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: GammaR -> R -> CH -> epsilonR -> SₑffH -> kappaR (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, AlphaI-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.