Reproducibility materials for "Financial Sustainability in Delayed Investment Difference Equations: Exact Reserves and Sharp Horizon Rates"

This record provides the scientific reproducibility materials accompanying the manuscript “Financial Sustainability in Delayed Investment Difference Equations: Exact Reserves and Sharp Horizon Rates” by Amr M. Y. Abdelaty.Mathematics Subject Classification (2020): Primary 39A22; Secondary 90C25, 90C31, 91B55. The associated study examines the initial liquidity required to maintain a permanent service-capacity floor in deterministic delayed investment difference equations with depreciation, bounded investment orders, and advance payment. Financial sustainability is understood as continued service provision with every investment payment funded without borrowing or subsequent cash injections. The examples use synthetic parameters; they do not measure environmental or social impact. The archive contains synthetic numerical data, exact rational certificates, computational witnesses, nine Python programs, and the numerical figure with its supporting inputs. Its evidence includes 16 selected rational certificates (14 base certificates and two longer-horizon refinements), 102 committed-loss terminal-correction rows, 49 wealth-only terminal-correction rows, three rational payment-domain examples, and 116 sufficient-policy and cash-budget constructions. The certificates, reporting tables and feasible-policy constructions have distinct evidentiary roles. The 116 constructions are not optimized finite-horizon values, and numerical examples do not replace the mathematical proofs in the associated manuscript. The README identifies the certified subset, additional diagnostic entries, and the scope and limitations of the supplied checks. The README also provides verification and regeneration commands, dependency information and guidance on interpreting the archived computational reports. File-level integrity information is supplied in MANIFEST.json and SHA256SUMS.txt. Funding: The project was funded under the Ongoing Research Funding Program (ORF-2026-1780), King Saud University, Riyadh, Saudi Arabia. License scope: Python source files in reproduction/ (*.py) are licensed under the MIT License. All remaining archive contents, including data, certificates, figures, documentation, configuration and integrity metadata, are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0). Contact: [e-mail]