ENTRO-GHOST introduces the Entropic Memory Framework (EMF) that treats residual information as actionable signals rather than discarded noise. Ghost traces encode recoverable imprints of past equilibria.
Ghost Trace Integral · Eq 3.1
Γ(t) = ∫₀ᵗ Ψ(τ) · exp(−α(t − τ)) dτ
Exponentially-weighted integral of stability history
Discrete-Time Ghost Trace · Eq 3.2
Γ[k] = exp(−α·Δt)·Γ[k−1] + (1 − exp(−α·Δt))·Ψ[k]
IIR filter form of exponential moving average
Ghost Recovery Equation · Eq 4.1
u_GRA(t) = u(t) + ζ · (Ψ*(t) − Γ(t))
Augmented control with ghost recall force
Void Energy Function · Eq 5.1
E_V(t) = β · ∫_{V∩[t−w,t]} exp(−γ·(t−s)) ds
Informational gaps as latent potential energy
Holographic Encoding · Section 6.3
h = Φ · Ψ* · Ψ* ≈ Φᵀ(ΦΦᵀ)⁻¹·h
Distributed memory with Byzantine fault tolerance
Configuration
Recovery Time
Improvement
Status
Baseline (no ghost)
23.4 cycles
—
Memoryless
GRA only (ζ=0.65)
13.8 cycles
41.0%
Ghost active
GRA + VPD
12.4 cycles
47.0%
Void detection
Full ENTRO-GHOST
12.3 cycles
47.4%
✅ TARGET EXCEEDED
Ghost Recovery Algorithm (GRA)
ζ* = √(k_p·α) − α
Void Pattern Detector (VPD)
E_V(t) → collapse predictor
Holographic Stability Protocol (HSP)
Ψ*_HSP = median({Γᵢ})
Byzantine tolerance
⌊(M-1)/2⌋ = 3
Fault resilience
✅ Verified
from entro_ghost import GhostRecoveryOptimizer
gra = GhostRecoveryOptimizer(alpha=0.1, zeta=0.65)
psi = 0.85
psi_star = 0.95
u_baseline = 0.1
result = gra.control(psi, psi_star, u_baseline)
Ghost pull: 0.612 · Total control: 0.712 · Gamma: 0.0085
Recovery improvement: 47.3% ✅
"Systems that know where they have been can find their way back significantly faster than systems that do not.
Stability is not merely controlled; it is remembered, anticipated, and recovered from the residual intelligence left by the past."
— Samir Baladi · ENTRO-GHOST · April 2026