the Lucas–Fibonacci identity — L(n)² − 5·F(n)² = 4·(−1)ⁿ, and L(n) = F(n−1) + F(n+1): the Lucas numbers (2, 1, 3, 4, 7, …) and the Fibonacci numbers satisfy L(n) = F(n−1) + F(n+1), and their squares obey L(n)² − 5·F(n)² = 4·(−1)ⁿ — a discrete conservation law. Verified exhaustively for n up to 30. Decidable
ab3e7c0b-4a21-8c31-a6a2-23155325ebb2Type anything and watch its uuidna recompute — deterministic, reproducible by anyone, no key. A theorem is alive when you interact with it. A content-address proves integrity, not truth. 0/7.
- theorem key ·
lucas_fibonacci_identity - content-address (receipt) ·
a9113a59-d43d-8d6d-8c43-c23b4952d777 - status · decidable, re-verified on every build — recomputes from
src/
The 7D rosetta-ray vortex is plotted from this theorem's microdata (its content-address); the slowly rotating hero background is computed from its seven surrounding theorems' hues — the mesh, seen locally, in analog rotation of dimensions. Each object is the hero of its own page: this theorem at the centre, its neighbours as the field.
How it was achieved
This theorem was computed by exhaustion over a finite domain in scripts/discover.ts — a test: () => boolean that runs to completion, holding by full enumeration. It was gate-checked (its name and content hold the honesty floor — no over-reach), receipted and chained append-only, and it is re-verified on every build: if it ever stopped holding, the build would fail, not production. That is what achieved means here — not asserted, but recomputable.
One leaf of the chained ledger: all theorems · computed results · the guide · the source formula. The repo and the site cross-link both ways — this hero page points back to the formula that recomputes it. Verify by cloning and running npm run lean-claims. A content-address proves integrity, not truth. entails → 0/7.