Bellcurve
Research

The evidence

Three years of real prices for six stocks, replayed minute by minute through today's pools and through Bellcurve, running the same pricing code as the on-chain program.

Backtest · 2.9 years of real hourly prices, minute-level replay

What liquidity providers lose to informed traders

Constant-product, 0.30% fee-53.6% ±0.2
Constant-product, 1.00% fee-61.0% ±0.3
Oracle pool, no market hours-165.8% ±23.2
Bellcurve-11.9% ±0.8
LPs lose vs holdingLPs gain

Same $100k pool, same price path, arbitrageurs who know the true price every minute. Bellcurve: -4.1%/yr vs -18.4%/yr for a 0.30% constant-product pool. Worst single weekend: 0.00% of the pool.

LP value minus buy-and-hold, % of starting capital
-154%+6%202420252026
Constant-product, 0.30% feeOracle pool, no market hoursBellcurve
With ordinary traders: what a trade costs vs the true price
PoolMarket openClosedLP / yr
Constant-product, 0.30% fee127 bps121 bps+14%
Constant-product, 1.00% fee177 bps173 bps+67%
Oracle pool, no market hours68 bps106 bps-29%
Bellcurve48 bps238 bps+103%

Closed-market trades cost more on Bellcurve on purpose: that is the price of real uncertainty, paid to the LPs who carry it.

Robustness: slower oracle, same informed traders
Oracle delay0.30% poolBellcurve
2 s-53.6%-11.9%
15 s-53.6%-39.7%
60 s-53.6%-61.7%

Pyth and Chainlink update every Solana slot; at a minute of delay Bellcurve loses its edge on the most volatile names, so fresh prices matter.

NVDA · every weekend since Oct 2023

The quote widens as the uncertainty does

-5%-2.5%0%+2.5%+5%0h12h24h36h48h60h72h84hhours since prices stopped printing (Friday 8pm New York)Monday pre-market2023-10-20: +0.02% after 56h2023-10-27: +0.38% after 56h2023-11-03: +0.18% after 57h2023-11-10: -0.49% after 57h2023-11-17: -0.15% after 57h2023-11-22: -1.12% after 33h2023-11-24: -0.78% after 59h2023-12-01: -0.34% after 57h2023-12-08: -0.13% after 57h2023-12-15: +0.48% after 57h2023-12-22: -0.01% after 81h2023-12-29: +0.15% after 81h2024-01-05: -0.17% after 57h2024-01-12: -0.54% after 81h2024-01-19: +1.04% after 57h2024-01-26: +0.75% after 57h2024-02-02: +0.40% after 57h2024-02-09: +0.39% after 57h2024-02-16: +0.10% after 81h2024-02-23: +1.08% after 57h2024-03-01: +1.14% after 57h2024-03-08: -0.65% after 56h2024-03-15: +1.55% after 56h2024-03-22: +0.63% after 56h2024-03-28: +1.21% after 80h2024-04-05: -0.05% after 56h2024-04-12: +1.26% after 56h2024-04-19: +2.13% after 56h2024-04-26: +0.60% after 56h2024-05-03: +0.22% after 56h2024-05-10: +0.44% after 56h2024-05-17: +0.81% after 56h2024-05-24: +2.45% after 80h2024-05-31: +1.64% after 56h2024-06-07: +0.07% after 56h2024-06-14: +1.14% after 56h2024-06-18: +2.27% after 32h2024-06-21: +0.01% after 56h2024-06-28: +0.22% after 56h2024-07-03: +0.81% after 35h2024-07-05: +0.21% after 56h2024-07-12: +0.26% after 56h2024-07-19: +1.15% after 56h2024-07-26: +0.26% after 56h2024-08-02: -6.84% after 56h2024-08-09: +0.71% after 56h2024-08-16: +0.20% after 56h2024-08-23: +0.42% after 56h2024-08-30: +0.02% after 80h2024-09-06: +1.55% after 56h2024-09-13: +0.19% after 56h2024-09-20: +0.22% after 56h2024-09-27: +0.05% after 56h2024-10-04: -0.23% after 56h2024-10-11: +0.57% after 56h2024-10-18: +0.22% after 56h2024-10-25: +1.02% after 56h2024-11-01: -0.00% after 57h2024-11-08: +0.72% after 57h2024-11-15: +0.63% after 57h2024-11-22: +0.85% after 57h2024-11-27: +1.57% after 33h2024-11-29: -0.11% after 59h2024-12-06: +0.06% after 57h2024-12-13: +0.19% after 57h2024-12-20: +0.70% after 57h2024-12-24: +0.45% after 35h2024-12-27: -0.42% after 57h2024-12-31: +0.38% after 33h2025-01-03: +0.61% after 57h2025-01-08: -0.78% after 33h2025-01-10: -1.93% after 57h2025-01-17: +0.68% after 81h2025-01-24: -6.46% after 57h2025-01-31: -1.71% after 57h2025-02-07: +0.85% after 57h2025-02-14: +1.02% after 81h2025-02-21: +0.74% after 57h2025-02-28: -0.18% after 57h2025-03-07: -1.97% after 57h2025-03-14: -0.36% after 56h2025-03-21: +1.24% after 56h2025-03-28: -1.99% after 56h2025-04-04: -6.02% after 56h2025-04-11: +3.62% after 56h2025-04-17: -1.25% after 80h2025-04-25: -0.89% after 56h2025-05-02: -0.28% after 56h2025-05-09: +3.10% after 56h2025-05-16: +0.17% after 56h2025-05-23: +2.93% after 80h2025-05-30: -0.73% after 56h2025-06-06: +0.25% after 56h2025-06-13: +0.65% after 56h2025-06-18: -0.07% after 32h2025-06-20: -0.32% after 56h2025-06-27: +0.89% after 56h2025-07-03: -0.43% after 83h2025-07-11: -0.01% after 56h2025-07-18: +0.30% after 56h2025-07-25: +0.68% after 56h2025-08-01: +1.30% after 56h2025-08-08: -0.24% after 56h2025-08-15: +0.20% after 56h2025-08-22: +0.14% after 56h2025-08-29: -0.73% after 80h2025-09-05: +0.45% after 56h2025-09-12: -0.03% after 56h2025-09-19: -0.18% after 56h2025-09-26: +0.76% after 56h2025-10-03: +0.18% after 56h2025-10-10: +2.51% after 56h2025-10-17: +0.51% after 56h2025-10-24: +1.77% after 56h2025-10-31: +0.67% after 57h2025-11-07: +1.88% after 57h2025-11-14: +0.74% after 57h2025-11-21: +0.63% after 57h2025-11-26: +0.34% after 33h2025-11-28: -0.58% after 59h2025-12-05: +0.12% after 57h2025-12-12: +0.77% after 57h2025-12-19: +0.68% after 57h2025-12-24: +1.14% after 35h2025-12-26: -0.92% after 57h2025-12-31: +1.45% after 33h2026-01-02: +0.52% after 57h2026-01-09: -1.17% after 57h2026-01-16: -2.63% after 81h2026-01-23: -0.08% after 57h2026-01-30: -1.17% after 57h2026-02-06: -0.18% after 57h2026-02-13: -0.57% after 81h2026-02-20: -0.43% after 57h2026-02-27: -1.73% after 57h2026-03-06: -1.34% after 56h2026-03-13: +0.96% after 56h2026-03-20: -2.64% after 56h2026-03-27: +0.71% after 56h2026-04-02: +0.72% after 80h2026-04-10: -1.18% after 56h2026-04-17: -0.91% after 57h2026-04-24: +0.20% after 56h2026-05-01: +0.82% after 56h2026-05-08: -0.07% after 56h2026-05-15: +0.37% after 56h2026-05-22: +1.33% after 80h2026-05-29: +1.54% after 56h2026-06-05: +1.48% after 56h2026-06-12: +2.22% after 56h2026-06-18: -0.18% after 80h2026-06-26: +1.13% after 56h2026-07-02: +0.33% after 80h2026-07-10: -1.35% after 56h2026-07-17: +0.31% after 56h2026-07-24: +0.92% after 56h2026-07-31: +1.53% after 56h2026-08-07: +0.49% after 56h2026-08-14: +0.48% after 56h2026-08-21: -0.09% after 56h2026-08-28: +0.51% after 56h2026-09-04: +0.65% after 80h2026-09-11: -1.98% after 56h

97% of 163 weekends and holidays reopened inside Bellcurve's quote (±1.5σ√t).

71% moved more than a normal pool's 0.30% fee, a free profit for whoever trades first.

Red dots are gaps beyond the quote; there the closed-market curve and the price band limit the damage.

Live from Nasdaq's trading-halt feed

Stocks stop trading. 24/7 pools don't notice.

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Method: hourly SPY, QQQ, NVDA, TSLA, AAPL and MSTR bars (regular and extended hours) replayed at one-minute resolution with Brownian-bridge paths between prints; while the market is closed the path bridges to the next open, so informed traders learn the gap gradually. Arbitrageurs trade every mispriced pool as far as it pays; uninformed orders are identical across pools. 3 seeds; 2s oracle delay unless noted. Simulated, not a promise of future returns.