Quantum Structural Theory of Harmony (QSTH M.5) — Operational Structural Ledger for Horizon Set II

This record contains the English final version of QSTH M.5 — Operational Structural Ledger for Horizon Set II, a methodological audit publication in the QSTH M.x Horizon Ledger Series. The publication follows QSTH 8.M.x — Horizon Ledger of the Settled Structure, QSTH M.0 — M-Independent Horizon: Alpha Closure of the Horizon Ledger, QSTH M.1 — Unit Hygiene and Alpha-I-Dim Audit, QSTH M.2 — Source Review of the Older Horizon Set Line, and QSTH M.3 — Calibration Atlas of Horizon Classes. It prepares the methodological transition toward QSTH M.6, where the microstate sieve, orbital classes, and distinguishability conditions are expected to be developed further. QSTH M.5 develops the operational ledger layer above the canonical Bekenstein–Hawking horizon entropy S_BH. It introduces S_eff^H as an operational horizon account, B_R as the regime-read ledger balance, and epsilon_R as the normalized ledger deviation. These quantities are not presented as freely adjustable parameters. They are admitted only under explicit audit conditions. The document includes: • an Epistemic Note / Methodological Brake• an Opening Diamond defining the role of S_BH, S_eff^H, B_R, and the Galois Ledger• a Terminology Lock for consistent use of operational horizon account, audited working page, ledger balance, normalized ledger deviation, right to read, and closure readout• the definition S_eff^H = S_BH − B_R• the normalization epsilon_R = B_R/S_BH• the Horizon Sudoku gate C_H(Gamma) as the right to use the operational horizon account• the Sackur–Tetrode lamp as a statistical guardrail for distinguishable microstates• the Galois Ledger as an orbital sieve against false microstates• the guarded entry into kappa_R as a closure readout• the Spin-Entropic Grid G_SE as a compatibility layer• the distinction between Planck, Sackur–Tetrode, Galois, and photon/readout lamps• the future role of TiM_R as a dynamic latch• the future/support role of alpha_EM as a possible electromagnetic readout handle• a Skeptics Contract• a status audit, failure modes, and a Mini-Mendeleev cut of M.5• appendices containing an equation capsule, audit registry, anchor registry, glossary, symbol registry, and failure registry The core methodological claim of M.5 is that QSTH must not win by calling a correction a ledger without the right to read. If B_R, epsilon_R, or S_eff^H add no audit, microstate, or test value above S_BH, their status must be downgraded to SUPPORT. If the necessary gates fail, the correct output is INCONCLUSIVE. This publication should be read as a theoretical and methodological audit framework. It does not claim empirical confirmation of QSTH, nor does it establish S_eff^H as a new physical entropy law. Its purpose is to define how candidate horizon accounts may be used without uncontrolled fitting and to prepare the transition toward the microstate sieve of QSTH M.6. Subjects / categories Physics — Theoretical PhysicsMathematical PhysicsQuantum PhysicsCosmology and Nongalactic AstrophysicsInformation TheoryBlack Hole Thermodynamics Related work note This publication follows QSTH 8.M.x — Horizon Ledger of the Settled Structure, QSTH M.0 — M-Independent Horizon: Alpha Closure of the Horizon Ledger, QSTH M.1 — Unit Hygiene and Alpha-I-Dim Audit, QSTH M.2 — Source Review of the Older Horizon Set Line, and QSTH M.3 — Calibration Atlas of Horizon Classes. It also prepares the methodological transition toward QSTH M.6, where the microstate sieve, orbital classes, and distinguishability conditions are expected to be developed further. Plain-language summary This publication asks a simple but strict question: if we introduce a candidate horizon account above the standard Bekenstein–Hawking entropy, how do we prevent it from becoming a freely fitted correction? M.5 answers by requiring an audit. The standard entropy S_BH remains the anchor. The operational account S_eff^H may be shifted only by a predefined ledger balance B_R. That balance must pass gates of topology, state, ledger definition, boundary readability, regime stability, statistical distinguishability, and Galois-inspired redundancy control. If these gates fail, the honest result is not a discovery claim, but INCONCLUSIVE. Final Zenodo caveat This document is a theoretical and methodological audit publication. It does not claim that QSTH is empirically confirmed, nor does it present S_eff^H as an established physical entropy law. The Bekenstein–Hawking entropy S_BH is retained as the canonical physical anchor. The quantities B_R, epsilon_R, and S_eff^H are treated as candidate operational structures whose use depends on explicit audit gates, failure modes, and the right to read. Suggested citation Stepanik, R. (2026). Quantum Structural Theory of Harmony (QSTH M.5) — Operational Structural Ledger for Horizon Set II: From the Bekenstein–Hawking Anchor to an Auditable Horizon Account. Quantum Structural Theory of Harmony, QSTH M.x Horizon Ledger Series, Author’s Edition, EN v1.0. Zenodo. https://doi.org/10.5281/zenodo.21134186 Copyright (C) 2026 Rostislav Stepanik