Information Conservation in Recursive Systems: The -1/12 Regularization Mechanism

We establish a comprehensive theory of information conservation in infinite recursive systems, with particular focus on the -1/12 regularization mechanism derived from Riemann zeta function analytical continuation. Building upon our previous work on ZkT tensor representations and observer-based computation, we demonstrate that stable infinite-dimensional systems require negative information compensation to prevent divergence. Key theoretical contributions include: (1) rigorous proof of the fundamental information conservation law Itotal = I++I−+I0 = 1 for all recursive systems; (2) mathematical derivation of the -1/12 compensation mechanism through zeta function regularization ζ(−1) = − 1/12 ; (3) demonstration that negative information acts as "computational dark matter" stabilizing infinite algorithmic processes; (4) establishment of holographic information encoding principles enabling finite boundary storage of infinite system states; (5) proof of information conservation under observer dynamics and k-bonacci evolution; (6) connection to quantum field theory renormalization and cosmological constant problems; (7) practical algorithms for implementing regularized computation in finite systems. We prove that the -1/12 mechanism is not merely mathematical convenience but an ontological necessity for stable infinite computation. These results provide the theoretical foundation for understanding how infinite complexity can emerge from finite resources while maintaining mathematical consistency.