Phinary stability core for sovereign domain algebra.
This repository formalizes the Fibonacci Contraction Theorem — a novel approach to the stability paradox in recursive domain systems using the golden ratio as a natural contraction attractor.
Standard contraction mappings require a factor q < 1. The Fibonacci sequence provides a natural basis (phinary / base-φ) in which the contraction-expansion duality is encoded directly into the number system. The ratio F(n+1)/F(n) → φ expresses this boundary.
apl/phinary.apl — Core computation in APL (Iverson notation)
lean/FibCore/ — Lean 4 formal theorems wrapping the APL core
docs/ — Specification artifacts
- APL — Kenneth Iverson's array language. The natural home of Fibonacci mathematics. Terse, symbolic, exact.
- Lean 4 — Formal verification layer. Every theorem machine-checked.
At the center of this system: are there infinitely many Fibonacci primes?
This is an unsolved problem in number theory. The phinary contraction theorem is well-defined regardless of the answer — but its deepest properties depend on it.
The phinary contraction factor κ = φ connects directly to the stability paradox in phase-invariant recursive transition models. Where standard PIRTM requires q < 1, the phinary basis reframes the question: in base-φ, what does "less than 1" mean?
The answer is not what you expect.
FCC-φ-∂-2026 — Ahmad Parr canonical. All derived work carries this mark.