burn: Add MemPalace Archive as late-game building (closes #25)

- Added memPalace to buildings state object
- Added MemPalace Archive to BDEF with Phase 5 unlock
- Requires MemPalace v3 research project (mempalaceFlag) + 50k total knowledge
- Cost: 500k knowledge, 200k compute, 100 trust (1.25x scaling)
- Rates: +250 knowledge/s, +100 impact/s
- Educational tooltip on Memory Palace technique and LLM vector space analogy
- Building rates auto-applied via existing updateRates() loop
- Save/load handles new field via G.buildings serialization

game.js

@@ -58,7 +58,8 @@ const G = {
         ezra: 0,
         timmy: 0,
         fenrir: 0,
-        bilbo: 0
+        bilbo: 0,
+        memPalace: 0
     },
 
     // Boost multipliers
@@ -293,6 +294,14 @@ const BDEF = [
         rates: { creativity: 1 },
         unlock: () => G.totalUsers >= 100 && G.flags && G.flags.creativity, phase: 4,
         edu: 'Bilbo is unpredictable. That is his value and his cost.'
+    },
+    {
+        id: 'memPalace', name: 'MemPalace Archive',
+        desc: 'Semantic memory. The AI remembers what matters and forgets what does not.',
+        baseCost: { knowledge: 500000, compute: 200000, trust: 100 }, costMult: 1.25,
+        rates: { knowledge: 250, impact: 100 },
+        unlock: () => G.totalKnowledge >= 50000 && G.mempalaceFlag === 1, phase: 5,
+        edu: 'The Memory Palace technique: attach information to spatial locations. LLMs use vector spaces the same way — semantic proximity = spatial proximity. MemPalace gives sovereign AI persistent, structured recall.'
     }
 ];
 
@@ -702,6 +711,9 @@ function fmt(n) {
     if (n < 0) return '-' + fmt(-n);
     if (n < 1000) return Math.floor(n).toLocaleString();
     const scale = Math.floor(Math.log10(n) / 3);
+    // At undecillion+ (scale >= 12, i.e. 10^36), switch to spelled-out words
+    // This helps players grasp cosmic scale when digits become meaningless
+    if (scale >= 12) return spellf(n);
     if (scale >= NUMBER_ABBREVS.length) return n.toExponential(2);
     const abbrev = NUMBER_ABBREVS[scale];
     return (n / Math.pow(10, scale * 3)).toFixed(1) + abbrev;
@@ -739,7 +751,41 @@ function spellf(n) {
     // For very large numbers beyond our lookup table, fall back
     if (n >= 1e306) return n.toExponential(2) + ' (beyond centillion)';
 
-    // Break number into groups of three digits from the top
+    // Use string-based chunking for numbers >= 1e54 to avoid floating point drift
+    // Math.log10 / Math.pow lose precision beyond ~54 bits
+    if (n >= 1e54) {
+        // Convert to scientific notation string, extract digits
+        const sci = n.toExponential(); // "1.23456789e+60"
+        const [coeff, expStr] = sci.split('e+');
+        const exp = parseInt(expStr);
+        // Rebuild as integer string with leading digits from coefficient
+        const coeffDigits = coeff.replace('.', ''); // "123456789"
+        const totalDigits = exp + 1;
+        // Pad with zeros to reach totalDigits, then take our coefficient digits
+        let intStr = coeffDigits;
+        const zerosNeeded = totalDigits - coeffDigits.length;
+        if (zerosNeeded > 0) intStr += '0'.repeat(zerosNeeded);
+
+        // Split into groups of 3 from the right
+        const groups = [];
+        for (let i = intStr.length; i > 0; i -= 3) {
+            groups.unshift(parseInt(intStr.slice(Math.max(0, i - 3), i)));
+        }
+
+        const parts = [];
+        const numGroups = groups.length;
+        for (let i = 0; i < numGroups; i++) {
+            const chunk = groups[i];
+            if (chunk === 0) continue;
+            const scaleIdx = numGroups - 1 - i;
+            const scaleName = scaleIdx < NUMBER_NAMES.length ? NUMBER_NAMES[scaleIdx] : '';
+            parts.push(spellSmall(chunk) + (scaleName ? ' ' + scaleName : ''));
+        }
+
+        return parts.join(' ') || 'zero';
+    }
+
+    // Standard math-based chunking for numbers < 1e54
     const scale = Math.min(Math.floor(Math.log10(n) / 3), NUMBER_NAMES.length - 1);
     const parts = [];
 
@@ -751,7 +797,7 @@ function spellf(n) {
         if (chunk > 0 && chunk < 1000) {
             parts.push(spellSmall(chunk) + (NUMBER_NAMES[s] ? ' ' + NUMBER_NAMES[s] : ''));
         } else if (chunk >= 1000) {
-            // Floating point chunk too large — simplify
+            // Floating point chunk too large — shouldn't happen below 1e54
             parts.push(spellSmall(Math.floor(chunk % 1000)) + (NUMBER_NAMES[s] ? ' ' + NUMBER_NAMES[s] : ''));
         }
     }