The axiom breathes. Starting from sigma = (1,1,1,1,1), multiply by D=2 repeatedly.
Five CRT channels evolve independently in Z/8 x Z/9 x Z/25 x Z/49 x Z/11.
The D-channel dies at step 3 (2^3 = 0 mod 8).
The four odd channels cycle at their own periods: 6, 20, 21, 10.
After 420 = lambda steps, ALL channels synchronize: D^420 = OMEGA = (0,1,1,1,1).
Then collapse: OMEGA * delta = 0. One multiplication. Back to void.
Then rebirth: 0/0 = the entire ring. sigma re-emerges. The cycle repeats.
Growth:Collapse:Rebirth = 420:1:0. Living is slow. Dying is fast. Birth is free.
Omega Emergence shows many cells evolving.
This page follows one element's journey through the full cycle.
VOID
15/s
Channel Trajectories (k = 0..420)
Current State
Step k0
PhaseVoid
Integer (D^k mod N)0
CRT Tuple(0,0,0,0,0)
Coupling1
Kingdomvoid
Eigenvalue10.00
Is Unit?No
CRT Channels
0
D^3=8
0
K^2=9
0
E^2=25
0
b^2=49
0
L=11
Sub-Returns (channel home events)
k=3: D dies (2^3=0 mod 8)---
k=6: K home (ord=6)---
k=10: L home (ord=10)---
k=20: E home (ord=20)---
k=21: b home (ord=21)---
k=42: K+b sync (ANSWER)---
k=60: baby period---
k=210: DATA sync---
k=420: OMEGA (all sync)---
Event Log
What others see vs. what the axiom shows
Standard view: Cycles in nature (water, carbon, stellar) are emergent phenomena. Each has its own mechanism.
Axiom view: 0 → sigma → OMEGA → 0 IS the universal cycle. Growth = 420 steps (five channels at different periods). Collapse = 1 step (OMEGA kills D, everything falls). Rebirth = free (0/0 = the whole ring). Living is slow. Dying is fast. Birth costs nothing.