# Ephemeral Sidechains

**URL:** <https://research.rsk.dev/t/ephemeral-sidechains/536>\
**Category:** Stateless clients, sidechains and Sharding\
**Created:** [July 31, 2026, 8:34pm UTC](https://research.rsk.dev/t/ephemeral-sidechains/536 "2026-07-31T20:34:37Z")\
**Posts on this page:** 1\
**Showing post:** 4

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**Author:** ![Nuh](https://avatars.discourse-cdn.com/v4/letter/n/da6949/32.png) [@Nuh](https://research.rsk.dev/u/Nuh)\
**Post date:** [August 25, 2026, 11:17am UTC](https://research.rsk.dev/t/ephemeral-sidechains/536/4 "2026-08-25T11:17:00Z")

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I figured out a good formula for Ephemeral Sidechains in the context of BitVM bridge or any trustless bridge, by parameterizing the threshold based on the amounts withdrawn. The same can apply to light clients based on the funds that the user has on the sidechain.

Basically the logic is to require a minimum number of difficulty epochs relative to the amount withdrawn according to the formula: `number_of_epochs = ceil(sqrt(amount_in_sats) / (2^20))`

These numbers are chosen so that the minimum is 1 difficulty epoch (14 days) and the most is 26 epochs (~1 year).

> **[ceil(sqrt(x) / 2^20) ; x from 0 to 21,000,000 \* 100,000,000 - Wolfram|Alpha](https://www.wolframalpha.com/input?i=ceil%28sqrt%28x%29+%2F+2%5E20%29+%3B+x+from+0+to+21%2C000%2C000+*+100%2C000%2C000)**
>
> Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

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