Quantum Structural Theory of Harmony (QSTH 6.11) — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J

QSTH Publication 6. 11 introduces The Galois Ledger: a formal, audit-first module that treats a horizon/interface as a projection of microstates onto ledger invariants. Instead of chasing micro-detail directly, QSTH identifies a redundancy group (gauge rewrites) that preserves what the ledger can observe. In this framing, reduction entropy corresponds to orbit degeneracy (how many microstates are ledger-indistinguishable), while coherence appears as a structural constraint that limits orbit size. Core claim (LOCKED): Horizon = projection Π, G = rewrite redundancy; entropy = orbit size; coherence = orbit constraint. The paper provides a compact dictionary (Π: Ω → 𝓛, G, Orb (ω) ) and defines three operational interface signatures: S (spectral signature), T (topological signature), and J (flux signature), including a coherence ratio R = Jcoh / (Jcoh + Jᵣed + ε). To keep the framework testable, 6. 11 adds an audit classification layer called EADO, combining MODE (CANON/CAND) with evidence state (EMPTY/PARTIAL/FILL) and explicit triggers (spectral drift, topology change, flux shock with coherence drop). A Verification Map specifies PASS/FAIL/INCONCLUSIVE rules and requires pre-declared thresholds calibrated against noise/pipeline artifacts. The appendices include EADO pseudocode (Algorithms 1/1a/1b) and an EADO Quick Protocol (decision tree) for practical logging and reproducible evaluation. Status: EN CORE (clean), ready for Zenodo. Cross-reference (cleaner): complements QSTH 6. 9 (Audit/Verification Framework) and supports QSTH 6. 10 (The Fifth Dimension as an Account) by formalizing ledger invariance (Π: Ω → 𝓛, G, Orb, S/T/J). Nail-on-the-wall line: “If the ledger can’t tell it apart, it’s gauge. ” Related QSTH Zenodo records (recommended entry points) QSTH 1. 0 — Foundational Publication (DOI: 10. 5281/zenodo. 17455814) QSTH 1. 0 — Horizon Set (DOI: 10. 5281/zenodo. 18015679) QSTH 4. 1 — Planckian Horizon 2. 0: The Entropic Bridge between Quantum and Cosmological Reality (DOI: 10. 5281/zenodo. 17899867) QSTH 5. 2 — OMEG: The Operational Metric Plane of Entropic Geometrodynamics (DOI: 10. 5281/zenodo. 17937840) QSTH 6. 0 — The Info-Dim (I-Dim) Package (DOI: 10. 5281/zenodo. 18156387) QSTH 6. 5 — Planckian Horizon 2. 0 as a Ledger Boundary (DOI: 10. 5281/zenodo. 18649631) QSTH 6. 6 — Planckian Horizon 2. 0 as an Operational Entropic-Coherence Principle (DOI: 10. 5281/zenodo. 18701036) QSTH 6. 9 — I-Dim Elementary Coupling and Semi-I-Dim Classification of the Fine Structure Constant α ≈ 1/137 (DOI: 10. 5281/zenodo. 18864069) QSTH 6. 10 — The Fifth Dimension as an Account: A Ledger Formulation in (3+1) D (DOI: 10. 5281/zenodo. 18871791)