Quantum Structural Theory of Harmony (QSTH M.4) — κ_R(Γ): Topological-State Seal of Horizon Closure

This publication continues the QSTH M.x Horizon Ledger Series by introducing κ_R(Γ) as a candidate topological-state closure label for audited horizon configurations. Rather than treating κ as a freely adjustable residual, M.4 proposes that it may only be interpreted after an independent horizon configuration Γ_R has been established and successfully passed the methodological audit called Horizon Sudoku. The work develops the distinction between: horizon regime (R-signature), horizon configuration (Γ_R), ledger balance (B_R), effective horizon entropy (S_eff^H), and the candidate closure seal κ_R(Γ). The publication introduces the concepts of: Horizon Configuration Γ_R, Horizon Closure Condition C_H(Γ), Horizon Sudoku, Planck Lamp, Sackur–Tetrode Lamp, candidate statistical scaffold ε_R, regime-readable closure. Throughout the paper, methodological guardrails are emphasized. The de Sitter value κ_Λ = 1 is treated solely as a calibration reference and not as a universal physical law. The publication does not claim the discovery of a new physical constant. Instead, it proposes a structured audit framework specifying when a closure label may become physically meaningful. Within the architecture of the M.x series, M.4 represents the transition from symbolic algebraic expressions toward auditable structural readout. Related Works QSTH M.0 QSTH M.1 QSTH M.2 QSTH M.3 QSTH M.5 (prepared) QSTH M.6 (prepared) QSTH M.7 (prepared) QSTH M.Closure (prepared) Communities Quantum Physics General Relativity and Quantum Cosmology (gr-qc) Mathematical Physics Theoretical Physics Information Theory