Published July 20, 2026 | Version 1.0
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From Design Points to Machine-Checked Parameter Regions: Reusable Certificate Templates for Engineering Models

Authors/Creators

  • 1. Independent Researcher

Description

We present a reusable algebra for machine-checked certificates in declared engineering models, where supplied equations, inequalities, monotonicity directions, and perturbation bounds imply an encoded safety, lifetime, stability, or performance predicate. Four recurring rules describe meet, dominance, monotonicity, and margin perturbation across thirteen model domains and eight certificate geometries; a fifth deterministic uncertainty-penalty rule is implemented once as a generic conditional suite and is not instantiated in the thirteen domain suites. Stored manifests record 323 named conditional claims—189 in fourteen abstract suites and 134 in thirteen illustrative named-scenario suites—with zero sorry placeholders; the count includes direct condition restatements as well as derived arithmetic and algebraic consequences. Reported robustness quantities are slack budgets in margin units, not parameter-space radii without an additional sensitivity bound. The named values and comparisons are illustrative inputs, not empirical findings about the named products or systems. The proof tooling supports Lean 4 export, but none of the retained suites has a current-source Lean seal and this paper does not claim Lean-validated theorem equivalence. Formal checking establishes consequences of the declared assumptions; it does not validate the assumptions or the physical models. Keywords: formal verification, safety certificates, battery thermal safety, electromigration, battery degradation, catalyst design, phase stability, binding stability, screening bounds, uncertainty-penalized certificates, proof assistants, industrial design

Maturity: Draft. Part of The Latent research program.

Notes

Topic: ind_verified_design_certificates. Source: topics/ind_verified_design_certificates/paper.md. Status: Draft.

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References

  • Semenov, N. N. (1928). Zur Theorie des Verbrennungsprozesses. Zeitschrift für Physik, 48(7–8), 571–582. DOI: 10.1007/BF01340021
  • Frank-Kamenetskii, D. A. (1955). Diffusion and Heat Exchange in Chemical Kinetics. Princeton University Press. DOI: 10.1515/9781400877195
  • Black, J. R. (1969). Electromigration—A Brief Survey and Some Recent Results. IEEE Transactions on Electron Devices, 16(4), 338–347. DOI: 10.1109/T-ED.1969.16754
  • Bloom, I. et al. (2001). An Accelerated Calendar and Cycle Life Study of Li-Ion Cells. Journal of Power Sources, 101(2), 238–247. DOI: 10.1016/S0378-7753(01)00783-2
  • Nørskov, J. K. et al. (2009). Towards the Computational Design of Solid Catalysts. Nature Chemistry, 1, 37–46. DOI: 10.1038/nchem.121
  • Medford, A. J. et al. (2015). From the Sabatier Principle to a Predictive Theory of Transition-Metal Heterogeneous Catalysis. Journal of Catalysis, 328, 36–42. DOI: 10.1016/j.jcat.2014.12.033
  • Kaufman, L. and Bernstein, H. (1970). Computer Calculation of Phase Diagrams with Special Reference to Refractory Metals. Academic Press. https://archive.org/details/computercalculat0004kauf
  • Du, X. et al. (2016). Insights into Protein–Ligand Interactions: Mechanisms, Models, and Methods. International Journal of Molecular Sciences, 17(2), 144. DOI: 10.3390/ijms17020144
  • Bissantz, C. et al. (2010). A Medicinal Chemist's Guide to Molecular Interactions. Journal of Medicinal Chemistry, 53(14), 5061–5084. DOI: 10.1021/jm100112j
  • Pepe, M. S. (2003). The Statistical Evaluation of Medical Tests for Classification and Prediction. Oxford University Press.
  • Obuchowski, N. A. (2003). Receiver Operating Characteristic Curves and Their Use in Radiology. Radiology, 229(1), 3–8. DOI: 10.1148/radiol.2291010898
  • Gardner, T. S. et al. (2000). Construction of a Genetic Toggle Switch in Escherichia coli. Nature, 403, 339–342. DOI: 10.1038/35002131
  • Alon, U. (2007). Network Motifs: Theory and Experimental Approaches. Nature Reviews Genetics, 8, 450–461. DOI: 10.1038/nrg2102
  • Murray, J. D. (2002). Mathematical Biology I: An Introduction. Springer. DOI: 10.1007/b98868
  • Elowitz, M. B. and Leibler, S. (2000). A Synthetic Oscillatory Network of Transcriptional Regulators. Nature, 403, 335–338. DOI: 10.1038/35002125
  • Gantmacher, F. R. (1959). The Theory of Matrices, Volume II. Chelsea Publishing Company. https://old.maa.org/press/maa-reviews/the-theory-of-matrices-volume-2
  • Prajna, S. and Jadbabaie, A. (2004). Safety Verification of Hybrid Systems Using Barrier Certificates. Hybrid Systems: Computation and Control. DOI: 10.1007/978-3-540-24743-2_32
  • Edwards, A., Peruffo, A., and Abate, A. (2024). Fossil 2.0: Formal Certificate Synthesis for the Verification and Control of Dynamical Models. Proceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control. DOI: 10.1145/3641513.3651398
  • Nemouchi, Y. et al. (2019). Isabelle/SACM: Computer-Assisted Assurance Cases with Integrated Formal Methods. Formal Methods and Software Engineering. DOI: 10.1007/978-3-030-34968-4_21
  • Chaudhuri, A. et al. (2022). Certifiable Risk-Based Engineering Design Optimization. AIAA Journal, 60(2), 551–565. DOI: 10.2514/1.J060539
  • Eckert, C., Isaksson, O., and Earl, C. (2019). Design Margins: A Hidden Issue in Industry. Design Science, 5, e9. DOI: 10.1017/dsj.2019.7

Subjects

Formal verification
http://id.loc.gov/authorities/subjects/sh99005741
Proof theory
http://id.loc.gov/authorities/subjects/sh85107439