The Shaka-Zeta-L∞P Framework: Exact Arithmetic Quantization via Hard-Core Boson Fock Spaces

Executive Summary For 160 years, spectral approaches to the Riemann Hypothesis have encountered insurmountable topological obstructions. This monograph demonstrates exactly why these historical approaches failed and provides the rigorous mathematical resolution. The Obstructions Resolved: • The Continuous Failure: We prove that continuous models (Galerkin projections onto Laguerre bases) fail due to an exponential condition number divergence, causing inevitable systematic spectral misalignments. • The Fermionic Obstruction: We demonstrate that mapping primes to free fermions introduces parasitic Jordan-Wigner phase strings that fatally corrupt the Möbius function combinatorics. The Exact Solution: We establish a rigorous, non-approximated isomorphism between multiplicative arithmetic and the Fock space of Hard-Core Bosons (HCB). The local nilpotence of HCBs enforces the square-free constraint, while their global commutativity eliminates the phase string obstruction. Validation: The HCB quantum transfer operator is formalized using C*-algebra theory and reproduces the Möbius Dirichlet series exactly. This isomorphism is validated computationally to absolute IEEE-754 machine precision (relative error 1. 72 x 10^-15) across Fock spaces up to 4096 dimensions. This Record Contains: The Complete Theoretical Monograph (PDF): Full functional-analytic proofs, UHF algebra formalization, and numerical validation data. Interactive HCB Simulator (HTML): A standalone, browser-based laboratory. It allows reviewers to instantly visualize the topological obstruction of continuous models and verify the 10^-15 machine precision error of the Hard-Core Boson transfer operator in real-time. No installation required (runs locally in any modern web browser). Autonomous Python Source Code: Embedded directly within the manuscript appendix for immediate peer-review and absolute reproducibility.