Quantum Structural Theory of Harmony (QSTH M.6) — Galoisian Microstate Sorting: Microstate Ledger of Horizon Readability

QSTH M.6 presents Galoisian Microstate Sorting as a methodological and technical step in the QSTH M.x Microstate Ledger Series. It follows QSTH M.5, where the operational horizon account S_eff^H, the ledger balance B_R, and the normalized deviation epsilon_R were defined under explicit audit conditions. The central purpose of M.6 is to address the microstate origin of epsilon_R. The publication does not claim to provide a completed physical theory of horizon microstates, nor an empirical proof of QSTH. Instead, it defines how candidate microstates may be sorted into coherent, reductive, and unresolved classes before Omega_coh,R, Omega_red,R, B_R, epsilon_R, or kappa_R(Gamma) may be treated as non-free quantities. The proposed sorting framework uses Horizon Sudoku as the admissibility gate, the Galois projection Pi, the redundancy group G, orbital equivalence classes Orb_G(omega), the classifier chi_R, and the S/T/J stability test. Its core rule is that Omega_coh,R and Omega_red,R must not be assigned after the desired result is known. They must arise from a pre-declared microstate sieve. M.6 distinguishes three candidate variants of the sieve: a Boltzmann / Gibbs / Sackur–Tetrode statistical sieve, a quantum-information sieve, and a QSTH-specific Galoisian-horizon network. It also introduces the Spin-Entropic Grid G_SE, stability safeguards, failure modes, and a Skeptical Contract requiring no tuning, no double counting, representation stability, and the right to return INCONCLUSIVE. The contribution of QSTH M.6 is therefore methodological: it does not deliver a final number, but defines the right to sort and count candidate microstates. It prepares the transition from M.5 toward M.Closure by giving the Horizon Ledger branch its first explicit microstate-sieve core. Description This record contains the English final version of QSTH M.6 — Galoisian Microstate Sorting, a methodological microstate-sieve publication in the QSTH M.x Microstate Ledger Series. The publication follows QSTH M.5 — Operational Structural Ledger for Horizon Set II, where S_eff^H, B_R, and epsilon_R were defined as candidate operational horizon-account quantities under explicit audit conditions. M.6 addresses the next question: from which microstate classes may epsilon_R legitimately arise? QSTH M.6 does not claim to provide a completed physical theory of horizon microstates, nor an empirical proof of QSTH. Its purpose is to define a disciplined sieve for sorting candidate microstates into coherent, reductive, and unresolved classes before Omega_coh,R, Omega_red,R, B_R, epsilon_R, or kappa_R(Gamma) may be treated as non-free quantities. The document includes: • an Epistemic Note / Methodological Brake• an Opening Diamond defining M.6 as the answer to where epsilon_R comes from• the bridge from M.5 to M.6• the equation linking epsilon_R to Omega_coh,R / Omega_red,R• Horizon Sudoku as the admissibility gate for microstates• the Galois projection Pi• the redundancy group G• orbital equivalence classes Orb_G(omega)• the Galois Guardrail against false microstate counting• three sieve variants: Boltzmann / Gibbs / Sackur–Tetrode, quantum-information, and Galoisian-horizon network• the S/T/J operational microstate filter• the first M.6 classifier chi_R• the Spin-Entropic Grid G_SE as a compatibility layer• stability safeguards including Hessian, Lyapunov, covariant derivative, optimal control, and Dirac-spinor lessons• TiM_R as a future temporal latch• status audit, failure modes, and a Skeptical Contract• a Mini-Mendeleev audit• the recommended output of M.6• the bridge from M.6 to M.Closure• an equation capsule and publication/audit note The core methodological claim of M.6 is that epsilon_R must not be obtained by fitting the result. It must arise from a pre-declared microstate classification. If Pi, G, Orb, chi_R, and the S/T/J test are not defined, the correct output is INCONCLUSIVE. This publication should be read as a methodological microstate-sieve monograph. It defines the right to sort and count candidate microstates, not a completed physical theory of horizon microstates. Its CAND / SUPPORT / FUTURE statuses, PASS / FAIL / INCONCLUSIVE rules, and no-tuning guardrails are part of the result and should remain visible in all future revisions. Subjects / categories Physics — Theoretical PhysicsMathematical PhysicsQuantum PhysicsCosmology and Nongalactic AstrophysicsInformation TheoryBlack Hole ThermodynamicsQuantum Information Related work note This publication follows QSTH M.5 — Operational Structural Ledger for Horizon Set II, where the operational horizon account S_eff^H, the ledger balance B_R, and the normalized deviation epsilon_R were introduced under audit conditions. It also continues the M.x sequence following QSTH 8.M.x, QSTH M.0, QSTH M.1, QSTH M.2, QSTH M.3, and QSTH M.4. M.6 prepares the transition toward QSTH M.Closure by defining the microstate-sieve layer needed before the Horizon Ledger can claim a physically stable record-reading structure. Plain-language summary This publication asks a strict question: if QSTH uses a quantity called epsilon_R to describe a horizon-ledger deviation, where do the microstates behind that quantity come from? M.6 answers by building a sieve. It does not try to count every possible hidden configuration. Instead, it defines which candidate microstates may be admitted, which are coherent, which are reductive, and which must remain unresolved. The Galois Ledger prevents the same hidden rewrite from being counted as a new physical state. If the sorting rules are not defined before the result, the honest output is INCONCLUSIVE. Final Zenodo caveat This document is a theoretical and methodological microstate-sieve publication. It does not claim that QSTH is empirically confirmed, nor does it present a completed physical theory of horizon microstates. The quantities Omega_coh,R, Omega_red,R, B_R, epsilon_R, and kappa_R(Gamma) are treated as candidate operational structures whose use depends on admissibility gates, microstate classification, Galoisian redundancy control, failure modes, and the right to read. Suggested citation Stepanik, R. (2026). Quantum Structural Theory of Harmony (QSTH M.6) — Galoisian Microstate Sorting: Microstate Ledger of Horizon Readability. Quantum Structural Theory of Harmony, QSTH M.x Microstate Ledger Series, Author’s Edition, EN v1.0. Zenodo. Copyright Copyright (C) 2026 Rostislav Stepanik