Core Mathematical Formalisms, Empirical Redshift Calibrations, and High-Performance Computational Audit Pipelines for the Topological-Fluid Cosmological Model (TFCM)

Document 1: TFCM_Viscoelastic_Lagrangian_Formalism.pdf Zenodo Field: Description This tracking preprint establishes the complete, non-equilibrium mathematical foundation for the Topological-Fluid Cosmological Model (TFCM). By departing from standard general relativity formulations that treat the vacuum as an inviscid, continuous pseudo-Riemannian manifold, this document outlines an alternative field framework where spacetime acts as a dynamic, viscoelastic fluid substrate possessing distinct shear elasticity and structural memory profiles. The text provides rigorous mathematical derivations for the non-equilibrium fluid actions and formalizes the custom dynamic stress-energy tensor ($\Sigma_{\mu\nu}$) that arises from metric-substrate coupling. It details the exact evolution of the 1:3:5:8 harmonic distribution equations, demonstrating how chaotic, high-energy primordial vacuum fluctuations ($\sim 10^{110}$ vacuum energy density bounds) are systematically channeled into localized, stable structural overtones. By modeling the early universe via Israel-Stewart causal hydrodynamics, this Lagrangian framework provides the explicit analytic toolkit required to compress the early acoustic sound horizon, offering a completely self-contained geometric resolution to the standard model clustering discrepancies ($S_8$ tension) and the Hubble crisis without requiring standard collisionless Cold Dark Matter (CDM) or speculative, unverified particle scalar fields. Document 2: TFCM_Redshift_Calibration_and_Observational_Mapping.pdf Zenodo Field: Description This supplemental research monograph delivers the empirical data validation metrics, redshift calibration parameters, and observational mappings that anchor the Topological-Fluid Cosmological Model (TFCM) to real-world astronomical data. The work functions as a precision bridge between abstract topological fluid theories and ultra-precision observational cosmology, providing exhaustive cross-analyses against modern spectroscopic surveys and cosmic backgrounds. The document outlines the specific empirical calibration protocols used to test simulation outputs against the European Space Agency’s Planck satellite Cosmic Microwave Background (CMB) anisotropy maps, late-time distance ladders, and the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) data. It explicitly documents the data tracking of the numerical expansion transitions (where computational parameters stabilize from an initial scaling state of $40$ down to $3.79$), showing how this macro-evolution locks the cosmic expansion parameter at an unassailable steady-state value of 73.04 km/s/Mpc. Furthermore, the text details the statistical distribution of cosmic voids, verifying an emergent, global spatial void volume fraction of 0.73 ($73\%$) paired with a $27\%$ condensed filamentary matter scaffolding. It provides the definitive empirical calibration data demonstrating that the observed "phantom crossing" anomaly ($w < -1$) and the large-scale gravitational clustering signals are natural signatures of a topologically bounded, self-optimizing fluid web. Document 3: TFCM_Python_Cosmic_Simulation_Audit.pdf Zenodo Field: Description This technical documentation and repository profile provide the exhaustive software architecture, verification metrics, and 9-point temporal audit scripts validating the extreme-scale computational execution of the Topological-Fluid Cosmological Model (TFCM). It serves as the definitive computational physics audit for the simulation runtime environments designed to model highly non-linear cosmological scale structures from first principles. The document outlines the high-performance computing (HPC) pipeline optimized for massive GPU architectures (such as NVIDIA B200/Blackwell infrastructure), handling an extreme-resolution grid volume of $2560^3$ comprising over 16.7 billion active memory-aligned voxels. It provides a granular breakdown of the custom elementwise CUDA kernels responsible for the execution, specifically detailing the zero-allocation laplacian_kernel used for frictionless fluid routing and the localized surgery_kernel (the Mizaan Regulator). The audit demonstrates the exact mathematical and computational mechanisms used to enforce non-reflecting boundary conditions (NRBC) and track the system’s quadratic density boundaries ($\rho - \rho^2$). By tracing the full 1000-step temporal loop, this audit file proves how the simulation pipeline successfully prevents singularity-driven floating-point overflows, suppresses numerical chaos, and totally eliminates catastrophic NaN (Not a Number) code divergence, providing a robust, reproducible execution model for advanced non-linear computational astrophysics.