HCB-CBC/ΔΩCt/N Executable Reviewer-Ready Pipeline for HCB-CBC/ΔΩCt Framework

ΔΩcₜN V3 is an operational package developed to accompany the HDC–CBC/ΔΩcₜ framework through a reproducible numerical implementation of trajectory-enabled correlational closure.

The package includes two main versions of the pipeline:

DeltaOmegaCtN_V3
A classic terminal-oriented version designed for direct execution, controlled sweeps, reproducible output generation and structural validation of the parameter space.

DeltaOmegaCtN_V3_Chat
A guided conversational version designed to facilitate step-by-step execution through assisted selection of families, anchors, execution depth and historical trajectory parameters.

The purpose of ΔΩcₜN V3 is to preserve the benchmark layer inherited from ΩCt/N while adding a dynamical trajectory layer for the correlational index. In this version, users can explore constant configurations, smooth transitions and ΔΩcₜ trajectories through explicit controls such as the potential model, effective closure strength, dynamical branch, normalization convention and reference correlational value.

The pipeline is intended as a reviewer-ready structural validation environment. It supports reproducible sweeps, trajectory tests, proxy-level observational diagnostics, result classification and identification of the first rupture sector. It is not intended to replace full cosmological codes such as CLASS, CAMB or hi_class, nor does it constitute a final Bayesian inference engine. Its role is to provide a lightweight, transparent and executable tool for evaluating the structural admissibility of correlational trajectories within the HDC–CBC/ΔΩcₜ framework.

This release also includes the official user manuals in Spanish and English:

Manual_Oficial_DeltaOmegaCtN_ES_V3
Official Spanish user manual, including installation instructions, execution modes, configuration options, output interpretation, known limitations and recommended usage practices.

Manual_Official_DeltaOmegaCtN_EN_V3
Official English user manual, including installation instructions, execution modes, trajectory controls, output interpretation, known limitations and recommended usage practices.

Version V3 corrects and consolidates the operational implementation with respect to previous transitional versions. It includes full deltaomegact support, bilingual execution aliases, an explicit quartic potential option, operational normalization, proxy-validation policy, declared dependencies and updated launchers.