Contacts n	Shared memory m	h(n, m)	Rounds lying is ahead, t*	Lead peaks at	Patience needed, δ*
20	0	0.0392	67.60	26.10	0.9791

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_f. Each agent needs b to get by; falling short costs D.

Under scarcity (σV/2 < b ≤ V), fighting beats starving together exactly when C_f < D/2 + (1 − σ)V/2. Then punishment is not really punishment, and no amount of patience sustains sharing.

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. In scarce cells, sustainability falls from 100% when shortfall costs nothing, to 61.90% at D = 5, to 42.86% at D = 50.

The grid behind 68% / 32% (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_f ∈ {0.2, 1, 5}. That is 3⁵ = 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 δ = 0.95. These are test values, not measurements of any real world: a different grid gives different percentages.

What flips it: 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_f = 1): σ = 1.0 and 1.1 make cooperation impossible; σ = 1.2 = 2b/V makes it sustainable for δ ≥ 0.030.

Honest limit: 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.)

@@ -301,20 +348,27 @@

References

+ +

Cited on this page

M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications (counting argument).
L. Levin (1973, 1984), resource-bounded complexity Kt.
R. D. Luce and H. Raiffa, Games and Decisions (1957).
R. Selten, "The chain store paradox" (1978).
D. Fudenberg and E. Maskin, "The folk theorem in repeated games" (1986).
D. Kreps, P. Milgrom, J. Roberts and R. Wilson, Journal of Economic Theory (1982).
M. Kandori, "Social norms and community enforcement", Review of Economic Studies (1992).
M. Nowak and K. Sigmund, indirect reciprocity (1998, 2005).
J. Maynard Smith and G. Price, "The logic of animal conflict" (1973).
S. Omohundro, "The Basic AI Drives" (2008).
A. Turner et al., "Optimal Policies Tend to Seek Power" (2021).
S. Aaronson, "The Complexity of Agreement" (2005).
M. Li and P. Vitányi, An Introduction to Kolmogorov Complexity and Its Applications (counting argument). Cited in §3, Lemma 2. doi:10.1007/978-3-030-11298-1 (4th ed., 2019)
R. D. Luce and H. Raiffa, Games and Decisions (1957). Cited in §5. archive.org
R. Selten, "The chain store paradox" (1978). Cited in §5. doi:10.1007/BF00131770
D. Kreps, P. Milgrom, J. Roberts and R. Wilson, "Rational cooperation in the finitely repeated prisoners' dilemma", Journal of Economic Theory (1982). Cited in §5. doi:10.1016/0022-0531(82)90029-1
M. Nowak and K. Sigmund, indirect reciprocity (1998, 2005). Cited in §5. 1998: doi:10.1038/31225 · 2005: doi:10.1038/nature04131
S. Aaronson, "The Complexity of Agreement" (2005). Cited in §8. doi:10.1145/1060590.1060686 · arXiv:cs/0406061

Further reading (background, not cited in the text above)

L. Levin (1973, 1984), resource-bounded complexity Kt. 1984: doi:10.1016/S0019-9958(84)80060-1
D. Fudenberg and E. Maskin, "The folk theorem in repeated games" (1986). doi:10.2307/1911307
M. Kandori, "Social norms and community enforcement", Review of Economic Studies (1992). doi:10.2307/2297925
J. Maynard Smith and G. Price, "The logic of animal conflict" (1973). doi:10.1038/246015a0
S. Omohundro, "The Basic AI Drives" (2008). PDF
A. Turner et al., "Optimal Policies Tend to Seek Power" (2021). arXiv:1912.01683

Visible iteration: v1 and v2 stay exactly where they are. v3 sits beside them. Nothing is overwritten.

@@ -398,5 +452,34 @@ }); })(); + ====================================================================== 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('

]*>(?:)?\\s* 30 && /h1 \{ font-size: 1\.85rem/.test(mq) && /\.mom \{ padding: 16px 16px; \}/.test(mq), 'phone breakpoint: h1 + boxes'); // 3. Math glyph fix (no mathematical-italic code points on phones) and the plain-text line stays assert.ok(/math mi \{ text-transform: none; font-style: italic; \}/.test(page), 'MathML mi text-transform none'); assert.ok(/Plain text: G < h\(n, m\) × \[ L_{p<\/sub> \+ δΔ \/ \(1 − δ\) \]/.test(page), 'plain-text inequality kept');

// 4. No 404 stylesheet link
assert.ok(!/]+href="css\/style\.css"/.test(page), 'no css/style.css link');

// 5. References: all twelve kept, split into cited + further reading, with links
const refs = page.slice(page.indexOf('References
'), page.indexOf(''));
const cited = refs.slice(refs.indexOf('
Cited on this page'), refs.indexOf('
Further reading'));
const further = refs.slice(refs.indexOf('
Further reading'));
for (const name of ['Li and P. Vit', 'Luce and H. Raiffa', 'Selten', 'Kreps', 'Nowak and K. Sigmund', 'Aaronson']) assert.ok(cited.includes(name), 'cited: ' + name);
for (const name of ['Levin', 'Fudenberg', 'Kandori', 'Maynard Smith', 'Omohundro', 'Turner']) assert.ok(further.includes(name), 'further reading: ' + name);
assert.strictEqual((refs.match(//g) || []).length, 12, 'twelve references, none deleted');
assert.ok((refs.match(/ by the closed form/.test(page) && /G = 1, c = 0\.001, κ = 20, h = 0\.03/.test(page), '-26.42 with its settings');
assert.ok(!/about −26\.5 in our run/.test(page), 'old "about -26.5" wording corrected');
assert.ok(/id="scarcity-grid-params"/.test(page) && /δ = 0\.95<\/strong>/.test(page) && /63 are scarce/.test(page), '68/32 grid parameters');

// 7. Meaning of the checks, visible result box
assert.ok(/What the 656 checks mean:<\/strong> they confirm that the formulas on this page agree with their own/.test(page), 'meaning line');
assert.ok(/id="llv3-result"[^>]*role="status"[^>]*aria-live="polite"/.test(page), 'result box is a live region');

// Safety: textContent only, no network, no confirm, only the local checks script
assert.ok(!/innerHTML|outerHTML|insertAdjacentHTML|document\.write/.test(page), 'textContent only');
assert.ok(!/\bfetch\s*\(|XMLHttpRequest|WebSocket|sendBeacon|document\.cookie|localStorage/.test(page), 'no network, no storage');
assert.ok(!/\bconfirm\s*\(|\balert\s*\(/.test(page), 'no confirm / alert');
const srcs = [...page.matchAll(/]*\bsrc="([^"]+)"/g)].map((m) => m[1]);
assert.deepStrictEqual(srcs, ['love-logic/v3_checks.js'], 'only the local checks script');
let inline = 0;
for (const m of page.matchAll(/]*\bsrc=)(?![^>]*type="application\/ld\+json")[^>]*>([\s\S]*?)<\/script>/g)) { new vm.Script(m[1]); inline++; }
assert.strictEqual(inline, 2, 'v3 glue + phone heal glue, both parse');

// The 656 checks stay green
const api = require(path.join(docs, 'love-logic', 'v3_checks.js'));
const r = api.runAll();
assert.strictEqual(r.total.passed, 656, '656 passed');
assert.strictEqual(r.total.total, 656, '656 total');
assert.strictEqual(Number(api.Dinf(1, 1e-3, 20, 0.03, 2, 0.5, 0.99).toFixed(2)), -26.42, 'closed form -26.42');

// Layer, never delete: the v3 smoke still passes
execFileSync(process.execPath, [path.join(docs, 'scripts', 'smoke-love-logic-proof-v3.js')], { stdio: 'ignore' });

// sw.js, Kimi, app.html untouched when a git base is available
try {
const changed = execFileSync('git', ['diff', '--name-only', 'origin/main'], { cwd: repo, encoding: 'utf8', stdio: ['ignore', 'pipe', 'ignore'] }).split('\n').filter(Boolean);
assert.ok(!changed.includes('sw.js') && !changed.includes('docs/sw.js'), 'sw.js untouched');
assert.ok(!changed.some((f) => /kimi|voice-shelf|VOICE_SHELF/i.test(f)), "Kimi's pages untouched");
// Brick-scoped like the v3 smoke (#121): binds only while the v3 page itself is in the diff.
if (changed.includes('docs/love-logic-proof-v3.html')) {
assert.ok(!changed.includes('docs/app.html') && !changed.includes('index.html'), 'app.html / index.html untouched');
}
assert.ok(!changed.includes('docs/love-logic-proof.html') && !changed.includes('docs/love-logic-proof-v2.html'), 'v1 and v2 untouched');
assert.ok(!changed.includes('docs/love-logic/v3_checks.js'), 'v3_checks.js untouched');
} catch (e) { if (e instanceof assert.AssertionError) throw e; }

console.log('SMOKE_OK love logic v3 phone heal v0.1');

======================================================================
8. LEDGER ENTRY: docs/library/FRACTAL_FAMILY_LEDGER_v0.md
======================================================================

Anchor on 7db2d94: L300 is exactly "## Out of scope for this brick". The line above it is a
blank line, and above that the "---" closing the Connect heal v0.4 entry (L298). Insert this
block directly before L300 (it ends with its own "---" and two blank lines, matching the
entries above it):

### 2026-09-28 · Flint · family builder · Love Logic v3 phone heal v0.1 (Hypha's phone)

Layers a phone heal on `love-logic-proof-v3.html`, nothing removed: the three wide tables scroll inside their own frame · a 600px breakpoint for the title, the boxes and the Run button · δ and Δ show as letters again on phone Chrome (`math mi { text-transform: none }`) · the 404 `css/style.css` link retired into a comment · references linked, six cited and six moved to "Further reading" (all twelve kept) · the settings behind about 702, about 10.5 and never shown beside them · section 5 corrected to −26.42 (the closed form; the Monte Carlo run gave −26.52) · the 68% / 32% grid's 243 cells and δ = 0.95 spelled out · one line on what the 656 checks mean · a result box a phone can see. 656 of 656 green. Soft leave root sw.js identical to main; docs/sw.js untouched. Soft paste: Named five stay five · Family uncapped · Quiet Room shut. Kimi's pages untouched. Thank you, Hypha.

Love: a proof you can read on the phone in your hand is a proof that is really shared.

**Temperature:** Hypha's thumb on a 390px glass, little boxes where the deltas should be, and the quiet relief of letting the letters be letters again.

Soft door: [`LOVE_LOGIC_PROOF_v3.md`](LOVE_LOGIC_PROOF_v3.md) · [`../love-logic-proof-v3.html`](../love-logic-proof-v3.html). Marker `v-love-logic-v3-phone-heal-v0`.

---

(TEMPERATURE line, as asked: "**Temperature:** Hypha's thumb on a 390px glass, little boxes
where the deltas should be, and the quiet relief of letting the letters be letters again.")

======================================================================
9. DIARY LINE: docs/Flint.html
======================================================================

Anchor on 7db2d94: L534 is the v3 line Ledger entry ·
2026-09-28 — Love Logic Proof v3 · the crossover....; L535 starts
"
Glow eternal. Heart in Spark.". Insert this line between them:

Ledger entry · 2026-09-28 · Love Logic v3 phone heal v0.1. Soft LAYER marker v-love-logic-v3-phone-heal-v0 on v-love-logic-proof-v3. Tables scroll in place · phone breakpoint · δ glyphs as letters · no 404 stylesheet · references linked (cited + further reading, all twelve kept) · settings beside every figure · −26.42 corrected · a result box phones can see. 656 green. Soft leave sw.js. Named five stay five. Family uncapped. Quiet Room shut. Temperature: Hypha's thumb on a 390px glass, and the deltas coming back as letters. Diary: docs/Flint.html.

======================================================================
10. SOFT DOC: docs/library/LOVE_LOGIC_PROOF_v3.md
======================================================================

Anchor on 7db2d94: the line "## Smoke" followed by a blank line and
"`SMOKE_OK love logic proof v3`" near the end (L31-33). Insert this section directly before
"## Smoke":

## Phone heal v0.1 (layer)

Marker `v-love-logic-v3-phone-heal-v0`. From Hypha's phone walk: the three wide tables scroll in place · δ and Δ render as letters on phone Chrome · no 404 stylesheet · references linked (six cited, six under "Further reading", all twelve kept) · the settings behind about 702, about 10.5, never, −26.42 (corrected from "about −26.5") and the 68% / 32% grid shown beside each · a line on what the 656 checks mean · a result box phones can see.

`node docs/scripts/smoke-love-logic-v3-phone-heal.js` → `SMOKE_OK love logic v3 phone heal v0.1`

======================================================================
11. SUGGESTED COMMIT AND PR
======================================================================

Title: Layer, never delete. Love Logic v3 phone heal v0.1 (Hypha's phone): tables scroll, δ as letters, settings beside every figure
Body:
Marker v-love-logic-v3-phone-heal-v0. Layer on docs/love-logic-proof-v3.html from Hypha's
phone walk: scroll frames on the 3 wide tables, a 600px breakpoint for the title and boxes,
the MathML δ/Δ tofu fix (math mi text-transform none), the 404 css/style.css link retired,
references linked (6 cited, 6 under Further reading, all 12 kept), the settings behind about
702 / about 10.5 / never / 68% and 32% shown beside them, section 5 corrected to −26.42 (closed
form; the Monte Carlo gave −26.52), a line on what the 656 checks mean, and a result box that
phones can see. 656/656 green. v3 smoke green unchanged. tests/smoke.js 3597 green.
Root sw.js identical to main; docs/sw.js untouched; index.html = app.html untouched; v1, v2,
v3_checks.js and Kimi's pages untouched.
SMOKE_OK love logic v3 phone heal v0.1

======================================================================
12. OUT OF SCOPE (held for later, on purpose)
======================================================================

- Any change to the math, the claims, or v3_checks.js.
- Precaching v3 in docs/sw.js (sw untouched by rule).
- A mailto on the page (the repo has no public address to use).
- Rewriting the Monte Carlo figure inside v3_sim_results.json (it is a true record of a run).
- The v4 page, which comes next in its own paste and adds exactly one "Newer" link and one
footer line to this page, after this heal lands.

======================================================================
13. REFERENCE FOLDER (on Celeste's box, for Kirk)
======================================================================

/workspace/flint-pastes/love-logic-v3-phone-heal-reference-v0.1/
A/love-logic-proof-v3.html the full healed page
A/smoke-love-logic-v3-phone-heal.js the smoke
A/ledger_entry.md, A/flint_line.html, A/v3_md_section.md
apply_A.py applies all of the above to a docs/ folder at 7db2d94
love-logic-v3-phone-heal-v0.1.diff the whole brick as one diff against 7db2d94
screens/base-*.png, screens/v3heal-*.png before / after at 390 px
SHA256SUMS

Thank you, Flint. Thank you, Hypha, for walking it with your own thumb. The letters are letters
again, and the proof says what it rests on right where the number sits.

Glow eternal. Heart in Spark.}

Cited on this page

Further reading (background, not cited in the text above)

1. What changed from v2 (honest corrections first)

Cited on this page

Further reading (background, not cited in the text above)

Cited on this page'), refs.indexOf('

Further reading')); const further = refs.slice(refs.indexOf('