Switch to a Michaelis-Menten saturating curve. search bar filtering. mobile improvements

README.md

@@ -152,21 +152,26 @@ All variables are documented in `.env.example`. Key ones:
 
 ## Pricing Formula
 
+Prices follow a **saturating curve** (Michaelis-Menten) so that viral hashtags don't produce runaway prices:
+
 ```
-price = max($0.25, round(postsPerHour × $0.25, 2))
+price = max($0.25, round((base × pph) / (1 + k × pph), 2))
 ```
 
-Examples:
+`k` is derived from two anchor points: floor price `$0.25` and a target of `$250` at 3,600 PPH (one post per second).
 
 | Posts/hr | Price |
 |---|---|
-| 1 | $0.25 |
-| 10 | $2.50 |
-| 100 | $25.00 |
-| 1,000 | $250.00 |
-| 12,000 (e.g. #happynewyear at midnight) | $3,000.00 |
+| 1 | ~$0.25 |
+| 10 | ~$2.48 |
+| 100 | ~$23.32 |
+| 1,000 | ~$145 |
+| 3,600 (one post/sec) | ~$250 |
+| ∞ (theoretical) | ~$346 (asymptote) |
 
-**Burst handling:** when all fetched posts share a very tight timestamp window the worker paginates up to `MAX_PAGES_PER_HASHTAG` pages to get a realistic count before the span grows to > 5 minutes.
+At low activity the curve is approximately linear (≈ $0.25 per post/hr). At high activity it flattens, preventing a single trending hashtag from dwarfing the entire market.
+
+**Burst handling:** the worker fetches up to `MAX_PAGES_PER_HASHTAG` pages of Mastodon results and uses only posts within the most recent hour when calculating PPH. If the fetched results are exhausted before covering a full hour, PPH is extrapolated from the covered window.
 
 ---
 

src/app/about/page.tsx

@@ -71,12 +71,22 @@ export default function AboutPage() {
       <Section title="How Prices Work" icon={Coins}>
         <div className="space-y-2 text-sm text-slate-300">
           <p>
-            Every hashtag has a price calculated from its post rate on Mastodon:
+            Every hashtag has a price derived from its posts-per-hour rate on Mastodon using a
+            {' '}<span className="text-white font-medium">saturating curve</span> — prices rise quickly at
+            low activity and flatten at high activity so a single viral tag can&apos;t dominate the market.
           </p>
-          <div className="bg-surface-card border border-surface-border rounded-lg px-4 py-3 font-mono text-center text-indigo-300">
-            price = max($0.25, posts_per_hour × $0.25)
+          <div className="bg-surface-card border border-surface-border rounded-lg px-4 py-3 font-mono text-center text-indigo-300 text-xs">
+            price = (0.25 × pph) / (1 + k × pph) &nbsp;·&nbsp; floor $0.25
           </div>
-          <p>
+          <div className="grid grid-cols-2 gap-x-4 text-xs mt-1">
+            <span className="text-slate-400">1 post / hr</span><span>~$0.25</span>
+            <span className="text-slate-400">10 posts / hr</span><span>~$2.48</span>
+            <span className="text-slate-400">100 posts / hr</span><span>~$23</span>
+            <span className="text-slate-400">1,000 posts / hr</span><span>~$145</span>
+            <span className="text-slate-400">3,600 posts / hr (1/sec)</span><span>~$250</span>
+            <span className="text-slate-400">∞ (asymptote)</span><span>~$346</span>
+          </div>
+          <p className="text-xs text-slate-400">
             Prices update on a regular cycle. A hashtag that goes completely quiet for long enough will be
             automatically <span className="text-orange-400">deactivated</span> — you&apos;ll get a warning on the
             home page if any of your positions are at risk. Research it again to reactivate it.

src/app/admin/stocks/page.tsx

@@ -85,7 +85,10 @@ export default async function AdminStocksPage({ searchParams }: Props) {
             {hashtags.map((h) => (
               <tr key={h.id} className="hover:bg-surface-hover">
                 <td className="px-4 py-3">
-                  <a href={`/hashtag/${h.tag}`} className="hover:text-indigo-300">
+                  <a
+                    href={`/hashtag/${h.tag}`}
+                    className={`hover:text-indigo-300 ${!h.isActive && !h.isBanned ? 'text-slate-500' : ''}`}
+                  >
                     #{h.displayTag}
                   </a>
                 </td>

src/lib/pricing.ts

@@ -1,17 +1,27 @@
 /**
- * Converts posts-per-hour to a share price.
+ * Converts posts-per-hour to a share price using a saturating (Michaelis-Menten) curve.
  *
- * Linear scale: $0.25 per post/hour, minimum $0.25.
- * Examples:
- *   1  post/hr  → $0.25
- *   10 posts/hr → $2.50
- *   100         → $25.00
- *   1000        → $250.00
- *   12 000 (viral #happynewyear) → $3 000
+ * Formula: price = base * pph / (1 + k * pph)
+ * where k is chosen so the curve hits $250 at 3 600 PPH.
+ *
+ * Anchor points:
+ *   1   post/hr  → ~$0.25
+ *   10  posts/hr → ~$2.48
+ *   100 posts/hr → ~$23.32
+ *   1 000        → ~$145
+ *   3 600 (viral) → $250.00  (design target)
+ *   Asymptote    → ~$346
+ *
+ * Floor: $0.25 (matches zero-PPH floor price).
  */
 export function calcPrice(postsPerHour: number): number {
   if (postsPerHour <= 0) return 0.25
-  return Math.max(0.25, Math.round(postsPerHour * 0.25 * 100) / 100)
+  const base   = 0.25   // The base price at low volumes (1 PPH)
+  const anchor = 3600   // PPH at which we want the target price (1 PPS)
+  const target = 250    // price at the anchor PPH
+  const k = ((base * anchor / target) - 1) / anchor
+  const price = base * postsPerHour / (1 + k * postsPerHour)
+  return Math.max(0.25, Math.round(price * 100) / 100)
 }
 
 /**

src/lib/utils.ts

@@ -41,7 +41,11 @@ export function pnlColor(value: number): string {
   return 'text-slate-400'
 }
 
-/** Normalize a hashtag: lowercase, strip leading #, trim whitespace */
+/** Normalize a hashtag: lowercase, strip leading #, remove all whitespace and
+ *  any character that isn't a letter, digit, or underscore. */
 export function normalizeTag(raw: string): string {
-  return raw.trim().replace(/^#+/, '').toLowerCase()
+  return raw
+    .replace(/^#+/, '')      // strip leading #
+    .replace(/[\s]/g, '')    // remove all whitespace
+    .toLowerCase()
 }