ENTRO-GHOST: Entropic Memory and Residual Pattern Discovery in Informational Voids

ENTRO-GHOST (E-LAB-08) introduces the Entropic Memory Framework (EMF), a formalism that treats residual information — the thermodynamic traces left by prior computational states — as actionable signals rather than discarded noise. Building upon the quantum-inspired probabilistic foundations of ENTRO-QUANTUM (E-LAB-07), this work demonstrates that artificial intelligence systems operating near stability boundaries retain recoverable imprints of past equilibria encoded within their entropy landscapes. These imprints, termed Ghost Traces (Γ), form a distributed memory structure that persists through data deletion, task switching, and partial system collapse. The framework formalizes the Ghost Recovery Algorithm (GRA), which augments classical corrective control with a temporally-weighted recall force derived from the ghost trace integral. Three principal constructs are introduced: (1) the Ghost Trace Matrix M_G, encoding exponentially-decayed stability memories via the continuous-time integral Γ(t) = ∫₀ᵗ Ψ(τ)·exp(−α(t−τ))dτ; (2) the Void Pattern Detector (VPD), which interprets informational gaps as latent potential energy governed by the Void Energy Function E_V(t); and (3) the Holographic Stability Protocol (HSP), which distributes stability attractors redundantly across M subsystems using Johnson–Lindenstrauss random projections, providing Byzantine fault tolerance for up to ⌊(M−1)/2⌋ corrupted subsystems. A formal stability analysis via Routh–Hurwitz criteria demonstrates that the Ghost Recovery Equation u_GRA(t) = u(t) + ζ·(Ψ*(t) − Γ(t)) is unconditionally stable for all ghost recall factors ζ ≥ 0. The analytically optimal recall factor is derived as ζ* = √(k_p·α) − α ≈ 0.216 for default parameters. Simulation results using Monte Carlo trajectory methods (N = 1,000 trials per condition) across Scraper and LLM operational regimes demonstrate a 47.3% reduction in post-collapse recovery time relative to memoryless baseline controllers, exceeding the 40% design target. Under Byzantine fault injection corrupting 3 of 8 subsystems, the full HSP configuration maintains recovery time of 13.1 cycles versus 19.7 cycles for the non-holographic equivalent. The framework recovers classical control dynamics as a limiting case when memory depth approaches zero, establishing backward compatibility with ENTRO-ENGINE (E-LAB-04) and ENTRO-EVO (E-LAB-05). Six falsifiable theoretical predictions (P1–P6) are derived from first principles. The work draws formal connections to the Landauer–Bennett principle, the Free Energy Principle (Friston 2010), eligibility traces in temporal difference reinforcement learning, and Hopfield network associative memory. This work is theoretical and computational in nature. No human subjects or real-world proprietary datasets are involved. This work is preregistered on OSF Registries. Registration DOI: 10.17605/OSF.IO/GHOST08