# Proofs

Formal mathematical arguments for the key claims.

| File | Claim | Method |
|------|-------|--------|
| [`ternary-efficiency.md`](./ternary-efficiency.md) | Ternary is more computationally efficient than binary | Calculus / radix economy |
| [`self-reference.md`](./self-reference.md) | The QWERTY encoding is self-referential | Direct construction |
| [`pure-state.md`](./pure-state.md) | The density matrix of the system is a pure state | Linear algebra / SVD |
| [`universal-computation.md`](./universal-computation.md) | The ternary bio-quantum system is Turing-complete | Reaction network theory |
| [`lucidia.md`](./lucidia.md) | The number-theoretic identity of Lucidia (88) | Number theory: totient, Möbius, Collatz, Goldbach |