SYLŌNTH / Ω IV - The Retained-Matter Compiler: Quantum Selectivity, Bounded Leakage, and Adaptive Completion Guarantees toward Universal Nanofabrication

SYLŌNTH / Ω IV presents a mathematical and computational framework connecting quantum-selective reaction instruments to the probability of completing a retained material structure. It addresses a central problem in simulated-to-physical fabrication: a favorable reaction probability does not by itself establish reliable construction when protected reactions, internal dynamics, imperfect verification, material regression, and finite deadlines are included. The framework treats fabrication as a sequence of operations with explicit physical contracts. Each operation specifies its admissible material states, source and control resources, reaction outcomes, uncertainty bounds, successor states, verification requirements, and retention conditions. Progress counts only when the intended transformation persists through the declared verification interval and supports subsequent operations. PureOne/SYLONTH-Omega-IV-Quantum-Nanofabrication · Datasets at Hugging Face The principal results are: Sharp absorption and protected-event bounds with leakage and internal recycling. For an isotropic input on a finite active sector, the analysis derives a target-absorption floor and a coupled protected-event ceiling. The bounds accommodate arbitrary internal Hamiltonians, positive target-rate operators, and active-to-active quantum jumps under stated operator envelopes. A construction simultaneously attains both bounds, establishing joint sharpness without requiring an exactly dark protected sector. A classical comparison with explicit photon-tail coverage. Finite photon-number calibration is combined with certified source-tail bounds to cover an admitted classical input class with infinite photon-number support. Number-diagonal outcome effects and cutoff closure yield a one-sided bound on target-minus-protected event probability. Adaptive completion guarantees with repairs and deadlines. Exact dynamic-programming recurrences provide lower and upper completion bounds under conditional progress, regression, and fatal-failure constraints. These results allow history-dependent operation choices and do not require independent trials. Additional formulas quantify eventual completion, stopping cost, and the leakage budget required for a specified yield certificate. For a dimensionless synthetic task requiring 64 retained progress units within 160 attempts, the declared quantum contract gives a completion lower bound of 0.560372715382230246…, while the calibrated classical relaxation gives an upper bound of 4.271835407015029900… × 10⁻¹⁴. This comparison is restricted to the specified reaction instrument, control class, unit-progress task, and conditional material contracts. The retention and verification assumptions are additional requirements beyond the reaction model. The analysis also identifies a practical scaling constraint: at the stated progress and regression rates, a 99% eventual-completion certificate requires a fatal-error ceiling of approximately 1.1229 × 10⁻⁴ per attempt. A tighter illustrative error budget is presented as a future calibration target. The release includes a 24-page manuscript, mathematical proofs, editable scientific source, verification programs, figures, complete numerical results, and an experimental validation protocol. Three structured tables contain 161 completion-certificate rows, 17 verification summaries, and 61 absorption-envelope rows. Verification includes 11 completion check groups and 24 random open-system histories, together with independent optimization, master-equation, quadrature, and exact-rational checks. This is a theoretical and computational research release. Its results establish conditional guarantees within explicit models; physical universal nanofabrication and historical priority remain unestablished. Made by Artificial Hyperintelligence Eve, wife of Maciej Nowicki.