MorphoFlow® Core: Mathematical–computational framework for reproducible three-dimensional submarine-canyon geomorphometry

MorphoFlow® Core v1.0.0 presents the three-dimensional geometric–mathematical foundation and computational architecture of a reproducible framework for three-dimensional submarine-canyon geomorphometry. Its objective is to establish an explicit and traceable correspondence among geomorphological objects, their formal three-dimensional geometric definitions, computational operations, validation procedures, and the resulting morphometric outputs. Part I formalizes submarine-canyon geometry in three-dimensional Euclidean space through a bathymetric surface, a longitudinal thalweg, transverse profiles, left and right canyon margins, and the fundamental points P1–P4, from which transverse and longitudinal morphometric metrics are derived. Part II documents the three-dimensional computational realization of these definitions through a deterministic twelve-stage workflow (MorphoFlow® v1.0.0) encompassing DEM preparation, input validation, geometric construction, morphometric calculation, independent verification, visualization, longitudinal analysis, downstream positioning, and final integration. MorphoFlow® Core preserves bidirectional traceability among geomorphological meaning, three-dimensional mathematical formalization, computational implementation, validation, and reproducible output. The framework is independent of any specific submarine canyon and is intended to serve as a stable and citable methodological reference for reproducible three-dimensional geomorphometric analyses. This version consolidates, integrates, and extends a documented sequence of previous methodological and computational developments by the author. The antecedent Zenodo records and software releases are linked as related works in order to preserve the provenance and versioned traceability of the methodological development. MorphoFlow® Core v1.0.0 constitutes the reference three-dimensional geometric–mathematical and computational specification upon which MorphoFlow® v1.0.0, the associated reproducible three-dimensional workflow, is implemented. The stable executable version of that workflow will be archived subsequently as a separate and citable record. The Core formally defines what is measured, through which three-dimensional geometric objects and relationships, and under which validation logic, whereas the workflow operationalizes those definitions through a three-dimensional, reproducible, and auditable computational implementation. This Zenodo record preserves a stable and versioned methodological snapshot of MorphoFlow® Core v1.0.0. Its DOI provides a persistent link between scientific results and the exact definition of the three-dimensional framework used to obtain them. Future modifications or extensions of the framework should be documented through new versions, without retrospectively altering the scientific meaning of this version. MorphoFlow® is a registered trademark owned by Marco Antonio Viveros Velásquez before INAPI Chile, Registration No. 1507891.