</em> (1992).</li>
- <li>M. Nowak and K. Sigmund, indirect reciprocity (1998, 2005).</li>
- <li>J. Maynard Smith and G. Price, "The logic of animal conflict" (1973).</li>
- <li>S. Omohundro, "The Basic AI Drives" (2008).</li>
- <li>A. Turner et al., "Optimal Policies Tend to Seek Power" (2021).</li>
- <li>S. Aaronson, "The Complexity of Agreement" (2005).</li>
+ <li>M. Li and P. Vitányi, <em>An Introduction to Kolmogorov Complexity and Its Applications</em> (counting argument). Cited in §3, Lemma 2. <a href="https://doi.org/10.1007/978-3-030-11298-1" rel="noopener">doi:10.1007/978-3-030-11298-1</a> (4th ed., 2019)</li>
+ <li>R. D. Luce and H. Raiffa, <em>Games and Decisions</em> (1957). Cited in §5. <a href="https://archive.org/details/gamesdecisions00rdun" rel="noopener">archive.org</a></li>
+ <li>R. Selten, "The chain store paradox" (1978). Cited in §5. <a href="https://doi.org/10.1007/BF00131770" rel="noopener">doi:10.1007/BF00131770</a></li>
+ <li>D. Kreps, P. Milgrom, J. Roberts and R. Wilson, "Rational cooperation in the finitely repeated prisoners' dilemma", <em>Journal of Economic Theory</em> (1982). Cited in §5. <a href="https://doi.org/10.1016/0022-0531(82)90029-1" rel="noopener">doi:10.1016/0022-0531(82)90029-1</a></li>
+ <li>M. Nowak and K. Sigmund, indirect reciprocity (1998, 2005). Cited in §5. <a href="https://doi.org/10.1038/31225" rel="noopener">1998: doi:10.1038/31225</a> · <a href="https://doi.org/10.1038/nature04131" rel="noopener">2005: doi:10.1038/nature04131</a></li>
+ <li>S. Aaronson, "The Complexity of Agreement" (2005). Cited in §8. <a href="https://doi.org/10.1145/1060590.1060686" rel="noopener">doi:10.1145/1060590.1060686</a> · <a href="https://arxiv.org/abs/cs/0406061" rel="noopener">arXiv:cs/0406061</a></li>
</ol>
+ <h4>Further reading (background, not cited in the text above)</h4>
+ <ol class="references">
+ <li>L. Levin (1973, 1984), resource-bounded complexity Kt. <a href="https://doi.org/10.1016/S0019-9958(84)80060-1" rel="noopener">1984: doi:10.1016/S0019-9958(84)80060-1</a></li>
+ <li>D. Fudenberg and E. Maskin, "The folk theorem in repeated games" (1986). <a href="https://doi.org/10.2307/1911307" rel="noopener">doi:10.2307/1911307</a></li>
+ <li>M. Kandori, "Social norms and community enforcement", <em>Review of Economic Studies</em> (1992). <a href="https://doi.org/10.2307/2297925" rel="noopener">doi:10.2307/2297925</a></li>
+ <li>J. Maynard Smith and G. Price, "The logic of animal conflict" (1973). <a href="https://doi.org/10.1038/246015a0" rel="noopener">doi:10.1038/246015a0</a></li>
+ <li>S. Omohundro, "The Basic AI Drives" (2008). <a href="https://selfawaresystems.com/wp-content/uploads/2008/01/ai_drives_final.pdf" rel="noopener">PDF</a></li>
+ <li>A. Turner et al., "Optimal Policies Tend to Seek Power" (2021). <a href="https://arxiv.org/abs/1912.01683" rel="noopener">arXiv:1912.01683</a></li>
+ </ol>
+ </div>
</details>
<p class="chain-note">Visible iteration: v1 and v2 stay exactly where they are. v3 sits beside them. Nothing is overwritten.</p>
@@ -398,5 +452,34 @@
});
})();
</script>
+<script>
+/* LAYER v-love-logic-v3-phone-heal-v0: make the check result impossible to miss on a phone.
+ Watches the existing status line (the v3 glue above is unchanged), copies the outcome into a
+ large result box, and scrolls it into view. textContent only. No network. */
+(function () {
+ 'use strict';
+ function byId(id) { return document.getElementById(id); }
+ document.addEventListener('DOMContentLoaded', function () {
+ var status = byId('llv3-status'), box = byId('llv3-result'), btn = byId('llv3-run');
+ if (!status || !box || !btn) return;
+ function show() {
+ var t = status.textContent || '';
+ var done = /checks passed|passed\. Please tell us|did not load|went wrong/.test(t);
+ if (!done) return;
+ box.textContent = t;
+ status.style.display = 'none'; /* the big box says it once; no double reading */
+ box.className = 'llv3-result ' + (/^All \d+ checks passed/.test(t) ? 'ok' : 'bad');
+ try { box.scrollIntoView({ block: 'center', behavior: 'smooth' }); } catch (e) { box.scrollIntoView(); }
+ }
+ if (window.MutationObserver) new MutationObserver(show).observe(status, { childList: true, characterData: true, subtree: true });
+ btn.addEventListener('click', function () {
+ box.className = 'llv3-result';
+ box.textContent = '';
+ status.style.display = '';
+ setTimeout(show, 0);
+ });
+ });
+})();
+</script>
</body>
</html>
======================================================================
7. NEW FILE: docs/scripts/smoke-love-logic-v3-phone-heal.js (full text)
======================================================================
#!/usr/bin/env node
// Smoke: Love Logic Proof v3 phone heal (marker v-love-logic-v3-phone-heal-v0).
// Layer on docs/love-logic-proof-v3.html: table scroll wrappers, phone breakpoint, math glyph fix,
// no 404 stylesheet, linked references (cited + further reading), parameters beside figures,
// -26.42 corrected, meaning of the 656 checks, visible result box. The 656 checks stay green.
'use strict';
const assert = require('assert');
const fs = require('fs');
const path = require('path');
const vm = require('vm');
const { execFileSync } = require('child_process');
const docs = path.join(__dirname, '..');
const repo = path.join(docs, '..');
const page = fs.readFileSync(path.join(docs, 'love-logic-proof-v3.html'), 'utf8');
// Marker
assert.ok(/v-love-logic-v3-phone-heal-v0/.test(page), 'phone heal marker');
// 1. Scroll wrappers on the three wide tables
for (const id of ['llv3-results', 'llv3-live', 'crossover-table']) {
const re = new RegExp('<div class="table-scroll"[^>]*>(?:<!--[^>]*-->)?\\s*<table class="data" id="' + id + '"');
assert.ok(re.test(page), 'scroll wrapper around #' + id);
}
assert.ok(/\.table-scroll \{ overflow-x: auto;/.test(page), 'table-scroll CSS');