Φ
RUNNING LIVE IN YOUR BROWSER

The Experiments

Not screenshots — real computation. Every experiment below runs the actual NUMEN mathematics on your machine, right now. Move a slider, type a word, watch it converge to φ⁻¹.

EXPERIMENT 01 · CGOS 6D

CGOS Coherence Calculator

The master formula. Set the six cognitive dimensions and watch the geometric mean resolve into a live coherence score and gate state. The gold marker is the golden-ratio convergence target φ⁻¹.

πNecessity0.720
φEfficiency0.618
ΩComplexity0.550
τTiming0.660
ψBatching0.600
βBenefit0.700

C = (π × φ × Ω × τ × ψ × β)1/6

0.638625
AAttune

TARGET φ⁻¹

0.618034

DISTANCE

0.020591

gold marker = φ⁻¹ convergence target

EXPERIMENT 02 · BANACH

Phi Convergence Simulator

A contraction map has exactly one fixed point, and every starting value is pulled toward it. Pick any seed and run it — the iteration collapses onto φ⁻¹ = 0.618033 within a handful of steps.

xn+1 = 1 / (1 + xn)   →   φ⁻¹ = 0.618033…   (a Banach contraction — every seed converges)
1.00

ITERATION

0

VALUE

1.000000

ERROR

3.82e-1

EXPERIMENT 03 · GTAC

Quaternary Encoder

NUMEN encodes everything in four gates — Growth, Transcend, Attune, Converge — chosen by each symbol's phi-value. Type anything and watch it become quaternary code in real time.

CT0.41
oA0.60
hG0.28
eT0.42
rT0.46
eT0.42
nC0.98
cG0.19
eT0.42
mG0.37
eT0.42
aC0.95
sG0.07
uG0.31
rT0.46
eT0.42
dC0.80
5
G · Growth
8
T · Transcend
1
A · Attune
3
C · Converge
0.469
mean φ
EXPERIMENT 04 · RESONANCE

Prime Resonance Garden

Plant thousands of nodes on the golden angle 137.508° and let the prime indices light up. This is how NUMEN lays out phi-addressed memory so nothing collides.

600

ANGLE

137.508°

PRIMES

109

GROWN

0

Gold = prime index · blue = composite. Planted on the golden angle so nothing ever overlaps — the same rule sunflowers use.

EXPERIMENT 05 · FIBONACCI

The Golden Ratio, Derived

Where φ⁻¹ comes from. Consecutive Fibonacci ratios march straight onto the same convergence target every other experiment shares.

12final error 3.15e-6
Fn₋₁ / Fnratioconvergence
1 / 20.500000
2 / 30.666667
3 / 50.600000
5 / 80.625000
8 / 130.615385
13 / 210.619048
21 / 340.617647
34 / 550.618182
55 / 890.617978
89 / 1440.618056
144 / 2330.618026
233 / 3770.618037

Consecutive Fibonacci ratios fall straight onto φ⁻¹ = 0.618033… — the same target CGOS converges to.