Proofs

Formal mathematical arguments for the key claims.

📖 All proofs use standard mathematical methods. For background on the underlying research, see REFERENCES.md.

File	Claim	Method
`ternary-efficiency.md`	Ternary is more computationally efficient than binary	Calculus / radix economy (Knuth, 1980)
`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 (von Neumann, 1932)
`universal-computation.md`	The ternary bio-quantum system is Turing-complete	Reaction network theory (Turing, 1936)
`chi-squared.md`	Chi-squared goodness-of-fit and independence tests	χ² statistic / contingency tables
`lucidia.md`	The number-theoretic identity of Lucidia (88)	Number theory: totient, Möbius, Collatz, Goldbach
`inverse-reaction.md`	Every reaction has an opposite reaction (TNEG); Chargaff's rules and the Euler product follow	Balanced ternary algebra
`peano-derivative.md`	The derivative does not break Peano; Gödel proved a boundary, not a collapse	Meta-level analysis / QWERTY

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.