> For the complete documentation index, see [llms.txt](https://docs.on.nexus/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.on.nexus/hodifi/invariants.md).

# Invariants

* Custody separation: Borrower controls BTC. Lender controls funds.
* Atomic alignment: EVM withdrawal and BTC unlock are coupled through `x` for the main path and `y` for the fallback path. `T` defines the default path.
* Oracle minimization: No price feeds are required for liquidation. The Cosigner is liveness only.
* Auditability: SPV proofs, EVM events, and disclosure of `x` or `y` are publicly verifiable.

This time sequence avoids overlap with System Architecture. Architecture explains what components exist and how they are bounded. Lifecycle explains when and how they interact.