Quantum Structural Theory of Harmony (QSTH M.x) — Horizon Ledger of the Settled Structure: From Horizon Invariants to the Microstate Ledger of Structure

Abstract This publication opens the QSTH 8.M.x / M.x branch as a horizon-scale continuation of the closed QSTH 8.x condensation sequence. It does not present QSTH as a completed physical theory; rather, it defines an audit-oriented roadmap for investigating whether already settled structure can carry an invariant horizon-scale account across regimes and scales. The document introduces the Horizon Ledger of the Settled Structure as a structured framework connecting the Condensation Branch, which creates record-bearing structure, with the Ledger Branch, which reads and audits that record. The central computational backbone is expressed as a staged sequence from regime definition and horizon admissibility to effective horizon entropy and the closure label:Gamma_R -> R -> C_H -> epsilon_R -> S_eff^H -> kappa_R(Gamma). A key addition is the integration of the Galois Ledger as an older formal module of QSTH. In this reading, the horizon is treated as a projection from microstates to ledger invariants, redundancy is represented as a rewrite group, and entropy is interpreted through orbit size. This provides a formal sieve for distinguishing genuine changes in the horizon account from mere rewrites of microstate representation. The publication defines the roles of M.0 through M.Closure, introduces four main layers of the M.x branch — Horizon Ledger, Horizon Sudoku, Microstate Ledger, and Galois Invariance Layer — and formulates a skeptical contract with explicit failure modes, status separation, and INCONCLUSIVE outcomes. The aim is not to prove an M-independent horizon, but to create a disciplined publication space in which the question can be pursued safely, layer by layer. Description This record contains the English final version of QSTH 8.M.x — Horizon Ledger of the Settled Structure, an opening note and roadmap for the M-series of the Quantum Structural Theory of Harmony. The document follows the closure of the QSTH 8.x condensation sequence and prepares the transition toward Horizon Set II. It frames M.x as the horizon-scale audit of already settled structure, rather than as an isolated equation or premature physical claim. The publication includes: an Epistemic Note / Methodological Brake, the transition backbone from QSTH 8.x to M.x, the architectural split between Condensation Branch and Ledger Branch, Alpha_I-Dim as a candidate bridge parameter, the main computational backbone of M.x, the Galois Ledger as a formal invariance layer, the impact of Galois projection, rewrite redundancy, and orbit size on the M.x framework, the Universal Admission Principle, the Planck Lamp / Planck Sun readability motif, the roadmap from M.0 to M.Closure, the four main layers of M.x, the skeptical contract and failure modes, stability and geometric instruments for future M.Closure, and a short insertable summary. Related work note This publication follows the QSTH 8.XC closure note of the 8.x condensation sequence and opens the M.x / Horizon Set II branch. It should be read as a roadmap and methodological entry point, not as an empirical confirmation of a completed physical theory. Plain-language summary This publication opens a new QSTH branch asking whether already settled structure may carry a horizon-scale ledger: an invariant account readable across scales. It connects the earlier 8.x condensation sequence with a new M.x audit framework and introduces the Galois Ledger as a formal way to distinguish what the ledger truly sees from what remains only a microstate rewrite. Final Zenodo note / caveat This document is a theoretical and methodological working publication. It does not claim empirical confirmation of QSTH, nor does it present the M-independent horizon as an established physical object. Its purpose is to define a disciplined roadmap, computational backbone, failure modes, and audit gates for future work.