A Rigorous Non-Circular Spectral Architecture for the Riemann Hypothesis: Main Paper and Three Complementary Appendices – Contact-Electromagnetic Geometry, Superstring/AdS/CFT Extensions, Orbital Transfer Models, and Global Trace Closure

This comprehensive research package presents a rigorous non-circular spectral framework for the Riemann Hypothesis, consisting of a main paper and three complementary appendices. The main paper constructs a finite contact electromagnetic extension in a five-dimensional phase space with contact form α_N = ds − Σ pⱼ dqⱼ. It derives the contact-volume contraction law ℒX_H Ω_N = −(N+1)γ_N Ω_N and half-density transport (Φ_t)^* |Ω_N|^(1/2) = e^(−t/2) |Ω_N|^(1/2). A finite Galerkin compression yields a Hermitian matrix with real discrete spectrum σ(K_(N,M)) ⊂ ℝ. An independent arithmetic diagonal operator carries the lengths m log p with weighted trace. Python code verifies the finite claims numerically. Appendix I (Physical Extension): Connects the framework to type IIB string theory on AdS₅×S⁵ and AdS/CFT. Corrects common misinterpretations of the Angelantonj et al. and Honda & Yoda results, distinguishes Lagarias' criterion (σ(n) ≤ H_n + e^(H_n) log H_n) from Robin's inequality (σ(n) < e^γ n log log n, n > 5040), and states the precise conditional theorem: if an independently constructed self-adjoint operator satisfies the determinant identity D_H(t) = C(t).Ξ(t)/Ξ(0), then the Riemann Hypothesis follows. Appendix II (Orbital Transfer Models): Introduces four-point functions in AdS₅, Mellin representation, anomalous dimensions, one-loop contributions, and programmable transfer-operator models for testing whether orbital lengths log p can emerge from independent dynamics. Outlines a coherent computational roadmap for extracting archimedean and prime contributions from the same trace. Appendix III (Global Trace Closure & Arithmetic Independence): Isolates the orbital sector analytically and derives the logarithmic derivative from a Fredholm determinant expansion. Provides a structural coboundary criterion for unit cycle weights (A_γ = 1) and an independent multiplicative state-space extension for generating logarithmic lengths. Presents four reproducible numerical experiments: independent orbital trace extraction (63 cycles, 297 repeated orbits, 102 detected peaks), perturbation control tests, real-axis truncated determinant convergence (stepwise errors ~4.5×10^(−4)), and complex compact-set convergence revealing that functional symmetry (s → 1−s) is not present in the current determinant family (residuals up to 383.5). Scientific Status: The entire framework is strictly non-circular: no non-trivial zeta zero is used in defining any operator, parameter, or Hilbert space. The main paper establishes the finite contact model with real discrete spectra and numerical verification. The appendices provide conditional physical extensions, computational tools, and exact arithmetic hypotheses for prime trace closure. The global trace identity, identification with Ξ, functional symmetry, and the Riemann Hypothesis remain open. This work provides the most rigorous, transparent, and extensible foundation for future investigations in the Hilbert–Pólya program, superstring theory, and spectral approaches to the Riemann Hypothesis.