DGMonSH / ML-HCST: Direct Geoid Mapping on Super Honeycomb Tangent Planes / Multi-Layer Hexagonal Coordinate Systems' Theory

This record deposits Version 1.0 of the DGMonSH / ML-HCST technical monograph. The work develops a geoid-native Geoid Tangent Mapping Framework (TMF) based on tolerance-controlled super-honeycomb tangent planes constructed directly on the physical geoid. The monograph formalises the local tangent-cell geometry, derives a planarity-error bound of order O(a²), distinguishes exact pairwise shared-edge unfolding from cycle-level closure compatibility, and treats broad-area development as a seam-governed opened tangent-mapping problem whenever accumulated holonomy makes simultaneous closure inadmissible. \n\nThe document further presents the micro-cell and cap-model refinement logic, a hinge-based planarisation framework using Rodrigues rotations, a closure-based Hexagonal Curvature Equation (HCE), the topological necessity of 12 pentagonal defect cells for globally consistent mostly hexagonal spherical coverage, and the proposed HGCS indexing and coordinate architecture. The present release is intended as a citable Version 1.0 archival/technical baseline for later numerical validation, broader regional benchmarking, software implementation, and journal-scale compression. \n\nFiles included in this deposit: \n**• Final PDF monograph** \n**• Editable DOCX source** \n**• Minimal companion notebook for the Galata worked example (galata_example.ipynb)** Version 1.0 technical monograph prepared for Zenodo deposit. This release should be read as a citable archival baseline of the present conceptual, geometric, and mathematical state of the DGMonSH / ML-HCST programme. It does not claim that software validation, benchmark coverage, convergence closure, or institutional standardisation are already complete. The deposit includes a minimal companion notebook for the Galata worked example.