Arithmetic Shadow of κ: Primorial Selection of the Mod-30 Sector-Weight Partition Ratio

v2 update (April 7, 2026): Added supplementary computation: TCP energy-scale sweep across 52 known particles using E_bind(τ) = τ·(1-κ(τ))²·r̄·E₀. Contents of supplementary_grand_sweep.zip:- 5-mode Grand Sweep (τ×E₀ 2D, primorial comparison, Riemann zero crossings, energy gap analysis, neutrino regime)- Computation engine (Python/OpenCL, 1409 lines)- Raw CSV outputs (6 files) and JSON summaries- Full reproduction in < 1 second Key results:- 36/36 particles matched within 3% (E₀=100 GeV fixed)- 52/52 with E₀ as variable- 4 particles (W, Z, Higgs, top) double-confirmed at TCP-MF crossing points- 15 energy desert regions identified #--------------------------------------------------------------------------------------------------This repository contains the manuscript, figures, and supporting data for: "Arithmetic Shadow of κ: Primorial Selection of the Mod-30 Sector-Weight Partition Ratio" We investigate the arithmetic structure underlying the observed partition ratio κ ≈ 0.8509 using the primorial ring spectrum of reduced residues modulo primorial numbers. A sector-weighted observable R(τ), defined from sector sizes and the exponent n(τ)=ln(3/2)/τ, reproduces the observed partition ratio at the independently established scale parameter τ* = 0.145 with minimal deviation for mod 30. An extended primorial ladder test across m ∈ {6, 30, 210, 2310, 30030} shows that mod 30 uniquely approaches the distinguished point (τ*, κ), followed by monotonic divergence along higher primorial layers. Null tests further indicate that the effect depends on sector geometry rather than residue counting alone. This upload includes the LaTeX source, rendered figures, computation code, and numerical data tables used in the manuscript. #-------------A Korean version of the manuscript (PDF) is also included in this repository.이 논문에는 한글 버전 PDF 파일도 함께 게시되어 있습니다.