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This version aims to refine the mathematical framework of the Directional Anisotropy Gravity (DAG) model with a focus on specific quantum mechanics.

April 18, 2026Open Access

Directional Anisotropy Gravity DAG — Substrate Sector, v11: Quantum Kinematics and Direction-Orbit Coupling Hamiltonian

Key Points

This version aims to refine the mathematical framework of the Directional Anisotropy Gravity (DAG) model with a focus on specific quantum mechanics.
Refinement of core mathematical framework limiting to the single-excitation Hilbert space per node
Incorporation of the Direction-Orbit Coupling Hamiltonian
Utilization of open-system derivation techniques
Application of the Shannon/von Neumann theorem and tensor-network area law
Correction of Lindblad sum index to reflect accurate node interactions
Completion of single-node motion equations
Introduction of a new section on effective sound speed from the Direction-Orbit Coupling

Abstract

v11 of the DAG substrate sector. Replaces v10. This version restricts scopeto the mathematically controlled core: the single-excitation Hilbert spaceC⁶ per node, the Shannon/von Neumann coincidence theorem, the tensor-networkarea law, the Direction-Orbit Coupling (DOC) Hamiltonian, the open-systemderivation of the memory field via Nakajima–Zwanzig / Born–Markov, thesemiclassical limit via adiabatic elimination (restoring forceΓᵣel = 12 η²/Γdec), discrete U (1) gauge links on the substrate graph, decoherence / pointer basis, and the effective DOC sound speed. All speculative programme material (extended 18-channel substrate, axis-pair doublet hypothesis, SM gauge structure, three generations, anomaly cancellation, Higgs sector, running couplings, TOE Lagrangian, cosmogony, constants) has been moved to a companion paper, "DAG Substrate sector — Gauge Structure Programme, v1". 10. 5281/zenodo. 19614270 Changes from v10: - corrected Lindblad sum index (I=1. . 6 rather than I≠J) - completed single-node equation of motion- new §9. 3 "Effective sound speed from DOC"- 10 new bibliography entries- scope narrowed to substrate-core content only

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