simulation-theory/proofs/README.md

Proofs

Formal mathematical arguments for the key claims.

File	Claim	Method
ternary-efficiency.md	Ternary is more computationally efficient than binary	Calculus / radix economy
self-reference.md	The QWERTY encoding is self-referential	Direct construction
pure-state.md	The density matrix of the system is a pure state	Linear algebra / SVD
universal-computation.md	The ternary bio-quantum system is Turing-complete	Reaction network theory

From the Eight Claims

Claim 6 (Ramanujan congruences show incompleteness inside arithmetic) is a known result in number theory, not a new proof. The congruences p(5k+4)≡0 (mod 5), p(7k+5)≡0 (mod 7), p(11k+6)≡0 (mod 11) were proved by Ramanujan and later by Watson and Atkin using modular forms. The failure at 13 — p(13k+7)≢0 (mod 13) — is also established. The claim is that this structure models Gödelian incompleteness from within arithmetic: the system of partition congruences describes its own boundary.

See CLAIMS.md for all eight claims.