Zₜ = log(1 + Eₜ)
ZEOZO — The Canonical Formula of Living Entropy
Every age has its formula.
For geometry, it is y = mx + c — the line that still defines space.
With ZEOZO, that line is redefined — bounded, damped, alive.
It is still the slope, but now an entropy-aware core.
A living canonical: universal, stable, zero-centric.
Entropy is no longer chaos — with ZEOZO, it speaks as signal.
A measure that rises with drift and falls with recovery.
A compass that works the same across every domain.
In earthquakes, it warns before rupture.
In AI and telecom, it steadies signals before collapse.
In medicine, it reveals anomalies before they turn critical.
In ZEOZO, zero is not zero, and center is not center.
Edge zero is not ground zero, and edge center is not mid center.
Traditional science waits to measure the edge of change.
ZEOZO captures the drift much earlier, before it becomes visible.
This early signal opens a path to alignment and stability.
And it condenses into a single line of clarity.
Zₜ = log(1 + Eₜ) — an early signal, bounded and alive.
Try it yourself
You don’t need a lab or a dataset to feel the difference.
Copy the script below, save it as zeozo_demo.py, and run with Python.
It will compare three views of the same sequence:
- a straight line (y = mx + c)
- Shannon entropy
- ZEOZO (Zₜ = log(1 + Eₜ))
import math, numpy as np
def zeozo(x, lam=0.1, eps=1e-6):
E = 0.0
Z = []
for xi in x:
y = (xi - np.median(x)) / max(np.median(np.abs(x - np.median(x))), eps)
E = (1 - lam) * E + lam * (y ** 2)
Z.append(math.log(1 + E))
return Z
def shannon_entropy(x, base="e"):
n = len(x)
if n == 0:
return 0.0
probs = [1/n] * n # uniform example
if base == "e":
logf = math.log
elif base == "2":
logf = lambda v: math.log(v, 2)
elif base == "10":
logf = lambda v: math.log(v, 10)
else:
raise ValueError("base must be 'e', '2', or '10'")
return -sum(p * logf(p) for p in probs if p > 0.0)
# Example run
x = np.linspace(0, 50, 200) # input series
line = 2 * x + 5 # classic y = mx + c
entropy = shannon_entropy(x) # Shannon entropy (uniform)
zeozo_vals = zeozo(line)
print("Line sample (y=mx+c):", line[:5])
print("Shannon entropy (uniform):", entropy)
print("ZEOZO first 5 values:", zeozo_vals[:5])
Reading the results:
Run the script, and three truths stand clear.
The line, y = mx + c, climbs without limit.
Shannon entropy stays flat, speaking only once.
ZEOZO moves alive, step by step, rising then steadying.
From this simple form, Zₜ = log(1 + Eₜ), a revolution begins.
ZEOZO: A Revolution Across Domains
ZEOZO is proof that simplicity can transform science.
In earthquakes, it speaks days before rupture with clear warning.
In storms and snow, it lifts forecasts by more than twenty percent.
In telecom, it steadies networks hundreds of milliseconds earlier.
In medicine, it reveals hidden anomalies before they surface.
In geometry and design, it uncovers patterns invisible to lines.
Zₜ = log(1 + Eₜ), reshaping entropy across domains.
Explore New Canonical Entropy Formula
ZEOZO-Core
https://github.com/OMPSHUNYAYA/ZEOZO/blob/main/GETTING_STARTED.md
y = m x + c, redefined
Explore Shunyaya Projects:
Introduction to Shunyaya Framework
https://github.com/OMPSHUNYAYA/Shunyaya-Symbolic-Mathematics-Master-Docs
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Disclaimer
Observation-only; not for safety-critical decisions.
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