Quantum Structural Theory of Harmony (QSTH M.1) — Unit Hygiene and Alpha-I-Dim Audit: The Planck-Cosmic Coupling Identity

Abstract This publication presents QSTH M.1 as the first unit and scale audit of the M-independent horizon framework after QSTH 8.M.x and QSTH M.0. It does not claim a completed physical theory or empirical confirmation of an M-independent horizon. Its purpose is to test whether the first equation layer of the M-series survives dimensional analysis, algebraic rewriting, calibration logic, and explicit failure modes. The central result is the Planck-Cosmic Coupling Identity, which follows from defining Alpha-I-Dim as the dimensionless ratio between the Planck length and the cosmological Lambda-length. This yields the identityLambda * l_P^2 = 3 * alpha_I-Dim^2,showing that Alpha-I-Dim is not a freely added symbol but the square-root form of the same Planck-cosmic coupling that appears in the M-independent horizon skeleton. The publication then rewrites the M-independent horizon skeleton into the Alpha-I-Dim Horizon Closure Equation:alpha_I-Dim^2 * (S_eff / k_B) = pi * kappa(Gamma).This alpha-form is shown to be dimensionally clean provided that kappa(Gamma) remains a dimensionless topological-state label. A de Sitter calibration is also derived, givingalpha_I-Dim^2 * (S_Lambda / k_B) = pi,with kappa(Gamma)=1 and C_topo=3pi in the pure cosmological reference regime. After the M.5/Galois update, the document also clarifies that S_eff^H is no longer a free entropic correction: it has a legitimate candidate derivational path through epsilon_R, the ratio Omega_coh,R / Omega_red,R, and the Galois orbital sieve Pi, G, Orb, S/T/J. The empirical calibration of this construction remains open, but its internal computability has been constructively closed at the scaffold level. The publication distinguishes CORE mathematical identities from CAND physical interpretations and FUTURE operationalization. It concludes with a skeptical contract requiring unit hygiene, de Sitter calibration, Galois invariance, independent extraction of kappa(Gamma), and the possibility of failure. Description This record contains the English final version of QSTH M.1 — Unit Hygiene and Alpha-I-Dim Audit: The Planck-Cosmic Coupling Identity, a technical publication of the QSTH M-series following QSTH 8.M.x — Horizon Ledger of the Settled Structure and QSTH M.0 — M-Independent Horizon: Alpha Closure of the Horizon Ledger. The publication investigates whether the first equation skeleton of the M-independent horizon framework remains dimensionally clean and algebraically controlled when rewritten through Alpha-I-Dim. It establishes that Alpha-I-Dim is a dimensionless scale-coupling handle defined as lP/LΛl_P / L_\LambdalP/LΛ, and that the Planck-cosmic coupling can be rewritten as ΛlP2=3αI−Dim2\Lambda l_P^2 = 3\alpha_{I-Dim}^2ΛlP2=3αI−Dim2. The document includes: an Epistemic Note / Methodological Brake, the transition axis after QSTH 8.x / 8.M.x, the definition of Alpha-I-Dim and the cosmological Lambda-length, the Planck-Cosmic Coupling Identity, unit hygiene of the first identity, the original and Planckian forms of the M-independent skeleton, the Alpha-I-Dim Horizon Closure Equation, unit hygiene of the alpha equation, de Sitter entropic compensation and calibration, a numerical sanity check, a Galois brake for M.1, a distinction between what M.1 proves and does not prove, a Mini-Mendeleev audit, failure modes and a skeptical contract, an equation capsule, and a transition note toward QSTH M.2. 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. Its purpose is to establish a disciplined unit-clean scaffold for the Alpha-I-Dim / Planck-Cosmic Coupling layer of the M-series. Related work note This publication follows QSTH 8.M.x — Horizon Ledger of the Settled Structure and QSTH M.0 — M-Independent Horizon: Alpha Closure of the Horizon Ledger. It provides the first unit and scale audit of the M-independent horizon skeleton and prepares the transition toward QSTH M.2, which is intended as a source review of the older Horizon Set line, S_eff, R-Signature, C_topo, kappa(Gamma), Alpha-I-Dim, and the Galois Ledger. Plain-language summary This publication asks whether the first equation layer of the M-independent horizon framework is dimensionally clean. It shows that Alpha-I-Dim is not a decorative symbol, but the square-root form of the Planck-cosmic coupling between the Planck length and the cosmological Lambda-length. The result does not prove a completed physical theory, but it gives QSTH M.x a clean unit-tested scaffold for future horizon-ledger work. 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 unit-clean technical scaffold, candidate equations, calibration references, status separation, failure modes, and audit gates for future work. Subjects / categories Physics — Theoretical PhysicsMathematical PhysicsQuantum PhysicsCosmology and Nongalactic AstrophysicsInformation Theory