CRR FRAMEWORK
Coherence-Rupture-Regeneration dynamics governing
multi-scale temporal processes in this simulation.
§1 COHERENCE INTEGRAL
C(x,t) = ∫ L(x,τ) dτ
Coherence accumulates as the integral of local
activity L over time. Discrete implementation:
CRR.scale.C += CRR.scale.L
§2 RUPTURE DYNAMICS
δ(now) when C ≥ Ω
Scale-invariant "choice-moments" occur when
accumulated coherence reaches threshold Ω.
The Dirac delta marks ontological present.
if (CRR.scale.C >= CRR.scale.omega) {
CRR.scale.C = 0; // Reset
CRR.scale.rupture = 1; // Event
}
§3 REGENERATION
R = ∫ φ(x,τ) · exp(C/Ω) · Θ(...) dτ
Post-rupture regeneration with exponential
memory weighting. exp(C/Ω) determines
historical coherence accessibility.
→ Large Ω: all history weighted equally
→ Small Ω: peaked at highest coherence
§4 CROSS-SCALE CASCADE
Rupture at scale n drives coherence input
L at scale n+1 (regeneration coupling):
photon.rupture → molecular.L += 0.15
molecular.rupture → cluster.L += 0.25
cluster.rupture → surface.L += 0.35
surface.rupture → neural.L += 0.50
§5 Ω HIERARCHY
Threshold values increase with scale
(faster rupture at micro-scales):
Ω_photon0.8
Ω_molecular2.0
Ω_cluster5.0
Ω_surface12.0
Ω_neural30.0
Inter-scale ratio ≈ 2.5× (close to e ≈ 2.718)
§6 PHYSICAL OPTICS
n(λ) = A + B/λ²
Cauchy dispersion equation:
A1.3199
B0.00653 μm²
n_D (589nm)1.333
R = (R_s + R_p) / 2
Fresnel reflectance (unpolarized):
R_s = ((n₁cosθᵢ - n₂cosθₜ)/(n₁cosθᵢ + n₂cosθₜ))²
R_p = ((n₁cosθₜ - n₂cosθᵢ)/(n₁cosθₜ + n₂cosθᵢ))²
§7 MOLECULAR H₂O
H-O-H angle104.45°
H-bond cutoff0.35 (norm)
CoordinationTetrahedral
Clusters exhibit dynamic H-bond network
with Brownian motion + toroidal convection.
§8 COGNITIVE MAPPING
Optical → Neural pipeline:
Photon → Fresnel → Screen → Retina → V1
Neural/Photon Ω37.5×
Hierarchical depth~3.2 levels
log_π(Ω_neural/Ω_photon) ≈ 3.2
CRR Framework — A. Sabine (2024-2025)
cohere.org.uk