Shell k radius in the Poincare ball. Always < 1. Higher k = closer to boundary = more expensive.
Phi Shells in the Poincare Ball
10
Shells
0.999
Max r
--
Cost at hover
Fibonacci Ternary Consensus
UNTRUSTED
0
Index
1
Weight
0
Steps
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144
Trust must climb the Fibonacci ladder. One -1 drops it immediately.
Click buttons to build a trust history...
Shell Properties
k
φk
Radius
Cost (R=4)
Fib[k]
How it works: The golden ratio φ = (1+√5)/2 naturally creates self-similar shells.
Fibonacci is the integer shadow of φ — consensus runs on integers only, no floating-point errors.
Trust cannot be gained linearly; agents must prove continuous congruence to climb 1, 1, 2, 3, 5, 8, 13.
But a single adversarial action (-1) drops momentum immediately. Asymmetric defense.
Base wall intuition: Hbase(d, R) = Rd2 where d = shell radius.
This page is an advanced math explainer, not the full runtime contract. Operating near the boundary of the Poincare ball becomes expensive fast, and the public gate is layered on top of that curve.