EnGeΛ: Entangled Geometry Λ - Topological Fractal Memory of the Universe

Six observational anomalies—JWST's early massive galaxies, periodic tidal disruption events, quasar spin alignments across gigaparsec scales, Earth's 8.5-year inner core oscillation, TNO orbital clustering, and the NANOGrav monopolar signal (5.2σ)—only appear unrelated. We show they share a common origin. The EnGeΛ framework (Entangled Geometry Λ) identifies a topological coherence field characterized by two parameters: η ≈ 0.32, coinciding with the 3D percolation threshold, and K_real ≈ 0.46 Mpc/yr, matching the ratio Ω_m/Ω_Λ to within 0.2%. These values emerge independently from cosmological integration, planetary seismology, pulsar timing arrays, biological rhythm compression, molecular topology, and quantum constants—spanning over 60 orders of magnitude. The correspondence (1−η) ≈ Ω_Λ ≈ 0.68 suggests dark energy represents coherence entropy rather than exotic physics. Key results include: The "impossible" star formation efficiency of JWST Red Monsters (ε ~ 0.3–0.5) falls precisely within the η-resonance window. The NANOGrav monopole period (T ≈ 8 yr) matches the prediction T_PTA = T_ENSO/η with 91.8% agreement (Monte Carlo, N=10,000). The framework predicts a "Golden Window" (η ≈ 0.618) for abiogenesis, consistent with Early Earth's rotational dynamics and the geometric frustration of water. We provide falsifiable predictions with explicit thresholds, testable via Euclid, LSST, SKA, and CMB-S4 within the next decade.