Quantum Structural Theory of Harmony (QSTH M.0) — M-Independent Horizon: Alpha Closure of the Horizon Ledger

Abstract This publication presents QSTH M.0 as the first technical step of the M-series following the public opening of QSTH 8.M.x — Horizon Ledger of the Settled Structure. It does not claim a completed physical theory or empirical confirmation of an M-independent horizon. Its purpose is to formulate the first precise technical question of the M-series: whether already settled structure may carry an invariant horizon account across scales, and whether such an account can be expressed through Planck-cosmic coupling, Alpha-I-Dim, effective horizon entropy, topological closure, and the candidate closure label kappa(Gamma). The document introduces three entry equations for the M.0 framework: the M-independent horizon skeleton, the Planck-Cosmic Coupling Identity, and the Alpha-I-Dim Horizon Closure Equation. These relations are treated as candidate structural scaffolds, not as confirmed physical laws. Their role is to define what may be computed, under which dimensional constraints, and under which audit gates a horizon closure label may be read. A central contribution of the publication is the interpretation of Alpha-I-Dim as a candidate scale-coupling root connecting the Planck and cosmological layers. The publication also incorporates the Galois Ledger as a methodological invariance layer: the horizon ledger does not see all microstate paths, but only those invariants that survive projection, rewrite redundancy, and orbit-based equivalence. The text defines a nine-node Horizon Set as a CAND / structural-search hypothesis, introduces a Mini-Mendeleev audit table for the main motifs, clarifies the status of the Bridge Note after the Galois update, and formulates explicit failure modes and a skeptical contract. The aim of QSTH M.0 is not to prove the M-independent horizon, but to establish the first disciplined technical closure scaffold for the Horizon Ledger branch. Description This record contains the English final version of QSTH M.0 — M-Independent Horizon: Alpha Closure of the Horizon Ledger, the first technical publication of the QSTH M-series after the public opening note QSTH 8.M.x — Horizon Ledger of the Settled Structure. The publication refines the first M-series question: whether a settled structure, after passing through record formation, settlement, Temporal Ledger readability, and Horizon Ledger framing, may carry an invariant horizon account that is not reducible solely to local mass M. The document includes: an Epistemic Note / Methodological Brake, the relation of M.0 to QSTH 8.XC and QSTH 8.M.x, the transition axis from O-Dim to M-independent closure, the core question of QSTH M.0, three entry equations for the M-independent horizon scaffold, Alpha-I-Dim as a candidate scale-coupling root, the Galois Ledger as an invariance layer, the nine-node Horizon Set working hypothesis, a Mini-Mendeleev audit table, the status of the Bridge Note after the Galois update, failure modes and a skeptical contract, a roadmap from M.0 toward M.Closure, and a short insertable summary. This publication should be read as a theoretical and methodological working paper. It does not claim empirical confirmation of QSTH or of an M-independent horizon. It defines a disciplined technical scaffold, audit language, and failure-sensitive roadmap for future work. Related work note This publication follows QSTH 8.M.x — Horizon Ledger of the Settled Structure, which opened the M-series as the horizon-scale audit branch after the closure of the QSTH 8.x condensation sequence. QSTH M.0 is the first technical publication inside that M-series. It should be read as a candidate technical scaffold and methodological entry point, not as empirical confirmation of a completed physical theory. Plain-language summary This publication asks whether already settled structure may carry an invariant horizon-scale account across physical regimes and scales. It introduces Alpha-I-Dim as a candidate scale-coupling root between the Planck and cosmological layers and uses the Galois Ledger as a formal way to distinguish what the horizon ledger truly sees from what remains only a microstate rewrite. Final Zenodo caveat This document is a theoretical and methodological working publication. It does not claim that QSTH is empirically confirmed, nor does it present the M-independent horizon as an established physical object. Its purpose is to define a disciplined technical scaffold, candidate equations, status separation, failure modes, and audit gates for future work.