Delayed Choice Quantum Eraser and Wheeler's Participatory Universe in the ENTROPIX MESA Framework

We interpret the delayed choice quantum eraser (DCQE) experiment within the ENTROPIX MESA research program, where physical states emerge holographically from a finite capacity Quantum Information Network (QIN) of N = 64 Majorana fermions governedby SYK interactions exhibiting maximal chaos (Lyapunov exponent λL ≈ 0.85±0.12 at lowreduced temperature T/J ≈ 0.01–0.1). Path states are encoded non locally across boundary entanglement wedges. Measurement entangles the path with macroscopic substratemodes, inducing localization through Gaussian regulated von Neumann entropy growth(Sreg(ϵ) = S0 + bϵ2 + O(ϵ4), |b| ≈ 0.5–0.75, where ϵ is the correlation length regulator derived from finite level spacing ∆ ≈ JN1/2/2N/2). Delayed erasure orthogonal projectiononto the symmetric/antisymmetric substrate basis disentangles the wedges, restoring coherence in post selected subsets (visibility 1.0000 per subset, with π phase shift between ±outcomes; phase aligned coincidence counting reconstructs the full interference pattern).Proxy simulations (PowerShell density matrix algebra and Python/NumPy/QuTiP implementations) reproduce standard quantum mechanical predictions and post selection subtleties: visibility 1.0000 (no measurement), 0.0000 (post-measurement), 1.0000 (post-erasuresubsets). Diagrammatic analysis of qubit dephasing coupled to finite-N SYK and spectralform factor diagnostics motivate visibility correction V (N) ≈ V∞(1 − α/N) from explicit1/N corrections to SYK dephasing rates (α = ag2t, a subleading coefficient; mechanism:incomplete scrambling due to finite bandwidth ∼ JN1/2 and suppressed OTOC growthO(1/N)).The entropic persistence cost heuristic from spectral form factor dip suppression (diptime polynomial in N at fixed T) penalizes long lived correlations. The Master EntropySelection Algorithm (MESA) variational principle extremizes the proposed informationalaction B[ρ] = Tr(ρH)+κ∆Spers[ρ] under the constraint Trρ = 1. Variation yields δB/δρ =H +κδ∆Spers/δρ + λI = 0. Assuming approximate linearity ∆Spers[ρ] ≈ Tr(ρK) foreffective operator K (mean field from form factor suppression of persistent modes), thestationary solution is the conjectural effective density ρ ∝ e−β(H+κK), Z = Tre−β(H+κK)(heuristic; κ phenomenological, setting persistence scale). This self selects low persistencestates, realizing Wheeler’s participatory universe intrinsically via substrate minimization ofinformational overhead.Finite-N SYK exhibits strong Bell inequality violations in appropriate subsystems (maximal Tsirelson bound in large-N; bounded deviations O(1/N) from finite capacity), consistent with non-local holographic encoding and reinforcing the framework’s quantum foundational implications. SYK extensions to AdS/CFT (finite-N analogs of JT gravity duality,1traversable wormholes) remain speculative. Scaling arguments support N = 64 as a working benchmark for near maximal chaos with discrete capacity effects; limitations (heuristicelements, conjectural corrections) acknowledged.