Coherence → Rupture → Regeneration

Canonical CRR — Rupture occurs when C = Ω

exp(C/Ω) = exp(1) = e AT RUPTURE
δ fires when C ≥ Ω  |  R = exp(C/Ω) · H(t-t_rupture)
C accumulates
R = e at rupture
δ when C=Ω
0.70 — rupture at 70%
1.0x
1.8
CANONICAL CRR DYNAMICS — RUPTURE AT C = Ω
Coherence approaching threshold: 0%
COHERENCE C
0.000
∫L(x,τ)dτ
THRESHOLD Ω
0.700
rupture point
RUPTURE δ
0
C ≥ Ω ?
exp(C/Ω)
1.000
→ e at rupture
C(t) = ∫₀ᵗ L(x,τ) dτ coherence accumulates
δ fires when C ≥ Ω Ω is the rupture threshold
At rupture: C = Ω → exp(C/Ω) = e Euler's number emerges!
R = exp(C/Ω) · H(t-t_rup) regeneration feeds next cycle
ENVELOPE: Ω CONTROLS RUPTURE POSITION

In canonical CRR, rupture is not arbitrary—it occurs precisely when coherence C reaches threshold Ω.

At the moment of rupture: C = Ω, therefore exp(C/Ω) = exp(1) = e ≈ 2.718

Ω regulates Markov blanket porosity:
Higher Ω → more porous, faster cycling, liquid boundaries
Lower Ω → more solid, slower, locked into priors

The Shepard illusion emerges because amplitude peaks just before C hits Ω,
then regeneration (weighted by e) seeds the next cycle seamlessly.