I want a formula, calibrated and backtested on real Manifold data, that estimates the probability that a binary market will ever cross a given probability level p before it resolves.

The formula should:

• be based on real historical Manifold data, not intuition

• include some minimal evidence of backtesting (e.g., a few plots or numbers comparing predicted vs actual crossing frequencies)

• be provided as a clear, usable expression or a simple Python function I can plug into my code

• be reasonably accurate in non‑extreme cases (e.g., resolution date 2–52 weeks away, and >5 unique traders)

Prize: If someone provides a valid formula (see criteria above), I will tip 1,000 mana to the solver. If multiple people contribute meaningfully, I will split the 1,000 mana among them.

Resolution criteria: This market resolves YES if, before May 1, 2026:

1. someone posts a formula in the comments, and

2. shows at least minimal evidence that it was calibrated/backtested on real Manifold data, and

3. I judge the formula reasonable enough to use

Otherwise, it resolves NO.