Kenneth ChengMathematical modeling

Editorial project overview

From Simulation to Certificate

How does a diagonal restriction change the constructed robust decay lower bound as endpoint imbalance increases in one frozen positive leaky-transfer family?

Reproducible studyUpdated 30 Aug 2026
Technical figure from From Simulation to Certificate
A reviewed research figure synchronized from the private technical workspace. The original aspect ratio and labels are preserved.

Editorial overview

The literature gate returned COMPLETE / REFRAME because common diagonal, copositive, quadratic, switched, robust and scalable positive-system certificates are established. The local contribution is an auditable two-state evidence-hierarchy benchmark, not new control theory or a new solver.

Read From Simulation to Certificate for the Metzler family, stress construction, Lyapunov derivation, distinction between finite diagnostics and all-parameter endpoint certificates, exact 6/6 gate audit, development-selection boundary, rejected-to-revised figure history, reproduction hashes and locked next stages.

Key findings

  • At zero stress, diagonal and full constructed decay bounds agree to a relative 3.596327e-11 in the manufactured midpoint check.
  • At full stress, the dense finite diagnostic is 0.2676586726, the verified full certificate is 0.2676585204, and the verified diagonal certificate is 0.1040795885, giving a benchmark-specific diagonal gap of 0.6111480807.
  • The maximum full-to-dense gap is 5.686579e-7 and the largest 241-versus-121 construction-grid change is 6.763624e-5; neither statistic establishes global SDP optimality.

Limitations

  • The evidence covers one deliberately selected synthetic two-state affine segment and does not establish a general law of diagonal-LMI conservatism.
  • Dense and seeded spectral sweeps remain finite diagnostics, while the deterministic grid constructs feasible trace-normalized matrices without proving a globally optimal SDP solution.
  • No large-network scaling, physical system, experimental data, controller, safety conclusion, new theorem, or universal certificate ranking is provided.

Technical record

Detailed source, calculations, generated figures, and reproduction instructions are maintained in a private technical workspace. Public articles contain only manually reviewed interpretation and approved figures.

Version history

2026-08-30 — Curated overview reviewed against repository evidence.