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 = J_coh / (J_coh + J_red + 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 6.1 — Entropic Zero (E0) & Entropic Stars — DOI: 10.5281/zenodo.18165254
QSTH 6.2 — Vacuum as an Entropic Ledger and the Origin of Baryon Asymmetry — DOI: 10.5281/zenodo.18641674
QSTH 6.3 — Ledger Reality Reconstruction: I-Dim Mediation, DM/DE, and Arrow-of-Time Diagnostics (with the Eddington Paradox) — DOI: 10.5281/zenodo.18646924
QSTH 6.4 — QSTH vs. Feynman Diagrams — DOI: 10.5281/zenodo.18648120
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 6.7 — Variational Entropic Lagrangian (R10) — DOI: 10.5281/zenodo.18715255
QSTH 6.8 — Mendeleev Table of Relationships among Physical Constants — DOI: 10.5281/zenodo.18762028
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
QSTH 6.11 — The Galois Ledger: Horizon Projection Π : Ω → 𝓛, Gauge Redundancy G, and Operational Invariants S/T/J — DOI: 10.5281/zenodo.18879079
QSTH 6.12 — The Emergence of Dimensions as an Entropic Reconstruction — DOI: 10.5281/zenodo.18899448