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.
 
 ---