CRR EquationsActive
C(x,t) = ∫0t L(x,τ) dτ
δ(now) when C ≥ Ω
R[χ](x,t) = ∫ φ(x,τ)·exp(C/Ω)·Θ(t−τ) dτ
Ω = 1/π = σ² (variance = inverse precision)
CV = Ω/2 ≈ 0.159 (Z₂ prediction)
exp(C/Ω) → memory weighting at C=Ω: e ≈ 2.718
CRR formalises how systems accumulate history (Coherence), undergo discrete phase
transitions when constraints reach threshold (Rupture), and reconstitute through
exponentially-weighted memory selection (Regeneration). The exp(C/Ω)
term is the key: it determines which past moments are accessible during regeneration.
Low Ω → peaked weighting (only highest-coherence moments), creating rigidity.
High Ω → flat weighting (all history accessible), enabling transformation.
EEG Bands
Cross-frequency coupling: prefrontal theta (4–8 Hz) modulates visual and
cerebellar gamma (30+ Hz). In CRR terms, slower cortical rhythms provide the
Ω envelope within which faster oscillations undergo their own C→δ→R micro-cycles.
The cortical hierarchy scales by π per level.
Coherence C(t)
When C reaches Ω, the Markov blanket is saturated — the current boundary
configuration can no longer absorb perturbation. exp(C/Ω) = e ≈ 2.718
at the rupture threshold. This value appears identically in black hole physics
and neural hierarchical gain across 40 orders of magnitude.