Application of Cryptography for Controllability Results of Fractional Neutral Volterra-Fredholm Integro-Differential Equations with State-Dependent Delay
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Bibliographic record
Abstract
This paper utilizes the Caputo fractional derivative and a semigroup of compact and analytic operators to examine the controllability of fractional Volterra-Fredholm integro-differential equations with state-dependent delay. Controllability results are formulated using Schauder’s fixed point theorem, addressing the inherent difficulties brought about by the fractional dynamics together with state-dependent delays. The theoretical findings are validated through a detailed example and numerical simulations, demonstrating the convergence of solutions. Graphical representations are provided to better understand solution dynamics and highlight system complexity. Additionally, the applicability of the proposed system for cryptographic key generation is explored, showing that it can generate secure, unpredictable keys due to its chaotic behavior, sensitivity to initial conditions, and the interplay between key system parameters.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it