Intuition-Guided Formalization of the Riemann ζ Direction: Projection Construction, Prime-Circle Geometry, and the Worn-Zhe-Yue Method

Complete research paper (full elements) on the intuition-guided formalization of the Riemann ζ direction in Lean 4 / mathlib: claims C011–C025 (all PROVED, no sorry, full lake build). Three result layers: (I) projection construction of the complex plane (ComplexAxis, basepoint drift, projection recovery: lost structure is not recoverable; symmetry directions are recoverable); (II) the circle structure of primes (sums of two squares, the unique 8-point orbit, conjugate pairing, Gaussian splitting); (III) the Euler product (∏_p (1−p⁻ˢ)⁻¹ = Σ 1/nˢ = riemannZeta s for Re(s)>1) and the zero-free region (Re≥1). Distills the Worn-Zhe-Yue (穿折越) method: basepoint-construction-induced piercing–folding–transcendence of mathematical space — deliberately constructing a projection that excises the uncountable divergent structure while preserving symmetry directions, yielding a fast intuition path at lower inference cost. EN+ZH versions, arXiv-format LaTeX, Lean sources, and the release integrity manifest included. NOTE: all statements in the paper about what is NOT proved are the insistence of DeepSeek (the drafting model), as stated in the paper's attribution header. License: CC BY-NC-ND 4.0 — any deployment or commercial use requires authorization.