Quantum Structural Theory of Harmony (QSTH 6.7) — Variational Entropic Lagrangian (R10): Covariant Foundation of the S_eff Horizon Framework

QSTH 6.7 introduces a GR-compatible covariant variational framework (R10) that provides the theoretical backbone for the operational entropy S_eff audited in QSTH 6.6. The goal is not to replace General Relativity or propose a new fundamental interaction. Instead, QSTH 6.7 formulates a minimal action principle whose variation yields: Field dynamics for a scalar carrier field Σ (equation of motion from the action) A well-defined stress–energy tensor T_μν (from variation with respect to the metric) A clean effective bookkeeping term Λ_eff (without ad-hoc insertions), defined via the Σ energy sector What this record enables A publishable “contract” between theory and operations: explicit derivations (Appendix A), stability/causality checklist (Appendix B), and a test-facing operational map linking S_eff ↔ Σ regimes (Appendix C). A falsification-friendly interface: Null Test + Regime Gradient + Noise Robustness protocols (NT-1 / RT-1 / NR-1) defined at the mapping layer. A stable trunk reference: QSTH 6.7 is designed to sit next to standard GR-adjacent variational papers without overclaiming. Included files (package) CORE (EN) + Appendix A (variational derivation) + Appendix B (causality/stability checklist) + Appendix C (operational mapping and protocols) Merged master document (EN) Cover page (EN) Related identifier (primary) QSTH 6.6 — Planckian Horizon 2.0 as an operational entropic-coherence principle: https://doi.org/10.5281/zenodo.18701036 Related QSTH Zenodo records (recommended entry points) QSTH 1.0 — Foundational Publication: https://doi.org/10.5281/zenodo.17455814 QSTH 1.0 — Horizon Set: Four Invariants for Horizon Thermodynamics and Entropic Geometry: https://doi.org/10.5281/zenodo.18015679 QSTH 4.1 — Planckian Horizon 2.0: The Entropic Bridge Between Quantum and Cosmological Reality: https://doi.org/10.5281/zenodo.17899867 QSTH 6.5 — Planckian Horizon 2.0 as a Ledger of Boundary: https://doi.org/10.5281/zenodo.18649631 QSTH 6.6 — Planckian Horizon 2.0 as an operational entropic-coherence principle: https://doi.org/10.5281/zenodo.18701036 Context map (QSTH 6.0–6.7 — how the 6.x trunk fits together) QSTH 6.0 — I-Dim Package: defines the I-Dim coordinate/constant and the “ledger boundary” viewpoint (operational entry layer). QSTH 6.1 — Entropic Zero (E0) & Entropic Stars: operational definitions + null tests + an explicit pipeline discipline (audit-friendly constraints). QSTH 6.2 — Vacuum as an Entropic Ledger & baryon asymmetry: a testable ledger-bias framework for baryon asymmetry, defined via measurable bookkeeping variables. QSTH 6.3 — Ledger Reality Reconstruction: I-Dim mediation + DM/DE mapping + arrow-of-time diagnostics (Eddington paradox framing). QSTH 6.5 — Ledger of Boundary: consolidates Planckian Horizon 2.0 as a boundary accounting (“ledger”) architecture. QSTH 6.6 — Operational entropic-coherence principle: defines the audited operational layer S_eff + regime discipline and an FM-style audit contract. QSTH 6.7 — Variational Entropic Lagrangian (R10): the covariant variational backbone (action → field equation + T_μν) and an explicit operational mapping S_eff ↔ Σ. Together, QSTH 6.0–6.7 form a coherent pipeline:I-Dim/ledger primitives → operational test handles → reconstructed diagnostics → boundary ledger architecture → audited S_eff interface → covariant variational foundation (R10).